A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is $h_p = 219.0$ km, and it is moving with a speed of $v_p = 9.750$ km/s. The gravitational constant $G$ equals $6.67 imes 10^{-11} ext{ m}^3 cdot ext{kg}^{-1} cdot ext{s}^{-2}$ and the mass of Earth equals $5.972 imes 10^{24}$ kg. When the satellite reaches its apogee, at its farthest point from the Earth, what is its height $h_a$ above the ground? For this problem, choose gravitational potential energy of the satellite to be 0 at an infinite distance from Earth. $h_a = $ km
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First, we need to find the semi-major axis (a) of the elliptical orbit. We can use the conservation of mechanical energy to do this. The total mechanical energy (E) of the satellite is constant throughout its orbit and is given by: E = T + U where T is the Show more…
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