1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.

Question

a. Solve the equation for r.

Answer 1

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Answer 2

The weight of an object is essentially calculated using Newton's law of gravitation, given by:
Gm1m2/r², where
G=gravitation constant,
= 6.674 N(m/kg)²
r=distance between the centre of mass of two objects, in this particular case, the centre of the earth, and the object in question (whose weight is to be determined).
On the average, the radius of the earth is 6378.1 km
m1=mass of the earth (in this case)
= 5.974*10²⁴ kg.
m2=mass of the object in question.

Substitute the above values (in the appropriate units) for Gm1/r² should give the value of g, acceleration due to gravity, and should equal approximately 9.81 m/sec² for a mass m2 of 1 kg.

At different heights, the same formula can be used to calculate the acceleration due to gravity, substituting the appropriate values of r.

For more reading, see following article and related references:
http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation