You have a great summer job working for a movie studio. Your assignment is to ch

Question

You have a great summer job working for a movie studio. Your assignment is to check the script of an upcoming Star Wars movie for scientific accuracy. In one scene, the hero escapes by putting her spaceship through a wormhole in space. The engines have failed so the ship is coasting when it emerges in another part of the galaxy at the center of a binary star system. Both stars in the system orbit their center of mass and have equal mass. You need to determine the minimum speed of the spaceship when it emerges from the wormhole perpendicular to the plane of the orbiting stars so that it is not captured by the star system. When the movie is better defined, you will know the mass of each star, the radius of their orbit, and the mass of the spaceship. You assume that even a long time ago in a galaxy far, far away the gravitational constant is the same.

Please show work and explain

Explanation / Answer

For the problem, given initial kinetic energy of the ship = Change in potential energy

=> 1/2 m V^2 > 2*(Potential energy from each star)

Let the distance between each star = d

=> Intitial PE due to one star = G M m / (d/2)

Final PE = 0, since distance would be infinite.

Where M = mass of one star and G is universal gravitational constant

2* PE = 4 GmM/d

=> 1/2 m v^2 > 4 GmM/d

Simplifying, v > sqrt(8* GM/d) = minimum velocity required

Make sure you let me know the exact values when the entire script is ready ;)

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