I of IV :: a mathematician & an astronaut derive :: how to keep something in orbit?

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II of IV :: Reentry: "Apollo Atmospheric Entry Phase" 1968

On the left they were assuming a circular orbit. ( Yes they were ignoring elliptical orbits . as near-Earth is pretty much perfectly circular.) 
We can plug & chug too..
We know that G = 6.674×10⁻¹¹ m³kg⁻¹s⁻² and
M = 5.972×10²⁴ kg and 
r = 6357 km + 420 km = 6.777×10⁶ m
we know that :: 
v = √( GM/r )
= √( (6.674×10⁻¹¹)(5.972×10²⁴)/(6.777×10⁶) m²s⁻² )
= √( 5.881 × 10⁷ m²/s² )
= 7669 m/s
(we can also use GM/R2 (g) as 9.8 m/s²)

This video explains the geometry of return trajectory and reentry into the Earth’s atmosphere by the Apollo spacecraft, as well as the problems involved and the methods and actions for overcoming these problems.

Atmospheric entry : is the movement of human-made or natural objects as they enter the atmosphere of a celestial body from outer space, in the case of Earth from an altitude above the Kármán Line, (100 km).

This animation primarily addresses the process of controlled reentry of vehicles which are intended to reach the planetary surface intact.

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III of IV :: how women did the math That Put Men On The Moon

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IV of IV :: on my way up

Katherine G. Johnson, Dorothy Vaughan and Mary Jackson brilliant women working at NASA, who served as the brains behind one of the greatest operations in history: the launch of astronaut John Glenn into orbit.

A stunning achievement that restored the nation’s confidence, turned around the Space Race, and galvanized the world. The visionary trio crossed all gender and race lines to inspire generations to dream big.

Insanely talented team of high schoolers tell the story of the African American women behind America's success in the Space Race.

It's a Hidden Figures music video, written and performed by :: 

10th graders from Emmett J. Conrad High School in Dallas Texas

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