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Suppose a rocket is moving at radial velocity

The textbook has claimed that in Mars's frame, the energy of the rocket is conserved, while in the Sun's frame, this event is seen as an elastic collision between Mars and the rocket.

I can see how energy of the rocket is solely conserved in Mars's frame, like how objects in Earth's g-field have their energy conserved basically. But how does the "elastic collision" in the Sun frame work? What would be the equations of conservation of momentum/energy? You guys are welcome to introduce new variables to quantify/better illustrate your explanations. Thank you!

**vr**and tangential velocity**vt**in the Sun's gravitational field. At some time, the rocket enters the gravitational field of Mars (with the above mentioned velocities), and gravitation effects due to the Sun can be ignored. After more time, the rocket leaves the g-field of Mars. Let Mars move at velocity**vm**with respect to the Sun.The textbook has claimed that in Mars's frame, the energy of the rocket is conserved, while in the Sun's frame, this event is seen as an elastic collision between Mars and the rocket.

I can see how energy of the rocket is solely conserved in Mars's frame, like how objects in Earth's g-field have their energy conserved basically. But how does the "elastic collision" in the Sun frame work? What would be the equations of conservation of momentum/energy? You guys are welcome to introduce new variables to quantify/better illustrate your explanations. Thank you!

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