At what height will the acceleration due to gravity be 6.0 m/s^2 and what is the formula for this given the following:The acceleration due to...

The force of attraction due to gravity between an object
of mass m and the Earth of mass Me is G*m^Me/ r^2. This, in terms of the acceleration
due to gravity of the object is m*a

Equating the two m*g =
G*m^Me/ r^2

=> g = k/r^2, where k is a constant as
G*Me is a constant.

At a height of 7000 km the acceleration
due to gravity is 8.2 m/s^2

8.2 = k/
7000^2

=> k = 8.2 *
7000^2

The formula for the relationship between height and
the acceleration due to gravity is g = (8.2*7000^2) /
r^2

When the acceleration is 6 we have
:

6 = (8.2*7000^2) /
r^2

=> r = sqrt [(8.2*7000^2) /
6]

=> r = 8417 km.

The
required formula is g = (8.2*7000^2) / r^2 and the required
height is 8417 km.