Sunday, November 13, 2016

Largest Super Moon In 68 Years Visible Early Tomorrow Morning

The so-called "super Moon" will be extra super, visible early tomorrow morning - as Earth's natural satellite makes its closest approach in 68 years, specifically occurring at 6:21 EST. Indeed, it will be the closest approach of the Moon with the "super Moon" effect until the next on November 25, 2034.

For reference, Newton’s law of universal gravitation states:

F = G M1 M2/ r 2

That is,  the gravitational force of attraction F defined between two masses M1 and M2 separated by a distance r between their centers. In this case we reference the mass of the Moon M2 in relation to the mass M1 of Earth. (where G is the Newtonian gravitational constant, or:

G = 6.67384(80) x 10-11 kg-1m3 s-2.)

In the case of the above equation, for the super Moon  visible early tomorrow we are looking at a decrease in the separation  distance r from its average value of 240,000 miles to 221, 523 miles (according to NASA). This is a significant decrease which means that the force F must increase given F is inversely proportional to r2 .  

This yields the increase of F. But the increase in angular size  e.g. a) can also be computed based on the decrease in distance, say from r  say to r'.  Recall we examined angular measure in a recent post:

Therein it was noted that the Moon's angular diameter is 1/2 degree. This applies to the Moon at its average distance r. If we let the angular measure a (= 0.5 deg)  be for the distance r, then we can set up a ratio in terms of the angular sizes too, e.g. a'  to a.


r/ r'   =    a'/ a

So;    r' a'  =   ra  and a'  =    r x a /  r'  or:   (r/ r')  x a

= (240,000 mi/ 221,523 mi) x (0.5 deg) = 0.54 deg

This recognizes the angular size of the Moon visible from Earth is in inverse proportion to its distance from Earth, i.e. the less the value for r (given r' <  r) the greater the value of a (e.g. a')
From this relation, the interested and energetic reader should also be able to work out the relative increase in size referred to change in apparent lunar area. Hence using the linear radius at the average distance (2160 miles) then getting the apparent increase in area along the lines indicated above for angular width.  You should find a roughly 16% increase in apparent size based onn the ratio of areas at the two different distances.

Beyond that most people in the U.S. ought to have mo problem getting outside and "soaking up the view" in the parlance of NASA planetary geologist Noah Petro. Note at the time of closest approach the full Moon will be setting and the Sun rising on the east coast.  Prime viewing, in any case, will extend from tonight through tomorrow night given the difference in time (24 hrs.) will only make a tiny difference to the maximal angular size one would see at the NASA specified time.

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