Question

Stationary planets “A” and “B”, each with mass 1024 kg, are located 106 m away from...

Stationary planets “A” and “B”, each with mass 1024 kg, are located 106 m away from each other in the horizontal direction (x). Space capsule “C” with a mass of 1000 kg starts at rest 106 m from both “A” and “B”, so the three objects form an equilateral triangle. Assume that “A” and “B” have a fixed position and cannot move, while “C” is able to move freely.

  1. What is the net gravitational force vector on “C” at time t = 0?

  2. What is the kinetic energy of “C” when it passes half-way between

    planets “A” and “B”?

  3. Write an equation for the net acceleration vector of “C” due to

    gravity from “A” and “B”, as a function of the vertical position y of “C”.

  4. If planets “A” and “B” were instead free to move, how

    far apart from each other would they be when “C” passed between them? You can ignore the gravitational force of “C” on “A” or “B”.

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