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Working with gravitation - three problems

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1. Show by algebraically reasoning that your gravitation acceleration towards an object of mass M a distance d away is a=GM/d^2 and therefore doesn't depend on your mass.

2. Can a satellite coast in a stable orbit in a plan that doesn't intersect the earth center? Defend your answer. (Include 1 or more diagrams)

3. Students in a lab measure the speed of a steel ball lunched horizontally from a tabletop to be 4.0 m/s. if the tabletop is 1.5 m above the floor, where should they place a 20 cm tall tin coffee can to catch the ball when it lands?

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1.According to the Newton's law of gravitation, the gravitational force between two masses m1 and m2 is given by,

F = G*(m1*m2/R^2)
where G is the universal constant with value 6.67*10^-11 N m^2/Kg^2

Let m be the mass of your body and you are being attracted by the other body of mass M. Then by the above law we can write the force as,

F = G mM/d^2 where d is the distance

This force will produce an acceleration a on your body. Thus we can write
F = m*a (acording to Newton's ...

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