Solutions: Intermediate Astronomy Problems (4)

The problems at the end of the last instalment, and their solutions, in turn:

(1)(a) Calculate the ratio of the Earth's tangential orbital velocity to Saturn's given Saturn's sidereal orbital period is 10,746.9 days.

(b) Validate this is approximately correct if Saturn's mean orbital velocity is 9.664 km/s from an astrometric table.


Solution

(a) We have:

V2/V1 = (a2/a1) (T1/T2)

By convention we assign '1' to the inner planet (Earth) and '2' to the outer (Saturn). We have a1 = 1 AU and for Saturn (from Kepler's third law):

T2 = (10,746.9/365.25) yr. = 29. 4yr.

a2 = {[T2]^2}^1/3 = [(29.4)^2]^1/3 = 9.50 AU

Whence:

(V1/V2) = (a2/a1)^½ = (9.50)^½ = 3.08

So, the Earth's orbital velocity should be about 3.1 x faster than Saturn's

(b) Saturn's mean orbital velocity is 9.664 km/s from an astrometric table.

From the sample problem, V(Earth) = 29.78 km/s

Then: (V1/V2) = (29.78 km/s)/ (9.664 km/s) = 3.08


(2)At quadrature with the planet Mars, it is found (based on Fig. 1) that SP' = 1.53 AU, and SE' = 0.999 AU.

(a) From this deduce the distance P'E' and

(b) Hence, find the angular velocity of the planet as observed from Earth.


Solution

(a) SP' = 1.53 AU is the hypoteneuse of the right triangle, SE'P'. SE' = 0.999 AU is one leg. Then, from Pythagoras' theorem:

P'E' = [(SP')^2 - (SE')^2]^½ = [1.53^2 - 0.999^2]^½

P'E' = 1.15 AU

(b) To obtain the angular velocity as observed from Earth we first need to obtain angle SP'E' since we must find φ, knowing that: (90 - S'P'E' = φ). From trigonometry:

cos (SP'E') = adj/ hyp = P'E'/ SP' = 1.15/ 1.53 = 0.757

SP'E' = arc cos (0.757) = 40.8 deg

then: φ = 90 - S'P'E' = 90 - 40.8 deg = 49.2 deg

The geocentric angular velocity at quadrature is then:

V_p sin (φ)/ E'P'

To get V_p, note:

(V1/V_p) = (a_p/a1)^½ = (1.53)^½ = 1.23

So: V_p = (1/1.23) (29.78 km/s) = 24.2 km/s

and:

V_p sin (φ)/ E'P' = [(24.2 km/s)sin (49.2)]/ 1.15 = 15.9 km/s


(3) If Mercury's sidereal orbital period = 0.2408 yr. show that its tangential orbital velocity should be 47.87 km/s


Mercury is interior to Earth so designate with '1':

T1 = 0.2408 yr.

a1 = {[T1]^2}^1/3 = [(0.2408)^2]^1/3 = 0.387 AU


V2/ V1 = (a1/a2)^½

So: V1 = (V2)/(a1/a2)^½ )

where: V2 is for Earth (29.78 km/s) and:

(a1/a2)^½ = (0.387/1)^½ = 0.622

V1 ('Merc') = V2/ 0.622 = (29.78 km/s)/0.622 = 47.87 km/s


(4) Based on the information in (3)and given that Uranus' sidereal period = 83.747 yrs., show that Uranus tangential orbital velocity is approximately 5.477 km/s.

Solution

By convention we now assign '1' to the inner planet (Earth) and '2' to the outer (Uranus). We have a1 = 1 AU and for Uranus (from Kepler's third law):

T2 = 83.747 yrs.

By Kepler's 3rd law:

a2 = {[T2]^2}^1/3 = [(83.747)^2]^1/3 = 19.13

Whence:

(V1/V2) = (a2/a1)^½ = (19.13)^½ = 4.37

or: V2 ('Uranus') = V1/ (4.37)

where V1 = 29.78 km/s (Earth) so:

V2 = 29.78 km/s/ (4.37) = 6.8 km/s *

Explanation:


A cross check of other references (e.g. Abell, 'Exploration of the Universe', Appendix 8) discloses that this is the correct value! The 5.477 km/s from the Astrometric & Geodetic data sheet - is incorrect! It actually applies to Neptune, not Uranus.

We can check this: The semi-major axis of Neptune is 30.06 AU (from problem #5, 'Tackling Intermediate Astronomy 2').

By Kepler's 3rd law:

a2 = 30.06 AU

Whence:

(V1/V2) = (a2/a1)^½ = (30.06)^½ = 5.48

or: V2 ('Neptune') = V1/ (5.48) = (29.78 km/s)/ 5.48 = 5.43 km/s

It pays to double check! (Including the Examiner or the textbook!)

Why Eric Cantor is an Insane Nut.

Watching the devastation in the wake of Tropical Storm Irene, wrought in the reeling counties of Vermont (where I visited at least 3 times between 1997 and 1999,) brought a knot to my stomach and a heavy heart. Even one of my favorite small VT towns, Rochester, is now cut off from the outside world because of raging waters. The devastation in this tiny "Green Mountain" state is epic, with 210 roads washed away, towns ravaged from "once in a century" floods, and people in the midst of mind boggling misery. Their last place to turn is the federal government.

But what do we hear in the midst of this horrific storm damage and appalling misery? Diatribes from nincompoop and über-Tea bagger clown Eric Cantor, to the effect NO federal or FEMA assistance- funding will be forthcoming unless "offsetting spending cuts" of equal magnitude are made to other programs, whether Medicaid, Medicare, or to other towns still cleaning up, re-building after the Spring tornadoes, such as Joplin, Missouri. Is this man a degenerate, insane or what? Offsetting cuts in a time like this? With tens of thousands of people barely hanging on? With classic old covered bridges washed away, such as in the photo? What is he, nuts?

Cantor's cant is based on myths and outright lies propagated by him and his illustrious Gooper cohort, in particular that Obama has "overspent" and put us in a deficit hole of major proportions. This is all bollocks and codswallop and people need to know the truth! Cantor can't be allowed to deny critical aid to people in their greatest hour of need based on despicable lies!

To fix ideas, let's focus on two factors that Cantor harps on most in regards to President Obama: budget deficits, and his spending. To assist readers I have appended the relevant charts for each, respectively.

The numbers in these two charts come from Budget of the United States Government: Historical Tables Fiscal Year 2012. They are just the amounts that the government spent and borrowed, period, Anyone can go look then up. People who claim that Obama "tripled the deficit" are either misled or are trying to mislead, or outright lie to gain specious political advantage.

In the Deficit chart, one can easily see that over his tenure Bush's deficits consistently increased and at his last budget showed a $1.4 trillion deficit. This was fobbed off directly onto Obama. Nonetheless, despite a small uptick, Obama's projected deficits are in decline and his last budget showed a SURPLUS of $128 billion.

Next we come to the chart for Spending, on which Cantor bases his austerity arguments and refusal to assist current disaster areas of the country unless offsetting cuts are made elswhere. As may be seen on inspection, Bush's overall spending increase was 88% over his time, vs. 7.2% for Obama. If anything, Obama's spending immediately after he took office wasn't enough, and we ought to have had at least double the stimulus he implemented and with NO tax cuts! Had he done that, as opposed to the timid $797 billion deal laden with one-third tax cuts, we'd likely now be seing 8% or less unemployment as opposed to 9.1%. And Obama might be well on his way to a major election conquest.

Indeed, looking back, it has been Obama's consistent timidity in his policies which has thwarted a full economic recovery at every interlude. The latest was the cave-in on the debt-ceiling increase which included: 1) ceding critical ground to the Repukes by accepting only spending cuts with no tax increases, and (2) putting bothSocial Security and Medicare on the cutting room table. This a DEM president does not do, and even a neophyte needs to grok that! It may also explain part of his 38% approval rating and why he's losing support from all segments of his 2008 coalition. (Yes, jobs are important, but certain segments - such as women, 50% of whom in a recent poll now say he doesn't merit re-election, are more tuned into social service issues since they are the nation's primary caretakers)

As WaPo's Eugene Robinson put it, Obama needs to go big and bold in is jobs plan or face the political consequences - which might possibly translate into being a one termer. If he merely does more timid programs, advocating no more than payroll tax holidays or cuts, we're in deep shit. Or rather, he is.

As for Cantor, I am looking forward to him going back to his own constituents in Virginia and telling them that they can't expect any money to rebuild their damaged homes and properties...because, well,...."Washington spends too much".

Hopefully they'll respond by getting rid of this political idiot once and for all.

A Really Terrible Plan: Abandoning the Space Station

In two earlier blogs, I warned that the retrenchment of the Space Shuttle program was a terrible idea, not least because it was cost-ineffective. You have here a means of efficiently re-supplying a $100 billion-plus International Space Station, and you're going to give it up to depend on undependable Russian Soyuz rockets! Why, because of penny-pinching morons who prefer to count pennies while they now stand to lose dollars - mucho dollars!

