A satellite of mass 375 kg is in a circular orbit around Earth. Radius of the or

Question

A satellite of mass 375 kg is in a circular orbit around Earth. Radius of the orbit is 9900 km. The satellite has thruster that allow it to change either its speed or to change its distance from Earth.

a.)What is the speed of the satellite?

b.)What is its total mechanical energy?

c.)The satellite uses its radial thrusters for a short time. As a result, the satellite moves 900 km closer to Earth. What is the new potential energy of the satellite? Assuming energy conservation, what is the resulting speed after this orbit change?

d.)What speed would be required for a circular orbit at this radius? Judging from the actual speed of the satellite, is the new orbit circular? Should the satellite increase or decrease its speed to achieve a circular orbit with the new radius?

Explanation / Answer

a)

V = M*G/r

V = (5.97*10^24*6.67*10^-11)/9.9*10^6

V = 6342 m/sec (22832 km/h)

b)

g = M*G/r^2 = 5.97*10^24*6.67*10^-11/(9.9^2*10^12) = 4.063 m/sec^2

Em = -mgh+1/2mV^2 = m*(-4.063*3.5*10^6+6.342^2*10^6)

Em = 375 * (-4.063*3.5*10^6+6.342^2*10^6)

Em = 9.75 * 10^-9 J

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