Physics

Problem

![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/e6ed36a5b720/2025_11_20_e5791e6ab03a03ed3d63g-07.jpg) 1984M2. Two satellites, of masses

m

and

3 m

, respectively, are in the same circular orbit about the Earth's center, as shown in the diagram above. The Earth has mass

M_{e}

and radius

R_{e}

. In this orbit, which has a radius of

2 R_{e}

, the satellites initially move with the same orbital speed

\mathrm{v}_{\mathrm{o}}

but in opposite directions. a. Calculate the orbital speed

\mathrm{v}_{\mathrm{o}}

of the satellites in terms of

\mathrm{G}, M_{e}

, and

R_{e}

. b. Assume that the satellites collide head-on and stick together. In terms of

\mathrm{v}_{\mathrm{o}}

find the speed v of the combination immediately after the collision. c. Calculate the total mechanical energy of the system immediately after the collision in terms of G,

\mathrm{m}, M_{e}

, and

R_{e}

. Assume that the gravitational potential energy of an object is defined to be zero at an infinite distance from the Earth.

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