A communications satellite is in a circular orbit around Earth at radius R and velocity v. A rocket accidently fires quite suddenly, giving the satellite an outward radial velocity v in addition to its original velocity.(adsbygoogle = window.adsbygoogle || []).push({});

a) Calculate the ratio of the new energy to the old and new angular momentum to the old.

b) Describe the subsequent motion of the satellite and plot T(r), V(r), U(r), and E(r) after the rocket fires.

I'm not sure how to do this question.

For a) E = 1/2*mu*v^2 + L^2/(2*mu*R^2) - k/R where mu is reduced mass, L is angular momentum k = G*m1*m2, and E is the total energy.

The v in the first term is for radial velocity only, so it is zero initially because there is no radial velocity in a circular orbit. The energy after the rocket fires, but before any radial position change is equal to the equation as written.

For angular momentum to change without any additional tangential velocity there has to be a radial position change. But I'm not sure how to figure out the radius of the new orbit that the satellite would attain.

For b) T(r) is the kinetic energy, I'm not sure how to plot this since the kinetic energy has a dependence on the derivative of r.

V(r) is the effective potential, consisting of the second two terms in the above energy equation.

U(r) is just the gravitational potential energy.

E(r) is the total energy.

Could someone help please?

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# Homework Help: Orbital Energy Change

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