NASA's Just Launched Nancy Grace Roman Telescope Set To Begin Best Astronomy Era Yet

 

    SpaceX Falcon Heavy rocket launches NASA's Nancy Grace Roman Telescope  Sunday

The National Aeronautics and Space Administration launched a new flagship telescope yesterday: a powerful observatory that will study dark matter and hunt for exoplanets, from an orbit about one million miles from Earth.

A SpaceX rocket took off with the $4.6b instrument, called the Nancy Grace Roman Space Telescope, just before 7:30 a.m. ET Sunday from a launchpad in Florida. The launch went smoothly, setting up the 8m aperture telescope to fly out to the L2 Lagrange point. This is one of 5 Lagrange points, named after the mathematician Joseph-Louis Lagrange, e.g.

As seen in the graphic above, three Lagrange points (L1, L2 and L3) lie along the line of centers connecting the two major bodies, in this case the Sun (bright center) and Earth.  These are called "unstable" Lagrange points, while L4 and L5 are stable points.  All the points represent locations in space where the gravitational forces of a 2-body system (e.g. Sun-Earth) produce enhanced regions of attraction and repulsion. Locating a point of 'balance' means a spacecraft can then remain in position and reduce fuel expenditure. 

As NASA reports:

Roman pairs a large field of view with crisp infrared vision to explore vast swaths of the sky and probe deeply into cosmic history. This flagship mission will help astronomers explore dark matter, dark energy, and worlds outside of our solar system, known as exoplanets. Its surveys will support a broad range of research extending far beyond the mission’s main science goals.

“Roman is exactly the kind of success story we want to see across NASA,” said NASA Administrator Jared Isaacman. Adding:

“Roman will give us a new atlas of the universe, push the boundaries of discovery, and demonstrate what is possible when America’s space program pairs bold ambition with disciplined execution.”

In the words of Nicky Fox, associate administrator for the Science Mission Directorate at NASA Headquarters in Washington.

“With its large field of view and fast survey speeds, Roman will usher us into a new era of discovery and make the invisible visible, setting the foundation for humanity’s search for life beyond our solar system.”

During launch and early orbit, Roman uses the Near Space Network’s ground stations and relay satellites to exchange tracking, telemetry, and command data with ground controllers. About 70 minutes after launch, the Deep Space Network takes over communications and guides Roman toward the second Sun-Earth Lagrange point, or L2, about one million miles from Earth. 

Ironically, or perhaps not, Trump wanted to cancel this once- in -a lifetime project to "save money". (As if he knew anything about that!) Fortunately, according to a WSJ piece, more sober heads in Congress weren't having it and allowed it to go forward.  Amazing what some courage and a working spine can do!

  For sure the Grace Roman Telescope's orbital position at the L2 Lagrange point (which it will reach in about 100 days) will afford us access to previously undetected exoplanets, perhaps as many as 200,000 more - as well as possibly piercing the physical mystery underpinning dark matter and dark energy and their relationship.  I look forward - at least so long as I am around - to experiencing one of the most productive and exciting astronomy periods ever.

Stay tuned! 

See Also:

Fantastic New Images of Distant Cosmic Objects Prove Webb Telescope's $10b Worth

And:

The Vera Rubin Observatory Unveils New Astronomical Frontiers With A New Kind Of Telescope

And:

Alien Worlds: The Top Exoplanet Discoveries of 2013 | Space

And:

A Possible Exoplanet In Another Galaxy Identified Using Chandra X-Ray Telescope Records

And:

YouTube video:

Something Left the Sun. It May Reach Earth Tonight

Phase Spaces In Plasma Physics (Part 2): The Liouville Equation

 Recall in Part 1, we saw the density of systems for the (x₁, v₁) phase space is:

N(x₁ ,v₁ ,t) = d (x₁ -  X₁ (t)) d (v₁ -  V₁ (t))

Where:  x₁ = X₁ (t)),  v₁  = V₁ (t)) 

Analogously, in the 12-dimensional phase space (two particles considered) we saw from the Part 1 solutions (#2):  

(x₁, v₁, x₂, v₂ ) =  ( _x1 , y₁ , z₁, _vx1, _vy1,  _vz1, _x2 , y₂ , z₂, _vx2, _vy2,  _vz2,) 

And there is one system occupying the point:

x₁ = X₁ (t)),  v₁  = V₁ (t), x₂ = X₂ (t)),  v₂  = V₂ (t) i.e. at time t.  The density of systems in this phase space is then:

N( x₁, x₂ ,v₁ , v₂ ) =

d (x₁   -   X₁ (t)) d (v₁   -  V₁ (t))d (x₂   -    X₂ (t)) d (v₂   -   V₂ (t))  

Basically, then there is one system in 6No  -dimensional space, so by analogy with the density of systems expression e.g. for N( x₁, x₂ ,v₁ , v₂ ), we can write:

N(x₁, x₂ ,v₁ , v_{2 ....} x_No ,v_{No ,} t) = å^No _i=1      d (x_i   -   X_i (t)) d (v_i  -   V_i (t))

As with the Klimontovich equation, the Liouville equation is found by taking the time derivative of the appropriate density.  Given the already defined  density of systems is the product of 6No  terms then the time derivative must involve the product of  6No  terms.  We can use the expression:

¶ / ¶ t   d [ (x₁   -   X₁ (t)]  =  -   ¶   X_i/ ¶ t ·  Ñ x i  d [ (x₁   -   X₁ (t)] 