The news this a.m., that the International Space Station may have to be "abandoned" therefore showed me the pennypinching chickens had come home to roost. This occured, since the Russian re-supply rocket (the ISS 'Progress 44' launched from the Baikonur Cosmodrome at 9 a.m. EDT 7 p.m. Kazakhstan time, August 24) was scuttled five minutes and 25 seconds into flight, when the Soyuz rocket booster experienced a third-stage engine shutdown due to an "anomaly".

This showed in no uncertain terms the stupidity of depending upon an inferior medium for re-supply when the Shuttles had at least 5-6 more years of service in them. So what are the three remaining Shuttles doing now? Sitting in museums gathering dust! What is it about current American priorities that drives many of us batshit crazy? Well, their sheer stupidity - including the recent news that FEMA will not now be able to sustain reconstruction efforts for Joplin, MO and other tornado-whacked areas because the WH didn't ask for more FEMA funding (for which congressional denial could have been parlayed into huge political capital - but evidenlty they lacked the brains or foresight to use that!), and now with Hurricane Irene's devastation there isn't enough to go around. Smarts anyone? Anyone? Leadership? VISION?

SO now, the brainiacs who evidently decide these things, have concluded the best alternative - if the Russians have any more problems with the Progress unmanned Soyuz craft- is to abandon the ISS completely. Now, get this: even this abandonment will require at least three separate manned trips since there are 3 crew members on the ISS and the Russian rockets to ferry them back are also Soyuz- and only have room for one ISS member at a time - along with two Russian crew members!

This means three separate trips consuming enormous masses of fuel and at great expense will be needed to get all three ISS team guys back! And, get this too, there is a "tenfold greater chance" the space station itself will now be lost because the on-ground control of the station (say in case it encounters large, orbiting space debris) is nowhere near as good as in-station control. (They can't leave just one guy on the ISS because its basic running - from the solar powered generators, to environmental systems, to basic commands and micro-gravity experiments - need at least three!)

None of this need have transpired, and the worst thing is that a $100b investment (from multiple nations) now stands to be permanently lost. If this occurs, it will be a testimony to an era of unmatched human stupidity, misplaced priorities and greed. And yet more confirmation, every time I spot a new piece (say in WIRED magazine) to the effect 'people today are smarter than those in the Sixties' - that writing absolute bollocks is easier than ever.

Atheists Have to Show More Tolerance!

I know that Pastor Mike, my youngest brother, is not easy to take. Normally he is manageable in small doses, and even then the intensity can be wearing - unless one understands his military, police-background. Then, one can make some allowances. However, many atheists from around the world now attacking him with venom and death threats do themselves no favors, and in fact, play right into his hands. They show themselves to be no more tolerant than he is, and indeed- worse- because while he merely proposed a possible "national registry" of atheists in normal every day language, they have come back with emails laden with extreme foul or violent lingo.

In his latest blog (now with restricted access, by his invitation only as per email frmo his yesterday evening):

http://pastorstahl.blogspot.com/2011/08/free-atheist-e-mail-addressesfor.html

Pastor Mike actually published some of the invective-laden emails dispatched to him, while also adding that he now regards them as "his property to dispose of as he chooses" (with which I totally agree). Some of the examples (which Mike insists are not the worst):

"Hello,

I have seen your idea regarding the list of atheists, where they work and so on - I would like to say one thing, and one thing only. You are a pathetic excuse for human life. I "pray" that you get hit by a fucking bus asshole.

Fuck you."

--
Isn't the internet great. It allows shitheads like yourself to say shit that would, in real life get your head cracked open.

Hopefully you'll suffer the same fate fucking cunt.

Please turn to the loaded gun in your drawer, put it in your mouth, and pull the trigger, blowing your brains out. You'll be doing the whole world a favor. Shitbag.

I would love to smash your face in until it no longer resembled anything human, faggot.

Can you please remove yourself from the gene pool? Preferably in the most painful and agonizing way possible? Retard

Die painfully okay? Prefearbly by getting crushed to death in a garbage compactor, by getting your face cut to ribbons with a pocketknife, your head cracked open with a baseball bat, your stomach sliced open and your entrails spilled out, and your eyeballs ripped out of their sockets. Fucking bitch

I really hope that you get curb-stomped. It'd be hilarious to see you begging for help, and then someone stomps on the back of your head, leaving you to die in horrible, agonizing pain. Faggot

Shut the fuck up f aggot, before you get your face bashed in and cut to ribbons, and your throat slit.

Fuck off and die you worthless yank moron. Pity you didn't die on 9/11"

--
Save me from pastor Mike.

fuck you pastor mike. I'd like to give you a one way ticket to Jesus so the living won't have to put up with your bullshit.

I'll kick your mother fuckin believing ass straight to the Lord and you can believe that. All you suppositious fuckers keep mankind in the dark ages and killing one another over belief in God.

George"
---

Now, is this really the level to which WE, as atheists - and putative exponents of enlightened thought - have been reduced? Is this the best sort of response we can manage? Have we totally lost the ability to argue based on reason? Are we so seized by hatred that we can only froth at the mouth and allow our lizard brains to take over?

I mean, come on, fellow atheists! Grow up! Don't reduce yourselves to Mike's intolerance! Instead, if you do send emails, state in basic terms why and how you believe even the remote concept is a bad idea. Or, go through some of my past blog comebacks to the pastor, which - while they do show intensity and aggressive attitude, don't cross the line to writing things like "pity you didn't die on 9-11".

When this sort of vitriol is indiscriminately lobbed, it reduces all of us as atheists to no better than the most intolerant, nutbag fundies. I don't care if it's in an email either. In fact, it's just as bad or worse, because now you've delivered straight to his inbox loathsome material he can go on using indefinitely! The "gift that keeps on giving"!

Take some time, fellow atheists, before you so cheaply discharge your feelings - intense though they may be- in such reckless ways.

Yes, the guy is my brother - but this isn't about being overly protective to him as Mike can take care of himself. This is about we as atheists showing a higher standard and having some ballast when we insist that Christian fundamentalism is fundamentally intolerant. Because when we fire off such emails as those above, we lose our base argument before it even begins to be made!

Pastor Mike Makes the Atheist Blogs!

Seems like Pastor Mike - in the guise of a previous blog of his- has now made the rounds on the Net and is creating bedlam with hundreds of non-believers now putting him on their radar. This follows a post of his (last year, I believe) recommending that atheists be placed on national registries.

Incredibly, he actually managed to garner the attention of one of the top national atheists, PZ Myers (who achieved infamy by destroying a consecrated host at one time).

His blog on Pastor Mike is at:

http://freethoughtblogs.com/pharyngula/2011/08/28/pastor-mike-has-a-plan/

'Pastor Mike has a Plan'

Myers writes:

It is a familiar plan. It is the kind of plan that many totalitarian regimes would love to implement. Pastor Mike wants a list of all atheists.


Brothers and Sisters , I have been seriously considering forming a ( Christian ) grassroots type of organization to be named “The Christian National Registry of Atheists” or something similar . I mean , think about it . There are already National Registrys for convicted sex offenders , ex-convicts , terrorist cells , hate groups like the KKK , skinheads , radical Islamists , etc..

This type of “National Registry” would merely be for information purposes . To inform the public of KNOWN ( i.e., self-admitted) atheists . For example , let’s say you live in Colorado Springs , Colorado , you could simply scroll down ( from the I-Net site /Blog ) I would have , to the State of Colorado , and then when you see “Colorado Springs” , you will see the names of all the self-admitted atheist(s) who live there ( e.g., if an atheist’s name happened to be “Phil Small” ) . The individual’s physical address , and other known personal information would NOT be disclosed ( though , perhaps a photo could be ) .

Now , many (especially the atheists ) , may ask “Why do this , what’s the purpose ?” Duhhh , Mr. Atheist , for the same purpose many States put the names and photos of convicted sex offenders and other ex-felons on the I-Net – to INFORM the public ! I mean , in the City of Miramar , Florida , where I live , the population is approx. 109,000 . My family and I would sure like to know how many of those 109,000 are ADMITTED atheists ! Perhaps we may actually know some . In which case we could begin to witness to them and warn them of the dangers of atheism . Or perhaps they are radical atheists , whose hearts are as hard as Pharaoh’s , in that case , if they are business owners , we would encourage all our Christian friends , as well as the various churches and their congregations NOT to patronize them as we would only be “feeding” Satan .

Frankly , I don’t see why anyone would oppose this idea – including the atheists themselves ( unless of course , they’re actually ashamed of their atheist religion , and would prefer to stay in the ‘closet.’ ) .

Actually, there are good reasons to oppose it. It’s involuntary; many atheists promote the Out Campaign, and we think it would be great if more of us would step forward and of our own choice make our rejection of religion open. But many people also have good reasons to fear being outed, and the Pastor Mikes of the world are among them — he’s already threatening to harass atheists and organize boycotts. As you can see, he’s already comparing atheists to criminals, sex offenders, and the KKK…which is all rather ironic, given that his tactics are more like the oppressive and discriminatory actions of the Ku Klux Klan, who, by the way, would also probably love a list of known atheists in their neighborhoods.

