# hw sol 6 - Solutions to Homework#6 1 Use the equation of...

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Solutions to Homework #6 1) Use the equation of gravitational force, and divide the force equation for the first case (where the planets are their usual distance apart) by the force equation for the second case when they are five times closer: 25 1 25 1 5 2 2 2 2 1 2 2 1 2 1 2 2 1 = = = = d d d M GM d M GM F F d M GM F This way, the G and both M’s cancel out. The force is 25 times greater when the planets are one-fifth the distance apart. 2) Use the same technique of dividing the entire equation so you don’t have to worry about the constants G and M e (mass of the Earth). Treating the Earth as a mass concentrated at a point in its very center, the acceleration due to gravity at a distance R e (the radius of the Earth) is Now, divide this equation by the equation for

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