How would you use the Universal Gravitation equation $F=\frac{Gm_1m_2}{r^2}$ to calculate the weight of a person at a specific height above the earth?

If, for example, you were 6370m above the earth and you weighed 70kg, would it be as simple as doing $F=\frac{(6.67x10^-11)(5.98x10^24)(70)}{6370^2}$?

The question is asking me whether or not a persons weight goes down by a factor of 4, a factor of 2, stays the same, or goes up by a factor of 2 or a factor of 4. My initial train of thought would be that it doesn't change at all.

As you might be able to tell, I am very new to physics and am struggling to grasp this concept.

Thanks for taking the time to help me out.


I think you are confusing between mass and weight. Mass is invariable and its unit is Kg, and weight is the force with which earth attracts this mass. So, this force of attraction will be F = W = mg ; where m is your mass and g is the gravitational acceleration at that point.

As you go up, the distance between you and the center of earth increases and hence, according to newton's inverse square law of gravitation, force acting on you by the earth will decrease. So your weight will decrease.

And coming to your original question of calculating weight of any person, the formula you are using is absolutely correct. And in the same way you can find weight of anything at a distance r from earth. (However, you'll not use radius of earth all the time as "r", because if you are going up then add this additional distance too.)


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