I’m out. Pastor Mike can get to work compiling his own damn list, and he can put me right at the top of it. Would he also like me to get a tattoo, or maybe wear an armband with a big red A on it? We’re not ashamed, but many of us are rightly afraid of the cretinous thugs who follow Pastor Mike’s Jesus.


--------------------------------------------------------------------------------

By the way, heres a little eytmological information you might find entertaining.

CRETIN. ORIGIN late 18th cent.: from French crétin, from Swiss French crestin ‘Christian’ (from Latin Christianus), here used to mean ‘human being’, apparently as a reminder that, though deformed, cretins were human and not beasts.

People like Pastor Mike do force us to work harder to remember that Christians can be human beings, not beasts.



Some of the 183 responses- comments the blog attracted:

Pastor Mike restricts signups for his blog. He allows comments, but only from the fawning faithful.

---

Why not put is in work camps…at least it’s productive.

--

Let me guess.

Part II of Pastor Mike’s plan involves nights of terror followed by incarceration in concentration camps.

It’s all very xian though. Pastor Mike is your typical fundie xian death cult mass murderer wannabe.

In the bible, atheism is a death penalty offense, right up there with being a disobedient child or nonvirgin bride. And a few centuries ago, being an out atheist could get you killed.

Xians do have a 2,000 years of slaughtering people by the tens of millions. If it wasn’t for centuries of brave people putting them on a leash, they would still be doing it. One of the signs of a civilized society is not letting your religious kooks run around loose.

--

Honestly, if Bachmann were to be elected I would not be surprised at all if this actually happened.

--

if they are business owners , we would encourage all our Christian friends , as well as the various churches and their congregations NOT to patronize them

Can’t you just feel the love?
--

I’m ashamed to share a planet with people like this.

---

Dear Pastor Mike,

Put me on your atheist list. I live in San Antonio, Texas. That’s right. THERE ARE ATHEISTS IN TEXAS!!!!!!11!!!!!!!

Oh, and fuck you and the two asses your god-man rode into Jerusalem on (at the same time. It was pretty funny).

--

Ah yes, in fact let’s also make one for xian fuckwitsbelievers! Sure, you may take offense, being publicly listed in the same manner as sex offenders, but it’s all for a good cause! We care about you, we want to show you rationality, we want to save you from the dangers of xian beliefs. Can’t you see that we only want what is best for you? Sure, we may use such a list to boycott mega churches, and businesses run by xian extremists, but that is not the primary aim. Such actions would only be undertaken to save them from falling victim to a self-destructive ideology. I frankly cannot see why even xians themselves would not opt to register on such a list, unless of course they are ashamed for their own creed. Surely this is not the case…RIGHT?

--

Pastor Mike hasn’t really thought it through, thought being beyond him.

The No Religions run around 22% of the population, 67 million people, while the fundie death cultists run around 20-30% of the population.

It’s going to be difficult rounding up getting the names of that many people.

And US xianity is dying at 1-2 million people leaving per year. It’s going to be even more difficult when xianity is reduced to small weird FLDS type cults, living in out of the way places, torturing their women and children, and being widely considered as…social problems.

PS Cue the xian crazies with “but Pastor Mike isn’t a real xian”. Fallacies are all that have left.
--

@Jason;
Only a planet? I’m ashamed to share a universe with them. Anyway, if they want my details on a register, that’s fine by me. I already have a bumper sticker, another sticker on my front door and have had several letters published by my local paper, (all in deepest, darkest Sussex, U.K.) all of which proclaim my atheism.
I know that there are many people for whom coming out as an atheist is just impossible right now and I object to them being forced out, but for those of us in my position, where there is no problem in coming out, then I think that we should (but there should never be any coercion to do so).

--

I think it’s a great idea. Once the list starts growing past 6,000, think of the panic that would settle in their little town of 109,000. Imagine the quiet little old ladies who would go sign up for the list in solidarity.

I honestly can’t think of anything that would create more solidarity and cohesion in the community of non-believers. I heartily encourage him to begin his endeavor.

--
Usually idiots like this just make me angry, but this is just too outrageous. I’m honestly a little shocked by this. I guess I thought more of humanity than this; I thought we were beyond such things. I guess I was wrong.

---

I oppose national registries anyway. Like, all of them. And Pastor Mike’s arguments provide the reasons I think we all should.

But no matter how you threaten and harass, atheism isn’t illegal. I know you’d like to have the police force as your own personal army to do whatever you want to other people, Pastor Mike. That’s because you’re a delusional authoritarian thug who hates freedom.

Go take your Jesus into a dark room and fuck it. Maybe you’ll get on a national registry!

---

I teach at a prestigious catholic university so coming out as an atheist isn’t currently an option for me. Even revealing this fact anonymously gives me some trepidation, given the mouth-foaming fear of religious fanatics like Pastor Mike who doubtless would target people like me first. I’ve always wondered how many others are in the same predicament.
---
If I can get onto his website, this is what I’ll leave as a comment:

I’m an atheist. Come at me bro. My girlfriend is also an atheist, as well. We are atheists because we there is no empirical evidence to suggest that the god exist, nor even any reason to suggest that god is a legitimate possibility. There’s also massive amount of empirical data that demonstrates the impossibility of the bible being true, so if there is a god, it sure is not the Christian one. I can’t speak for all atheists, but I can tell what would generally convince us and what won’t convince us that god and Jesus are real.

Let’s start out by what will NOT convince us. We do not believe that the bible is true, nor do we believe that heaven or hell are real, so telling us bible verses will do absolutely nothing to convince us to become Christians and threatening us with hell does not scare us, because we don’t believe in that crap. Using the bible and threats of hell are only convincing to those who already believe in that stuff, and practically no atheist believes that stuff.

What will convince us is actual evidence that the bible is true or that god exists, and my evidence, I mean data. Something that’s testable and verifiable. In general, atheists view faith as a bad thing, because what faith really boils down to is believing stuff without evidence to support it. Remember, burden of proof is on the one who says that something does exist, not the atheists who won’t believe due to a lack of evidence.

--

Tackling Intermediate Astronomy Problems (4)

We now delve further into the intricacies of planetary motion, including using material presented in 'Tackling Simple Astronomy Problems', especially Kepler's 3rd or harmonic law. Recall from that law:

(T1/ T2)^2 = k(a1/ a2)^3

where T1, T2 are the periods, related to a1, a2 - the semi-major axes, as shown.

Now, it should be clear that once the sidereal period T of a planet is known, and also the semi-major axis a(or mean heliocentric distance) then the velocity of the planet in its orbit (assumed circular) can be computed, or:

V= 2π a/ T

Hence, for two planets, the ratio of their orbital velocities is:

V2/V1 = (a2/a1) (T1/T2)

where we intentionally allow the numbers 1 and 2 to refer to the inner and outer planets, respectively. As may deduced form Kepler's 3rd law:

T1 = [(a1)^3/k]^½ and T2 = [(a2)^3/k]^½

Substituting for T1 and T2 in the earlier form:

V2/ V1 = (a1/a2)^½

Now, in Fig. 1, the orbits for the Earth and a superior planet are shown, and the semi-majore axis are denoted by a and b, respectively. For any superior planet, b > a.

At opposition (the aligment SEP) the positions of Earth and planet are given as E and P, with velocity vectors V and V_p, tangential to their orbits. Now, from the expression for (V2/V1), V_p < V so the angular velocity of the planet as observed from Earth is:

(V_p - V)/ PE

and is in a direction opposite to the orbital motion, and hence is retrograde at opposition.

At the following quadrature, shown by configuration SE' P', the Earth's orbital velocity V is now along the line P'E' but the planet's velocity V_p has a component V_p sin(φ)) perpendicular to E'P'. The other component, V_p cos (φ) lies along the line P'E' and - like the Earth's velocity -doesn't contribute to the observed angular velocity of the planet.

The geocentric angular velocity at quadrature is then:

V_p sin (φ)/ E'P'


Example Problem:

a) Compare the orbital velocities of Venus and Earth, if the sidereal period for Venus is 224.69 d, and for Earth 365.25 d.

b) Verify this by using a Table of orbital velocities for the planets - given in km/s

We have:

V2/V1 = (a2/a1) (T1/T2)


By convention we assign '1' to the inner planet (Venus) and '2' to the outer (Earth). We have a2 = 1 AU and for Venus (from Kepler's third law):

T1 = (224.69/365.25) yr. = 0.6151 yr.

a1 = {[T1]^2}^1/3 = [(0.6151)^2]^1/3

a1 = 0.723 AU

Therefore:

V2/V1 = (0.7234)(1/0.6151)

V2/V1 = 1.175

(b) According to a Table of Orbital velocities in Astrometric & Geodetic Data:

V(Venus) = 35.02 km/s

V(Earth) = 29.78 km/s

Take the ratio (which must be 1.175)

V(Venus)/V(earth) = (35.02 km/s)/ (29.78 km/s) = 1.175

So, Venus' orbital velocity is 1.175 times Earth's


Other Problems:

(1)(a) Calculate the ratio of the Earth's tangential orbital velocity to Saturn's given Saturn's sidereal orbital period is 10,746.9 days.