The time density will be:

¶ N / ¶ t +  å ^No _i=1  V_i (t)  ·  Ñ x i   å^No _j=1      d (x_j   -   X_j (t)) d (v_j  -   V_j (t))  +

å^No _i=1    V'_i å^No _j=1      d (x_j   -   X_j (t)) d (v_j  -   V_j (t))  = 0

The next standard step employed by plasma physicists is to use the identity:  ad (a  -  b)  =  bd (a  -  b) to replace V_i   by v_i

Leading to:

V'_i (t) = q _si / m _si  [ E (x_i,t) + V_i /c  x  B( x_{i ,}t)]

Given that the products are just the density of systems, N, the equation for the time derivative of N(x₁, x₂ ,v₁ , v_{2 ....} x_No ,v_{No ,} t) 

becomes:

¶ N / ¶ t +  å ^No _i=1  V_i · Ñ x N +å ^No _i=1  V'_i (t)  ·  Ñvi N  = 0

which is the Liouville equation, and when combined with Maxwell's equations, viz. 

i)  Ñ X H  =  J    + ¶D / ¶ t

ii)             Ñ X E  =  - ¶B / ¶ t

iii)           Ñ · B  =  0   

iv)       Ñ · D  =  r    

is an exact description of a plasma.

Algebra II Review: Solutions To Algebraic Fraction Problems

 Simplify each of the following:

1) x²  - y²/ y²  - x²

Solution:

Factor numerator and denominator:

(x + y) (x - y)/ (y + x) (y - x)

Change sign of (y - x) in denominator to - (x - y):

Þ  

(x + y) (x - y)/ - (x - y) (y + x)

We can then cancel the (x - y)  factors in numerator and denominator:

=  -  (x + y) / (x + y)  =   -1

2)  27 a³ x²y ⁵  / 36 a ² x⁴y⁴

^Solution:  

^{Divide, first reducing 27/36 to 3/4 and paying attention to properties of exponents (the realm of Algebra I)}

^{3 a y  / 4 x2}

3) 2a ^1/2 (x + y)/  5 x a ^3/2

Solution:  

Apply quotient rule for exponents (from Algebra I):

a ^m /a ⁿ     =  a ^{m - n}

In this case, m = 1/2 and n = 3/2 so m - n =  1/2 - 3/2 =  -1

So:  a^{- 1}  =  1/ a

Then the fraction simplifies to: 

2 (x + y)/ 5 a x

4) (x -1) (2 - x) (3 - x)/ (1 - x) (x - 2) (x - 4)

Solution:  

Notice that the numerator contains (x - 1) and (2 - x), while the denominator contains (1 - x) and (x - 2). This indicates application of sign rule.  So, following the process in initial post, we rewrite the factors in the numerator to match those in denominator by factoring out (-1) in each, viz.

(x -1)  =  (-1) (1 - x)

(2 - x) =   (-1) (x - 2)

Substituting back into the numerator we obtain:

(1 - x) (x - 2) (3 - x)   (Rem: (-1) (-1) = +1)

So the algebraic fraction becomes:

(1 - x) (x - 2) (3 - x) /  (1 - x) (x - 2) (x - 4)

After canceling common factors:

(3 - x) / (x - 4)

Solutions To Phase Space Plasma Physics Problems

The  Problems:

1. (a)Write the phase space dimension for a 3-particle system.

(b) Write out the number density for this system.

Solutions:

a) We need the phase space formula: 6No  - D where No is the number of particles in the system.  In this case  No   = 3, so:

 6No  - D =   6 (3) -D  or 18 dimensions

b)  The number density for the system is:

N( X_i.... X_n ,V_{i ....}V_n ) = å ^No _i=1      d (X_i   -   X_i (t)) d (V_i  -   V_i (t))

Where  No    = 3,  so:

N( X₁, X₂ , X₃ ,V₁ , V_2., V₃ ) =

d (X₁  -  X₁ (t)) d (V₁   -  V₁ (t))d (X₂  -  X₂ (t)) d (V₂   -   V₂ (t)) d (X₃  -   X₃ (t)) d (V₃   -  V₃ (t)

2. We saw  (x₁, v₁)  = ( _x1 , y₁ , z₁, _vxi, _vyi,  _vzi)  is a 6-dimensional phase space.  What would be the number of dimensions for the 12-D  phase space:

 (x₁, v₁, x₂, v₂ )?

Write them all out in a bracket.

Solution:

(x₁, v₁, x₂, v₂ ) =  ( _x1 , y₁ , z₁, _vx1, _vy1,  _vz1, _x2 , y₂ , z₂, _vx2, _vy2,  _vz2,) 

3.  Show how V'_i  =   q/ m [ E (X_i ) + V_i   x  B( X_i )]

translates to Newton's 2nd law of motion.

(Hint: You need to incorporate the Lorentz force.)

Answer:

Given the nature of the plasma, charged particles of the system moving in magnetic field (B) the Lorentz force is:  

F = q ( E  + v x   B)

Or, in terms of Newton's 2nd law:

m (dv/dt) = ma = q ( E  + v x   B)

Or, to conform with the plasma expression:

V'_i  =   q/ m ( E  + v x   B)

Where: E =  E (X_i )       and: v x   B  = V_i   x  B( X_i )

Where the  X_i   are position dependent in the coordinate system.