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The "horizontal" velocity is 7770 - 30 t m/s. The horizontal distance travelled is the integral of that, 7770 t - 15² t meters, or 856 kilometers. The static vertical gravity acceleration $$ a_g $$ is 398600.44/6600² km/s² = 9.15 m/s². The "horizontal" velocity is 7770 - 30 t m/s. The horizontal distance travelled is the integral of that, 7770 t - 15² t meters, or 856 kilometers. The static vertical gravity acceleration $ a_g $ is 398600.44/6600² km/s² = 9.15 m/s².
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The vertical ( ≈radial ) downward acceleration is $$ a_g - v^2/r $$ = ( 9.15 - ( 7770 - 30 t )² / 6600000 ) m/s² = ( 777 t -1.5 t² ) / 11000 m/s², or 7.8 m/s² after 16. The vertical ( ≈radial ) downward acceleration is $ a_g - v^2/r $ = ( 9.15 - ( 7770 - 30 t )² / 6600000 ) m/s² = ( 777 t -1.5 t² ) / 11000 m/s², or 7.8 m/s² after 16.

DecelDescent1


Crude analysis, probably errors.


Start in circular equatorial orbit, decelerate for 160 seconds at 30 m/s² with 1 sec start and stop jerks.

Summary (approximate!!!)

start

end

time

0

160

seconds

radius

6600

6591

km

altitude

229

220

km

"horizontal" velocity

7700

3000

m/s

"horizontal" distance

0

856

km

"vertical" acceleration

0

7.8

m/s²

"vertical" velocity

0

710

m/s

"vertical" distance down

0

9

km

Start in a circular orbit at 6600 km altitude, 7770 m/s orbital velocity. Slow to 3000 m/s (approximately mach 10) at 30 m/s² horizontal deceleration in 160 seconds, including 1 second beginning and end jerks. Shave off the jerks, make the "end time" 159 seconds. Ignore Earth rotation (pessimistically) .

The "horizontal" velocity is 7770 - 30 t m/s. The horizontal distance travelled is the integral of that, 7770 t - 15² t meters, or 856 kilometers. The static vertical gravity acceleration a_g is 398600.44/6600² km/s² = 9.15 m/s².

The vertical ( ≈radial ) downward acceleration is a_g - v^2/r = ( 9.15 - ( 7770 - 30 t )² / 6600000 ) m/s² = ( 777 t -1.5 t² ) / 11000 m/s², or 7.8 m/s² after 16.

The vertical ( ≈radial ) downward velocity is the integral of the downward acceleration, ( 777 t² - t³ )/ 22000 m/s , or 710 m/s after 160 ( ≈159 ) seconds.

The vertical ( ≈radial ) distance dropped is the integral of the downward velocity, ( 1036 - t ) t³ / 264000 meters, or 8900 meters after 160 ( ≈159 ) seconds, an terminal altitude of 220 km (it doesn't drop much!).

This is a crude approximation of a deceleration profile, not optimized.

DecelDescent1 (last edited 2018-07-10 19:27:29 by KeithLofstrom)