(b) Validate this is approximately correct if Saturn's mean orbital velocity is 9.664 km/s from an astrometric table.

(2)At quadrature with the planet Mars, it is found (based on Fig. 1) that SP' = 1.53 AU, and SE' = 0.999 AU.

(a) From this deduce the distance P'E' and

(b) Hence, find the angular velocity of the planet as observed from Earth

(3) If Mercury's sidereal orbital period = 0.2408 yr. show that its tangential orbital velocity should be 47.87 km/s

(4) Based on the information in (3)and given that Uranus' sidereal period = 83.747 yrs., show that Uranus tangential orbital velocity is approximately 5.477 km/s.

"Methuselah" Nation on the Horizon? The Numbers Don't Support It!

Every day it seems, another pie-eyed concept or proposal gets column or air time in the corporo-media. These knuckleheads never once think of running the numbers before they publish most of this crap. Then, it's touted as if it bears some inherent, underlying gravitas.

The latest example of this human hubris appeared in The Weekend WSJ ('Living to Be 100 and Beyond', p. C1) in which it is claimed gerontologists and other scientists are working "furiously to make it possible for humans to achieve Methuselah life spans". The paragraph goes on to describe the range of strategies being studied, including diet, drugs and genetic therapy as well as replacing worn out organs. One guy, an Aubrey de Grey, actually has the chutzpah to boast:

"The first humans to live for 1,000 years may have already been born"

Really, Mr. Genius Gerontologist? And where do you suppose we will put all these millions of Methuselahs?

As noted already, in previous blogs, the commodities indices have been telling us something else: namely that the stores of resources, materials to support even the EXISTING human lives, are not there! One of the best indicators for this is provided by the Global Footpoint Network, at:

http://www.footprintnetwork.org/


According to this site, we currently need not one but one and one half EARTHS to sustain our current rate of consumption. This means it requires on average 1.5 years for the Earth to regenerate the resources humanity currently uses in one year! Thus, even if the estimate is high, we find that with current growth rates we'll soon reach the actual limits defined and dictated by this number - which means a tipping point and crash. See also:

http://www.dieoff.org/

Which goes one step further and discusses how the soon upon us Peak Oil will cause population to plummet!

Let us say, then, that this Methuselah scheme garners vast research funds and manages to even alter current American lifespans - extending them to 150 years or more. What then? Well, their claim is that all these additional oldsters won't be drains at all since "they'll be healthy and able to find productive work". Horse manure!

You are looking at a putative effect of adding some 600,000 people to the nation every 6 months who would otherwise have died. That is 1.2 million a year, this on top of the additional 10 million or so incoming immigrants and more like 35 million if their nations also undertake this Methuselah research and confer benefits to them. That translates into an additional 36 million-odd new Americans added each year! That means, assuming this Methuselah patch is emergent by 2014, we will have as many people as China (1.1 billion) by 2025.

And yet the economic growth prognostications call for only 140,000 jobs likely added per month for the next eight years - and it may not even be that much if the new austerity budget trend is enacted. Note that number is the "population replacement" number, meaning that there is no net gain in jobs if 140,000 is the maximum net jobs created each month. Now, add an effective number of 100,000 oldsters - presumably frisky and ready to work - and you will need at least 240,000 jobs created per month. But wait, there are younger people in the population too, and we can estimate that at least 300,000 per jobs a month will be needed to get all of them employed. That means we're looking at a total jobs production to support all these folks of at least 540,000 jobs created per month!

Now, maybe in another parallel universe this level of jobs is being created in an alternative America, but not in this one! Not with the low aggregate demand we're facing and forecast low growth the next 5-10 years. (For next year alone, economists at JP Morgan Chase & Co. have forecast a net loss of 1.8 percentage points in growth if the current austerity -belt tightening template is pursued.)

Apart from jobs, there is the competition for other resources and social services, the most critical of which (and the most expensive) is medical care. I mean, those yearly added 1,200,000 geezers (who are presumably not really geezers) will want to maintain themselves with whatever medicine promises, so you're now looking at medical inflation going through the roof. These geezers will likely want spare parts or organs replaced out the wazoo.

Then there is the food and water. If the world population grows by another 300 million per year, because of these Methuselah finds, where are all the livestock going to come from - not to mention grains- to feed them all? Where are the materials going to come from to build them houses, or even bicycles to get from place to place (forget about cars, in a Peak Oil world there won't be the oil to support them)? A recent Economist article ('The Revenge of Malthus') actually made the point that Paul Ehrlich - author of 'The Population Bomb' - would have won his original bet with Julian Simon (of the CATO Institute) in regards depletion of five key commodities: copper, chromium, nickel, tin and tungsten....if the bet were re-calculated today. (Of course, as the piece notes, Simon died in 1998).

All of the indices show we are facing catclysmic shortages in supply, which is to worsen as our global population possibly grows toward 10 billion by 2050. But, of course, if the Methuselah pushers succeed, we'll be looking at possibly 30 billion by then! Far from just the 5 key commodities, I'd be worried about where all the drinkable water is going to come from (never mind the amounts needed for agriculture) especially given the continued ravages of climate change and the prolonged droughts arising from it.

Last but not least, what use at all is living to 150 or "1,000" if Alzheimers makes formidable incursions? Right now, some researchers estimate as many as 15% of aging boomers could get Alzheimers, and no cure or solution has yet been found. If even just 10% of the yearly added 1,200,000 "Methuselahs" ends up with Alzheimers, you're looking at 10,000 new cases per month! Shit, there aren't that many nursing homes on the planet to care for them all!

Oh, and what about retirement and pensions? Or Social Security? The article in the W/E WSJ makes light of this, simply claiming that nearly all these Methuselahs will be "self-sufficient". Yes, well I suppose that's feasible if one can live off of air (assuming it isn't too fouled by all the extra pollution and greenhouse gases) or money grows on trees!

Maybe these gerontologists need to contact the Heritage Foundation group that made the proposal some years ago that the nation needs to encourage more older people to adopt unhealthy habits, like smoking, to render higher probabilities for EARLY demise, to save the assault on pension funds, Social Security, etc.

And here's one more suggestion: maybe instead of trying "furiously" to extend human life and multiply the quantity of elder folk, you idiots figure out more ways to render existing elders' years more quality -filled.

How about you then put more money and effort into finding a cure for Alzheimers, or at least what the precise dynamic is that incepts it? As opposed to finding a way for humans to add to the planet's carrying capacity (and rate of resource depletion) by adding too many unnecessary years to life.

Solutions to Special Relativity Problems (5)

Recall the last set of problems:

1) Assume that the lifetime of quasar 3c-9 is 1 million years as measured in its own rest frame. Over what total time span (in Earth-measured time) would its radiation be received at the Earth? (Assume 3c-9's velocity relative to the Earth remains constant)

2) Suppose that you happen to be moving at a velocity of 3c/4 past a remote observer who picks up a stopwatch and then sets it down. Using a high power telescope you observe he held the watch for 9 secs. How long would HE think that he held it?

3) An astronaut orbits the Earth at a distance of 7 x 10^6 m from its center for a week. How much younger than his twin on Earth is he when he lands? Assume standard orbital speed of 18,000 mph and neglect the rotation of the Earth.

4) Consider 3 galaxies: A, B and C. An observer in A measures the velocities of B and C and finds they are moving in opposite directions - each with a speed of 0.7c relative to him., i.e.

(0.7c) <--------(B)----(A)-----(C)-------->(0.7c)


What is the speed of A observed by someone in B?

What is the speed of C observed by someone in B?

The observer in A thinks that the two other galaxies are receding from him at a rate 1.4c. Show him how this is wrong, by providing the correct result.

---

solutions

(1) Let t = 10^6 yrs be the quasar's lifetime in its own rest frame. Then the total Earth-based time that its radiation will be received is:

t' = t [1 - v^2/c^2]^ ½

where v = 0.8c

so:

t' = (10^6 yrs.) [1 - (0.8c)^2/c^2]^ ½

t' = (10^6 yrs.) [1 - 0.64]^ ½ = 10^6 yrs(0.36)^ ½

t' = 0.6 (10^6 yrs.) = 6 x 10^5 yrs.

(2) Let delta t' = t2' - t1' = 9 secs

t2' = (t2 - 3c/4)(1 - 9/16))^-½

t1' = (t1 - 3c/4)(1 - 9/16)^-½

or:

t2' = (t2 - 3c/4) (7/16)^-½

t1' = (t1 - 3c/4) (7/16)^-½

whence:

(t2' - t1') = [(t2 - 3c/4) - (t1 - 3c/4)]/0.661

or: 9 sec = (t2 - t1)/0.661 and

delta t = 5.95 sec

(3) The speed of the astronaut is given by:

v = (2 gr)^½

and r = 7 x 10^6 m, g = 10 ms^-2

v = 11, 832 m/s = 3.94 x 10^-5 (c)

In the astronaut's frame, 1 week - 86,400 s x (7) = 604, 800 secs

For the twin on Earth:

t = t'/ [1 - v^2/c^2]^ ½

t = 604, 800.0002s

and so the time difference = 0.0002s, or the twin in orbit will be (t' - t) or 0.0002 s younger on his return.

