# What is the gravitational attraction of something weighing 100N, 100 meters above the earths crust?could you also give me the equation you used to find this out thanks

pohnpei397 | Certified Educator

The formula for finding this anwer is as follows:

Force of gravity = (G*m1*m2)/r^2

In this formula, G stands for the universal gravitational constant, m1 is the mass of one object (should be expressed in kg), m2 is the mass of the other object, and r is the radius that separates the centers of the mass of each object (should be expressed in meters).

So to get the actual answer for your question, you would need to know the universal gravitational constant (6.673x10^-11) and you would need to know the mass of the Earth and the distance from its center to a point 100 meters above the surface.  Once you know those, you can just plug the numbers into the formula.

6371 km is usually given as the average radius of the Earth.  Its mass is usually given as 5.9742 x 10^24 kg.

neela | Student

We are required to find gravitational attraction which is a force and not gravitational acceleration.

In the problem we use  gravtational force on the ground F1 = =100N = GMm/R^2 ........(1)  where m is the mass of the body, and R is the radius of the earth meters, and G is the gravitational constant.

The gravitational attraction at 100 meter  = h meter above the earth's crust is given by F2 = G*Mm/(R+h)^2 ...................(2) where M = is the mass of the earth.

Using the value of m from (1) in equation (2) we get:

F2 = GM[100N *R^2/(GM)]/(R+h)^2

= 100 N *(R^2/(R+h)^2

= 100*(6371000/(6371000+100))^2 Newtons., as R = 6371kms =6371000 meters is the mean radius of the earth.

=100*(6371000/6371100)^2 Newtons.

=100*(90.999968608) N

=99.9968608  Nwhich is less by 3.13916*10^(-3) than that on the ground.

get144 | Student

Thanks pohnpei397 so the final answer would be F=((6.673x10^-11*5.9742x10^24)*10)/6371100^2=9.821369238

Giving e the Force at this height, so the weight of the object would be roughly 98 N

This amount of height has not affected the weight much