Although events interrupted their mission, the astronauts of the space shuttle w

Question

Although events interrupted their mission, the astronauts of the space shuttle were originally supposed to modify the Hubble Space Telescope and launch it into a higher orbit about the Earth. The final orbit was to be elliptic with an apogee of 20,000 km. The perigee was to be the same as what the space shuttle had when it released to satellite, namely 6800 km from the center of the earth. The Hubble Space Telescope was expected to achieve this orbit by being given a push. What would the velocity have to be at the perigee to achieve this orbit?

Explanation / Answer

For an eliptical orbit the distance R between the satelite and the Earth is changing constantly. therefore also the speed is changing constantly. The speed of the satelite for a given distance R is

V(R) = sqrt[GM(2/R -1/a)]

where G is the gravitational constant G =6.67*10^-11

M is the Earth mass M=5.97*10^24 kg

a is the semi-major axis a = (20000-6800)/2 = 6600 km

(http://en.wikipedia.org/wiki/Elliptic_orbit)

With these values the speed at R = 6800 km (perigee) is

V = sqrt(6.67*10^-11*5.97*10^24*(2/6800*10^3 -1/6600*10^3)) =7535.5 m/s =7.535 km/s

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