(4) The speed of A observed in B = 0.7c, exactly equal to the speed of B observed in A, by principle of relative velocities.

To find the speed of C observed in B, we use relativistic addition of velocities or:

u = (u' + v)/ 1 + u'v/c^2

u = (0.7c + 0.7c)/ [1 + (0.7c)(0.7c)/c^2]

u = (1.4c)/ 1 + 0.49 = 1.4c/1.49 = 0.94c

"Greatest Generation" Has to be Based on More Than Media Hype

"The hallmark of a great civilization is its ability to wage peace, not war." - Gene Roddenberry

When one lives overseas for any length of time, especially in other English-speaking nations that formerly were part of the British Empire, the first thing noticed is an inherent conservatism in choice of language. Seldom, if ever, does one find the word "greatest" bandied about, whether in terms of a performance (say at the Royal Albert Hall in London), or a figure of sports or film, or a generation. There is an inherent understanding that the word - if overused- becomes trite and meaningless. Thus, the much ballyhooed understatement of the British, who may describe an especially well-acted play as "fair" while his American cousin babbles "the greatest".

So it is with the recent TIME piece with its front cover focusing on the "New Greatest Generation", describing those who either have served or are now serving in Iraq and Afghanistan. But interestingly, one letter writer responding to the piece, didn't agree. He wrote (p.2, TIME, Sept. 5):

"In updating the term 'Greatest Generation' you trivialize it. The term was adopted to honor those who fought in World War II'. More than 291,000 died in combat, 671,000 were wounded and more than 73,000 are still missing in action."

Even this only tells part of the story, and also misfires on the definition of the "Greatest Generation" - which encompassed not only those on the front lines - battling both the Japanese Empire (in the Pacific) and Nazi Germany (in Europe and N. Africa) but those at home making huge sacrifices. Those sacrifices included masses of women working on the weaponry assembly lines (symbolized by "Rosie the Riveter") to every citizen paying a much higher income tax to defray the costs of the war, and also accepting severe rationing on gas and food items. In other words, that entire generation sacrificed and was unified behind a single will to prevail over combined fascist -totalitarian empires that would have subjugated us with any less effort! So, to compare the current armed services (who let us not forget joined to be PAID for their service) with those of that era is nothing short of absurd.

To even remotely compare the relatively small set of those fighting the so-called "war on terror" to the most widespread war in human history, with more than 100 million military personnel mobilized across more than 40 countries, is nothing short of preposterous!

To compare a regionally-localized set of skirmishes (mainly in Iraq and Afghanistan) that saw paid volunteers facing IEDs, and roadside bombs - causing thousands of casualties to one which spanned the globe, ended up in the deaths of 60-70 MILLION, and included the use of nuclear weapons - is historically tone deaf and ignorant. Indeed, as the TIME letter writer observed, it trivializes the meaning of "greatest" to call the current troops or their connections, the "new Greatest generation".

But this has stuck in my craw ever since Bush Jr. launched the pre-emptive Iraq invasion in March, 2003 which - not to put too fine a point on it - was an illegal act. Thus, not at all like the justified entry into WWII, after Pearl Harbor, because Iraq had nothing, not one damned thing, to do with 9-11. Indeed, the U.S. invasion of Iraq had much more in common with the German invasion of The Sudetenland in Czechoslavakia, in 1938. "Shock and Awe" indeed! How about "Blitzkrieg 2"?

Many have also observed the Iraq invasion marked the U.S. violation of Principle VI of the Nuremberg laws, to wit:

PRINCIPLE VI "The crimes hereinafter set out are punishable as crimes under international law: "(a) Crimes against peace: "(i) Planning, preparation, initiation or waging of a war of aggression or a war in violation of international treaties, agreements or assurances; (ii) Participation in a common plan or conspiracy for the accomplishment of any of the acts mentioned under (i)."

Thus, in contrast to waging a war of DEFENSE against true aggressors, as in WWII, the U.S. under the Bush regime chose to invade a sovereign nation that had no part in any attack on 9-11. They did it for control of strategic oil reserves, and the biggest benefactors were linked corporations, such as Halliburton, Bechtel etc. These and other private corporate parasites reaped hundreds of billions in taxpayer money off the unprovoked Iraq incursion. Meanwhile, one could follow the Bushies' desperate efforts to try to parlay their invasion of Iraq on terms similar to WWII, such as comparing Saddam Hussein to Hitler - when their 'Shock & Awe' essentially ripped apart what was left of Saddam's air force in thirty minutes. Meanwhile, Hitler's Luftwaffe terrorized all of Europe and assisted in more than a half dozen invasions.

Even Afghanistan is something of a farce, as the U.S. was actually in the process of negotiating with the Taliban for oil pipeline rights before 9-11. Also - the actual perpetrators of 9-11 were Saudis, from Saudi Arabia - yet all their associates (including bin Laden relatives) were permitted to fly out of the country in the aftermath! Meanwhile, the small scale encounters and "fire fights" experienced in Afghanistan can't be compared in any legitimate way with the raging land and air battles seen just in the Guadalcanal campaign of WWII. See e.g.:

http://en.wikipedia.org/wiki/Guadalcanal_Campaign

Easily evident, despite all the over the top comparisons of the current terror war to WWII, is there is no comparison! The historical differences, not only of intensity but scale, are as vast a chasm as the Pacific Ocean itself.

So why does the popular press-media persist with its fulsome jabber and hyperbolic nonsense pseudo-analogies? One reason is because people, citizens are less historically educated today, so that they can get away with it! If people know very little of history, especially the great wars of history, then they won't know the difference if anyone claims the current "war on terror" is a real war (despite NO taxes being paid for it) and is on a par with WWII. It is simply gulped down with other refuse. Recall then Jefferson famous words in his 'Notes on Virginia':

"Every government degenerates when trusted to the rulers of the people alone. The people themselves therefore are its only safe depositories. AND TO RENDER THEM SAFE, THEIR MINDS MUST BE IMPROVED."

In other words, Jefferson believed that an unread populace - one which refuses to improve its collective mind- would be an easily manipulated and exploited populace, especially by a government determined to map out its own agenda. In this respect, the last ten years have seen military budgets explode on the basis of a specious "war on terror" while our domestic infrastructure and needs go begging. And yet, we behold puff pieces essentially praising those who were part of this military propaganda game. (Btw, for interested readers, please check out 'The Pat Tillman Story' now on HBO).

In the end, however, the only way out of this exploitative propaganda, which benefits only the Pentagon and its protectors in congress, is to expose the erroneous conflation and analogies wherever they appear.

Does this mean the service people returning from Afghanistan and Iraq merit no acknowledgement? No, it does not! They certainly merit at least as much as those who returned from Vietnam (a conflict which claimed 58,000 American lives) but as we've seen - no one in the corporate media has referred to that generation as 'great' in any way! So what gives?

This brings us to the second reason the corporo-media presses false analogies, especially concerning wars now and then. Because in a 24/7 news cycle any media outfit will grab onto anything in order to sell copy. You see it not only in news magazines, but newspapers as well. While in 1960 the choice and selection of stories would be strict, now - with over 30 cable news stations- it's indiscriminate. Thus, TIME's calling the current generation of warriors "great" makes total sense.

Now, another reader responding in TIME's letters section (ibid.), wrote that this group ought to be called "the greatest of a generation". But even this is replete with problems, because it essentially implies all those who were non-combatants (in two occupations which are questionable ab initio) are little better than chopped liver! So all those who volunteered (for less than one half the money) for 'Teach for America', or the Peace Corps, or 'Doctors without Borders' merit no kudos or attention on a par with those who blast out villages with suspected Taliban, raid homes or use drones to attack targets.

Sorry, but this cannot be right and nothing can make it so.

So what label is to be used? In an era in which truth and fact-checking is in short supply, and the bulk of our populace are historically challenged? Perhaps none. Maybe TIME ought to have left its heros as the "new No Names" or just the No Names. Once history itself puts them into proper perspective, perhaps a more objective parsing is possible.

Right now, I'd say it's premature, since - like Vietnam in 1968 - we still have zero idea of how either Iraq or Afghanistan will turn out.

At least in my dad's war, the nation (with strong allies) prevailed against its fearsome foes!

Introduction to Special Relativity (5)

Having dealt with time in the context of special relativity, we now consider what happens to length. We return to the diagram of systems S and S' moving relative to each other (Fig. 1) and consider a meter stick of length L (= 1 m) pointed in the +x direction and moving in that direction with velocity v. We can also think of it as being at rest in the S' system with one end at x' = 0 and another end at x' = L', initially.

