# Newton and Gravitation

### Problems on Newton's Law

Problem : If a space shuttle is launched from the equator, what eastward speed (relative to the ground) is required to propel it into a low-earth orbit ( r r e )? Take into account the rotation of the earth in this problem.

Problem : What if the space shuttle, instead of being launched from the equator, is launched from Melbourne, Australia, at a latitude of 38 o below the equator? Again, calculate the required eastwards speed.

Problem : Calculate the value for G which would be given by a Cavendish apparatus (in an imaginary universe) set up as shown:

Cavendish apparatus.
and with M = 5 kilograms, m = 1 kilogram, θ = 30 degrees, and r = 0.05 meters. Also, the force exerted by the fiber is given by F = 10-11sinθ .

Problem : Calculate g on the moon due to the moon's gravity. Compare this to the gravitational force exerted on a mass m on the moon due to the earth (ie. what is g for the earth at the height of the moon?)(The mass of the moon is M m = 7.35×1022 and its radius r m = 1700 kilometers, the earth-moon distance is r = 3.84×108 meters, the mass of the earth is 5.98×1024 kilograms).

Problem : A ball is dropped from a height of 1000 kilometers above the earth. Calculate the time taken for it to hit the ground as given by i) assuming g takes the value at the surface of the earth; ii) assuming g takes the value at the top of the ball's path. The mass of the earth is 5.98×1024 kilograms.

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