Problem1 : 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.
The earth rotates from west to east. The circumference of the earth is approximately c e

![]() ![]() ![]() |
Problem2 : 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.
The shuttle requires the same velocity to achieve low-earth orbit, but now in a direction 38 o northwards of due east. At this latitude, the radius of the earth is given by r ecos(38 o ) = 5.03×107 m and hence the tangential speed is
Problem 3: Calculate the value for G which would be given by a Cavendish apparatus (in an imaginary universe) set up as shown:

Cavendish apparatus.
F =![]() |
Problem 4: 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).
The value for g is given by: g =





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.
In the first case, we can just use the standard kinematical equation: x = 1/2gt2âá’t =