Its length in the system S' is therefore L'. At time t = 0 we take a photograph of the meter stick with a camera located in the S system. We inquire: What are the positions of the two ends of the meter stick in the S system? We can answer this by using the first of the Lorentz-Einstein transformations:

x = x' + vt'/(1 - v^2/c^2)^½

and

x' = x - vt/ (1 - v^2/c^2)^½


We opt to use the lower form rather than the upper, having already specified an instant at t = 0 and hence looking for simplification. Then:

x' = x / (1 - v^2/c^2)^½

Now, the end of the meter stick that is at x' = 0 in S' is found to be at x = 0 in S. The other end in S is seen to be at:

x = L' (1 - v^2/c^2)^½

This informs us the length of the moving meter stick in S so we can say that the length of the moving meter stick as seen by the camera is:

L = L' (1 - v^2/c^2)^½


As can readily be seen, this implies length contraction. For example, say the rod is moving at v = 0.6c, then the length L is (given L' = 1m):

L = (1 m) (1 - (0.6c)^2/c^2)^½ = 1m [(1 - 0.36c^2/c^2)^½

L = (1m) [0.64)^½ = 1m (0.8) = 0.8 m (or 80 cm instead of 100 cm)

(Remember also, by symmetry arguments of relativity, that the observer in the other system will argue that L' = L (1 - v^2/c^2)^½ so that from his viewpoint a meter stick will be similarly foreshortened.)

Readers may recall that something similar occurred in the time transformation, i.e. each of two relatively moving clocks ran slower with respect to the other than to itself.

This brings us back to the solution of the Michelson-Morley experimeent discussed in Instalment (1). For it is the curious, symmetric relativity in time and length (in direction of motion) which solves the paradox of the "missing ether wind" quite simply and logically. Moreover it is solved more fundamentally and satisfactorily than either Fitzgerald or Lorentz could manage.

Now, let's derive the new law for addition of velocities. Assume an object in the S' system starts at the point x' = 0 at time t' = 0. It moves with constant velocity u' (relative to S') and in the time t' it travels a distance x'.

By definition, u' = x'/ t'

We now ask 'How fast does this object travel according to the observer at rest in System S?'

This observer will see a velocity given by the formula:

u = x/t = (x' + vt')'/ t' + x'v/c^2 = (x'/t' + v)/(1 + x'v/t'c^2 )


u = (u' + v)/ 1 + u'v/c^2

This is the relativistic formula for addition of velocities. If u'
and v = c then the formula yields:


u = (c + c)/ 1 + c^2/c^2

u = 2c/ 1 + 1 = 2c/2 = c

If u' and v are less than c then u must always be less than c.


Example Problem:

Say two objects are moving at 3c/4 towards each other, then what is their relative velocity as recorded in a system S observing their approach?

u' = 3c/4 and v = 3c/4

then:

u = (u' + v)/ 1 + u'v/c^2 = (3c/4 + 3c/4)/1 + u'v/c^2


where: (3c/4 + 3c/4) = 3c/2

and:

u'v = (3c/4)x(3c/4) = 9c^2/16

Then:

u = (3c/2)/ [1 + 9c^2/16/c^2]

u = (3c/2)/ (1 + 9/16) = (3c/2)/ (25/16)

u = (3c/2) x (16/25) = 24c/25


Other Problems:

1) Assume that the lifetime of quasar 3c-9 is 1 million years as measured in its own rest frame. Over what total time span (in Earth-measured time) would its radiation be received at the Earth? (Assume 3c-9's velocity relative to the Earth remains constant)

2) Suppose that you happen to be moving at a velocity of 3c/4 past a remote observer who picks up a stopwatch and then sets it down. Using a high power telescope you observe he held the watch for 9 secs. How long would HE think that he held it?

3) An astronaut orbits the Earth at a distance of 7 x 10^6 m from its center for a week. How much younger than his twin on Earth is he when he lands? Assume standard orbital speed of 18,000 mph and neglect the rotation of the Earth.

4) Consider 3 galaxies: A, B and C. An observer in A measures the velocities of B and C and finds they are moving in opposite directions - each with a speed of 0.7c relative to him., i.e.

(0.7c) <--------(B)----(A)-----(C)-------->(0.7c)


What is the speed of A observed by someone in B?

What is the speed of C observed by someone in B?

The observer in A thinks that the two other galaxies are receding from him at a rate 1.4c. Show him how this is wrong, by providing the correct result.

Oldsters lining up to work past 65? Yeah, right!

Two recently delivered magazines (Saturday Evening Post, Mother Jones) have articles featuring radically differing claims. Which is to be believed, and which is most likely PR for the gullible set? Well, if truth is what's on the line, as opposed to PR and telling people what they NEED to hear instead of what they want to hear, I will put my money on Mother Jones (especially in light of the excellent exposes done the past two years including one on the Gulf oil spill and how the toxins are still around!)

In the cheery, upbeat Post article, 'The New Retirement', we're informed that "Americans are increasingly choosing to stay on the job after age 65 and money is only part of the story". Well, who'da thunk?

On the next page, we find the photos of two obviously well-provided for seniors at the top who were wealthy enough to actually retire early and buy an 85-acre farm where they "pursue their passion" by stuffing bouquets of flowers into canning jars and selling them. Well, nice work if you can get it! And, the couple informs us they're blissfully happy doing all that canning and insist: "If our health holds out we'll do this as long as we can".

And my first reaction, to this well-heeled but dumb pair is, WTF!? The rate of human knowledge is doubling every 4 years and you choose to waste your remaining years canning flowers!

But that's just me and maybe my own priorities are wrong. I happen to think that in a limited life time humans owe it to themselves to learn as much about their world and cosmos as they possibly can. And that doesn't mean wasting time canning miniature flower bouquets if you don't have to!

Anyway, the next lady we behold is a well-coiffed exec of 71 who absolutely has NO intentions of leaving her job as senior vice president of career services at the Ayers Group. Hell's Bells, I suppose if I was pulling down a 6-figure salary for just typing in data at a nice shiny new laptop every day I'd want to keep doing it too! And the lady exclaims:

"I just wouldn't know what to do with myself if I retired!"

Well, uh, how about reading a few books...not just romantic pot boilers from Jacqueline Susanne, but areas of astronomy, psychology, philosophy to broaden that bean counter brain? How about even traveling to other places, like Switzerland, or Sweden or India? To gain something beyond a parochial perspective?

But evidently the thought never crosses her brain. She's obviously content to remain in her little corporate cubbyhole until she croaks.

Now, basically I have nothing too much against such people - as I'm sure they'd also regard what I do as "wasting time" from their frame of reference. Nor do I have any major objections to the article for showing their lives. Where I have objections is when the article - not just this one but ANY of these 'work past 65' efforts (also common in the AARP Bulletins) - portrays the working and happy lifestyle as the one relevant to ALL seniors, by assuming everyone wants to work past 65. And worse, that all the jobs most available to seniors are the spiffy jobs! (Or self-created jobs.)

In other words, I object to propagating myths! To be judiciously fair then, the article ought to not merely have shown these comfy older folk ensconced in their comfortable and inviting domains of total control, but also those like the 101 -year old Wisconsin widow, shamelessly run over by a Walmart shopper last year while acting as a greeter. For it is a high crime against the elderly to make them think they can all be like the "passionate" and independent flower canners or the Ayers Group exec, and not end up like that 101 year old, slaving away to make ends meet (which is the only reason I can see for anyone working past 65 as opposed to doing a million other things now possible!)

But those down-scale work opportunites aren't reported! All we're told in the Post piece is that "the portion of Americans aged 65 and older in the work force has increased markedly in recent years". It goes on to state that in 2010, "an average of 17.4 percent of them were in the labor force". But it doesn't say the next thing: that 96% of that 17.4% senior labor force is buried in minimum wage-scut jobs...like Walmart greeters, or janitors, or low level store clerks or ...whatever Walmart's fancy euphemism is for them...oh right: Associates!

Now, again, if elderly folk need to work in such positions to keep body and soul together that is one thing, but I can't see a person voluntarily doing it when so little of life is left and so much is to be learned.

Meanwhile, as an antidote to this cheery codswallop, there is the Mother Jones piece: All Work and No Pay on how corporations have actually sped up their processes to wring more productivity from workers, while not increasing their pay. Slavery anyone? Well how about indentured servitude? There are actually 3 articles in succession, all equally depressing - especially the one disclosing how older workers' health is seriously threatened by the speed up at one large company. (The other facts, data can be seen in the graphic included)

So, given this, WHY would any elderly person choose it, unless they absolutely had to? The trouble is, reading the Post puff piece, one gets the notion that work is one big joy ride for most elderly and they only need ask and they can "telecommute" from home! Not bloody likely! All the main corporations that might hire older workers, demand face time..they want it so they can see you while you slave away mopping the floors, cleaning up the spills on aisle 8, and so on...and especially so they can take out 'Dead Peasant's insurance' on you. Thus, if you croak while cleaning up one of those spills, they collect all the $100k insurance they've taken out on YOUR life! (And oh, btw, they ain't telling you about it!)

Yes, telecommuting IS possible! My wife does it, from Colo. to Maryland! But, she had to have worked over 12 years in the Columbia, MD office, often 14 hours a day, to have proven her worth enough for them to have trusted her to work on her own time. Now, at 70, she works because she enjoys it, the remuneration is good, and she "keeps her brain engaged" (testing software).

