Question 9.13: Determine the orbital velocity of a spacecraft at an altitud...

Aircraft performance An Engineering Approach

Determine the orbital velocity of a spacecraft at an altitude of 200 km from the earth if the weightlessness is desired. Assume the gravity is 9.8 m/s² at the height of 200 km and the earth’s radius is 6371 km. Then, compare this velocity with the speed of sound at the sea level (i.e., 340 m/s).

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$g=\frac{V^2}{R}\Rightarrow 9.8=\frac{V^2}{200,000+6,371,000}\quad \quad \quad \quad (9.173)$

The solution of this equation yields

V=8,025 m/s = 8.02 km/s = 28,889 km/h

This orbital velocity is 23.6 times the speed of sound at sea level.

(9.173): $g=\frac{V^2}{R}$ where
m is the mass of the ISS or an astronaut
V is the linear velocity of the ISS or an astronaut
R is the radius of rotation (see Figure 9.4b)

9.4

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