(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a science fiction story, humans have built a large spherical spaceship for an interstellar journey of many generations; they have christened their ship Big Bird.

The mass of Big Bird is 7.496×1011 kg (the mass of an aircraft carrier is about 10^8 kg). Most of Big Bird's journey takes place at constant speed through the vacuum of interstellar space.

Big Bird is accompanied on its journey by a small satellite which is held in orbit about Big Bird solely by Big Bird's gravitational attraction. The satellite is called Little Bird and has a mass of 1000 kg.

Little Bird is in an elliptical orbit about Big Bird; the distance of closest approach is 5 km and the greatest separation distance is 40 km.

Find the difference in total mechanical energy for the system; i.e. mechanical energy at maximum separation minus mechanical energy at closest approach.

2. Relevant equations

E = K + U

K = 1/2mv^{2}

U = -Gmm/r

3. The attempt at a solution

I am a little confused on this problem. i only seem to know the equation for V for a circular orbit so i am not sure how to go about this problem.

would i maybe do this m_{L}= mass of little bird and m_{B}= mass of big bird

1/2m_{L}v^{2}+ -Gm_{B}m_{L}/ r_{1}- [1/2mv^{2}+ -Gm_{B}m_{L}/ r_{2}]

r_{1}= 40,000 m

r_{2}= 5,000 m

Thanks for any suggestions on what to do cause i am completely lost on how to go about this problem.

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# Homework Help: Object in elliptical orbit around another object

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