But make no mistake, 999 out of 1000 companies aren't just going to hand an oldster a check for working from home!

Another canard in the Post article is that "most work in America today is physically easier than it was a generation ago". This is true overall, but again, that doesn't mean it's easier for most senior citizens! Bear in mind despite all the hype over valuing "worker maturity" 90% of corps. still adhere to a Fortune 500 White paper issued in 1996 asserting that most workers deliver "diminishing returns" after age 50. Thus, most corporations aren't going to welcome the average elderly person into a high control, well paying job in this low aggregate demand environment. In fact, they're more often the first let go because it costs too much to sustain them on company health insurance plans.

Bottom line: Yes, there will be a certain lucky segment of those past 65 who will find work that is engaging, and in some way stimulating while it helps pay the bills. But most of the work available in the current recessionary environment is of the Walmart greeter or mopper or lower grade associate type. Not that that's bad, since when you need money anything will do. But that for a person who can afford to travel and improve his or her mind, to choose such a job instead, is total bollocks.

And maybe a sign of premature senility.

Solving Intermediate Astronomy Problems (3)

We now proceed to solve the two problems from the last set, one relatively easy, the other relatively more difficult!

To recap:

Problems:

1) Estimate the distance of Venus from the Sun at its most recent maximum elongation, if the angle of max. elong. was 46 degrees.

2) A recent observation of Mars 36.5 days after opposition showed an angle of elongation = 136 degrees. Find the distance of Mars from the Earth if Mars' orbital period = 687 days.


Solution for #1

The diagram for Problem 1 is shown, and the angle of maximum elongation.

We know, from the geometry:

SV/ SE = sin (SEV)

Then Venus' distance is:

SV = (sin(SEV)) SE

where: angle SEV = 46 deg and SE = a(E) = 1 AU

then:

SV = sin (46) 1 AU = (0.719) 1 AU = 0.719 AU


Solution for #2

The diagram for the configuration is shown for Problem #2, and the elongation angle which is also angle SE1p1 = 136 deg.

We are given t = 36.5 d, and we need to find the "gain" angle:

Θ = 360 (1/P - 1/P') t

where P, P' are the sidereal periods, or P = 365.25 d (Earth) and P' = 687 d (Mars)

Then:

Θ = 360 (1/365.25 - 1/687) (36.5) = 16.8 deg

which is none other than angle E1Sp1.

Now, angle E1p1S is required in order to get the distance - as the information at the bottom of the depiction shows.

We know:

Ep1S = 180 - [SE1p1 - E1Sp1]


and SE1p1 = 136 deg

So:

Ep1S = 180 - [136 deg - 16.8 deg]= 27.2 deg

Again, from plane trigonometry:

sin(p1E1S)/ Sp1 = sin(E1p1S)/ SE1

and, the ratio of planetary distances at time t:

Sp1/SE1 = sin (p1E1S)/ sin (E1p1S)

But:

E1p1S = 27.2 deg

and p1E1S = SE1p1 = 136 deg

Thus:

Sp1/SE1 = sin (136)/ sin (27.2)


Sp1 = (0.694/ 0.457) a(E) = 1.518 (a(E)) = 1.518 AU

Democrats Must Stop Playing Politics with the Bush Tax Cuts

The just-released Congressional Budget Office (CBO) report on projections of federal deficits over the next ten years was both infuriating and stomach-turning. It also reinforces David Wessel's WSJ column today ('Tracking Missteps Behind World's Economic Slump', p. A4) that "The U.S. government - congress and the White House- has an incoherent fiscal policy".

By that he means that half the time they blabber about "the risk of rising deficits", but on the other hand seek to make them much worse - such as extending the Bush tax cuts for all back in December. The other half of the time they blabber about "fiscal support" and creating jobs, but then set in motion immediate austerity and spending cuts measures that will have exactly the opposite effect. In any other universe, this behavior would be regarded as the evidence for insanity.

Anyway, the CBO sharply reduced its projections of total deficits over the next decade- reduced to $3.5 trillion up to 2021, BUT with major provisos and qualifiers. The biggest one is that ALL the Bush tax cuts will finally be allowed to expire next year as opposed to once again being re-animated like the Zombies of the 'Walking Dead'.

If this isn't done, and Obama and the Dems punk out again by playing politics (e.g. demanding the tax cuts be extended "only for those earning $250k and under") then we are in deep shit. The CBO then projects $5 trillion additional be added to the deficit to make a total of $8.5 trillion by 2021. Of course, honing in on the fine details not all the $5 trillion would arise from extending all the Bush tax cuts - it would more be like $4 trillion. The other $1 in deficits trillion would come from:

a) not stopping the payroll tax cuts ($115 billion each year, for a total of $230b over two years)

b) Allowing "doc fixes" each year for Medicare, so providers aren't dinged by payout cuts, leading them to dump or deny Medicare patients ($200b)

c) Not getting out of Iraq and Afghanistan by 2014.

The worst travesty of all would be that none of the painful forthcoming $1.3 trillion in spending cuts (due by end of Nov.) will lead to a 'savings' if the Bush tax cuts are re-animated again in December. Doubling down, the higher deficits would bring total public debt to 82% of GDP by 2021 up from 23.8% this year, according to The Wall Street Journal (p.A4)

Most interesting to me, was the same Journal piece noting that revenues were down to historic lows of 15.3% of GDP this year, compared to 18% of GDP historically. Clearly, this shows the need for higher revenues in taxes (at the very least repealing all the Bush tax cuts). Yet oddly, in its editorial ('What Austerity?") the Journal's brain trust makes the claim that not extending the Bush tax cuts would have a deleterious effect on jobs!

And yet the historic evidence shows this to be palpable bullshit. So, the Journal editors can say "Beam us up, Scotty!" all they want (ibid.), but THEY are the ones who need beaming up! I mean, they already conceded (even in the editorial) that revenues are at historic lows! Well, then get rid of the Bush tax cuts, which I for one do not regard as a real tax hike but rather returning to tax normalcy.

It would bring us back to the marginal rates of 39.5% in the Clinton era, during which 20 million decent jobs were created, and more importantly, people feltwealthier. (And this wealth effect was a major reason Clinton's impeachment proceedings over the Lewinsky indiscretion didn't get very far.)

Further, as economists James Medoff and Andrew Harless observed in their excellent book, The Indebted Society, 1995, p. 84, 'Let Them Eat Cake',

"high tax rates are associated with higher productivity growth"

There is a consistent and strong relationship. By contrast, for the years when Arthur Laffer's supply side dogma held, productivity retreated by more than 30% and debt exploded- exactly the opposite of what we've been sold. The classic example was the Reagan era for which Medoff and Harless note (p. 23):

"For the health of the economy, Reagan's policies turned out to be just about the worst thing that could have happened: investment did not increase, growth continued to stagnate, and the federal deficit ballooned to new dimensions."

Meanwhile, a more recent Financial Times Analysis of the Bush tax cuts (9/15/10, p. 24) passed in 2001 and 2003, showed they engendered "the weakest decade in U.S. postwar history for real, non-residential capital investment".

The FT analysis also observed that “during each decade from the 1950s to the 1990s, growth in real gross non-residential investment averaged between 3.5 percent and 7.4 percent a decade. During the 2000s it averaged a mere 1%”

This is evidence enough that the Democrats have to stop playing politics with these god damned tax cuts! It isn't good enough to simply pout and whine (as one D-congress critter recently, in an MSNBC interview): "We can't figure out a way to get ahead of the no tax narrative!

Well, too fucking bad! Figure out a way! What are you, imbeciles? Do you need brain transplants?

Start by leveling with your constituents that they can have either tax cuts delivering maybe $400 a year at most now, or their Social Security and Medicare later! BUT ..if they opt for the tax cuts now, they can't depend on getting their benefits later! They can't fucking have their cake and eat it!!!

Got it?

This is not brain science, or rocket science. We're not asking you buttbrains to delineate a trajectory to Mars for a 9-month trip and a payload weight of 20,000 kg. All we're asking is that you craft an efficient and convincing comeback to the Reptiles 'no tax' bullshit and STOP playing into their hands. This you did - whether you realized it or not, when you conceded to allowing "some" tax cuts to go through but not others. You are then defeated! Or, when you blather for a payroll tax cut or holiday when THAT is what helps pay FOR Medicare and Social Security! (Besides which, the evidence so far shows no signficant economic benefit from the payroll tax cut of 2% (WSJ, p. A4, op. cit.).

When the Dems wake up they might be worth more in the way of support. Until then I have to regard them as clueless, incoherent losers - politically deaf and dumb- and who will continue to be beaten like orphaned whelps by the Repups.

Tackling Intermediate Astronomy Problems (3)

One of the more important applications in intermediate astronomy is obtaining the relative distance to an inferior or superior planet in relation to the Earth. As we've seen before, it's easy to apply Kepler's 3rd law to obtain the basic dimensions of an orbit, namely the semi-major axis of the orbit - or the mean distance from the Sun. But things become somewhat more difficult when we seek to find the distance say, of the Earth to the planet, or the planet at a specific time - say before it commences retrograde motion.

So, we consider two cases:

(A) Inferior planet (see the diagram A)

As seen in instalment (3), the maximum elongation occurs when the planet's geocentric radius vector (pE in diagram A) is perpendicular to the planet's heliocentric radius vector, pV. Then by a careful measurement of the angle SEp, say over a series of nights around maximum elongation, one can obtain a value for the angle of maximum elongation. At such time the angle SEp is right-angled hence:

Sp/ SE = sin(SEp)

The quantity Sp/SE is therefore the distance of the planet from the Sun in terms of Earth units (or AU, astronomical units). Let Sp = R and SE = a(E) the semi-major axis for Earth's orbit, then:

Sp = R = sin(SEp) [a(E)]

Example:

If the angle SEp = 60 deg, find the planet's distance from the Sun.

Then: sin(SEp)= sin (60) = [3]^½/2 = 0.866

So: R = 0.866[a(E)]= 0.866 AU


Case (B) Superior Planet

In this case, we apply diagram (B), showing the planet at two successive positions, p and p1 and the Earth at E and and E1. This is a more difficult case but can be worked if the planet's synodic period S is known.

Here, we let the planet p be in opposition at some given time with the Earth and Sun (e.g. showing the alignment S-E-p in diagram (B). As we know, with opposition, the elongation is a straight angle or 180 degrees. Then after t days have elapsed the Earth's radius vector SE has moved ahead of the planet's as shown in comparing SE1 to Sp1. As can be seen, this reduces the angle of elongation from 180 degrees at opposition to angle SE1p1. This is then measured.

Now, over t days, the angle ESp will have increased from 0 (at opposition) to a value Θ given by:

Θ = [n - n(p)] t

where n, n(p) are the mean daily motions of the Earth and the planet, respectively. Using relations for the periods seen in instalment (3) we may write:

Θ = 360 (1/P - 1/P') t

where P and P' are the sidereal periods for the Earth and the planet, respectively/ Then, it follows by the relations seen in instalment (3):

Θ = 360 (1/S)

So, since t and S are both known, Θ can be obtained - that is, angle E1Sp1 is calculated. Hence, angle E1p1S can be found from:

angle E1p1S = 180 - angle SE1p1 - angle E1Sp1

From plane trigonometry we then obtain:

sin(p1E1S)/ Sp1 = sin(E1p1S)/SE1

or:

Sp1/ SE1 = sin(p1E1S)/ sin(E1p1S)

again, giving the distance from the Sun in terms of Earth's distance unit.

Problems:

1) Estimate the distance of Venus from the Sun at its most recent maximum elongation, if the angle of max. elong. was 46 degrees.

2) A recent observation of Mars 36.5 days after opposition showed an angle of elongation = 136 degrees. Find the distance of Mars from the Earth if Mars' orbital period = 687 days.

Life Originating from Space Rocks? Maybe.

For well over half a century, astro-biologists, astronomers and others have debated whether the theory of Panspermia might be valid, and if so, how would it manifest. The basic idea is that the "spores of life" would be carried to Earth, most likely on meteorites, and then the building blocks - given the right chemical reactions (say in the primitive reducing atmosphere) would have given rise to a prokaryotic cell.

Now, new findings may shed more light on this. A more recent analysis of a dozen meteorites found in Antarctica and elsewhere (e.g. Australia)conveys the strongest positive answer yet. In addition, the findings disclose the possibility that the components of extra-terrestrial DNA could have spontaneously formed in space.

As a brief refresher, meteorites (such as the Murchison meteorite shown, which impacted some 42 years ago in Murchison, Victoria, Australia) are space rocks that have made it through the Earth's atmospere and struck the ground. In actual fact, they are likely the remnant portions of much larger space rocks, most of which burned up on entry. The point is, it's conceivable that early meteorite bombardment might have seeded the Earth with the building blocks of life. This, as opposed to life originating autonomously on the Earth.

According to thr authors of a just-released report appearing in The Proceedings of the National Academy of Sciences:

"Meteorites may have served as a molecular kit providing essential ingredients for the origin of life on Earth and possibly elsewhere"

In effect, a qualified validation of Panspermia.

The key point is that all terrestrial plants and animals depend on DNA to store information. At the center of the ladder-like DNA molecule (see diagram) are ring-like structures called nucleotides. It is these tiny structures that scientists at NASA and the Carnegie Institute found in 11 of the 12 meterorites they examined.

Two of the samples, from the Murchison meteorite and one designated 'Loneolf Nunataks 94102', contained an array of nucleo-bases including those also found in DNA.

But another surprise was also found: each of the two samples mentioned also included exotic, or "extra-terrestrial" bases never seen before. This, according to Michael Callahan the NASA astro-geologist who analyzed the space rocks. Meanwhile, analysis of dirt and rocks in the vicinity of the meteorites showed no evidence of the same exotic nucleo-bases, hence contamination was unlikely. And in any case, the exotic nucleo-bases have never before been seen on Earth.

While amino acids have been found in other meteorites, this is the first time these DNA nucleo-bases have been uncovered. According to one Carnegie investigator:

"These molecules are at the core of life's blueprints. It's possible that the presence of these molecules in meteorites made us what we are today"

Indeed, and possibly made extra-terrestrials (hitherto undiscovered) what they are today too. Let us hope that if found, they are more like us in the best ways, and not the worst!

Stay tuned!

A Postscript: Even Wall Street Honchos are in CASH!

As we saw in the last blog, savers are under the gun what with the prospects of next to zero interest rates on their cash-fixed income savings. There are dire predictions afoot that the most diligent savers stand to lose, because of inflation eating away at their savings, and so they're being advised to take on some added risk. Well, one is justified in querying what the actual Wall Street Honchos, investors, traders, movers and shakers are doing with their own money. Are they following their own advice, or punking out? From the looks of things, the latter appears to be the case.

The eye-opener appeared in today's WSJ, p. C3, 'How Wall St. Invests Its Money in Hard Times'. It should also be an eye-opener to anyone who's turned on a Business or investing channel and been told by a green eyeshade type that "absolutely you must stay the course, and be in stocks"! Baloney!

The general tone of the article was that all the actual green-eyeshade types interviewed for the piece had their own money in "ultra-conservative" investments. According to one hotshot - an investment banker:

"I'm 80% in cash and Treasurys"

And the author notes this was a character who "in previous conversations hadn't failed to extol the virtues of complex derivatives"

Well so much for that! When the author asked the banker if he wouldn't now use some of those same derivatives in his own portfolio, he replied:

Not a chance! I don't want to take any risks!"

Fair enough, but if you guys - the wizards of finance - don't, why should any ordinary bloke?

Another guy, a member of big bank's management team, confessed that in the recent rash of market volatility he'd changed his allocations from 60% stocks and 40% bonds to a portfolio laden with U.S. government bonds and other investment grade paper (which usually refers to the "commercial paper" that appears in money market funds. In other words, this cat is as conservative as my wife and myself right now!

When the author of the piece pointed out that in order to change such allocations during the volatility the banker would have been selling in falling equity markets (hence, taking a significant loss), the guy actually responded:

"Right now, it's all about capital preservation. If I lose money in the process, so be it."

In other words, this whiz kid was so determined to get to safety he was prepared to sustain losses to change his investment allocations, reasoning a 4-10% hit on such a change was preferable to a 40% hit!

Of course, even as another acquistions banker is described as now veering "between pessimistic and very pessimistic" the author himself quickly reverts back to the norm of saying this isn't financial hypocrisy and little guys have no business following their example.

Really? How come?

The big difference between common folk and finance's upper echelons is that the latter already have a lot of money in the bank - from the cash portions of their bonuses and the sale of their shares in the good times. They don't really have to worry about their pensions. Most of us do. And we need high yielding investments to pay for them.

Again, bollocks! As I showed in the previous blog, one doesn't need the "risk of high yielding investments". Again, which is better? To lose (in the worst case scenario without making any adjustments to consumption) 4% a year to inflation, OR ...lose 40% every other year in a market correction, in which case you will never ever reach the breakeven point and will have to work until your 90?

People can make it without high risk investments, if they sustain a rigorous saving mode, no whim spending, period - then assemble enough to put into an immediate fixed annuity. Such regular monthly income, say $640 for an annuity taken at 65, with payment to beneficiaries for 10 yrs. in event of demise - can nicely supplement a Social Security check. It can also keep your money from running out, say if you have to regularly dip into principal to meet your IRS draw down obligations (an immediate annuity, once the computations are done, can meet the same requirements).

The choice, of course, lies with the average Joes and Janes. Do you want to try for an instant "jackpot" in Maul Street's equity markets casino (laden with risky, unregulated derivatives and flash traders)or will you commit to the slower, less sexy savings approach ending with preservation of sufficient capital to be used in the purchase of basic, no frills immediate annuities?

May I also remind readers, that they have been referred to as "dumb order flow" and "chickens to be plucked" by the Maul Street Street wizards and casino operators? Who, like the 'Wizard' in the land of Oz, never want you to see what actually goes on behind the curtain! Only to take their word that you need what they are peddling.

Need I say more?