# How do i find gravity given a radius and an altitude?

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1. Oct 5, 2014

### gcombina

1. The problem statement, all variables and given/known data

What is the acceleration due to gravity at an altitude of 1.00 x 10^6 above the earth's surface, given that the radius of the earth is 6.38 x 10^6 m?
How do i go about solving that?

2. Relevant equations
Using g = Gm/r^2

3. The attempt at a solution
g= GMm/(R+h)^2
H= height/altitude given

so

g = (6.67300 x 10^-11) (m) / [(6.38 x 10^6 m) + (1.00 x 10^6)]^2

*** my question is, what do I put as M and m? **

2. Oct 5, 2014

### Staff: Mentor

In your Relevant equations your formula for gravitational acceleration contains only one "m", and it represents the mass of the body that is causing the acceleration. In this case what is the object?

In your problem statement the "m" on the radius of the Earth is the units: m for meters. There should be units associated with the altitude figure, too. What are they?

It is very important to keep the units associated with values. You don't want to be mixing miles with centimeters in a calculation! Instructors will deduct marks if units are left off of results.

3. Oct 22, 2014

### drvrm

You need not put M, actually the acceleration due to gravity on earth is well known constant it is g=9.8 m/s^2
so put this value for GM/R^2 so you can calculate value of GM as you know radius of Earth R for acceleration due to gravity at height h now you calculate the Force on unit mass i.e. m =1 kg then you get result for value of g at an altitude.(actually Force per unit mass is acceleration; in your expression given above you have erroneously written g istead of force using newton's law of gravitation

4. Feb 22, 2016

### fizixfan

Gravity at altitude of 10^6 m
Gh = Go(re/(re+h))^2
Go = 9.80665 m/s^2
re = 6367444.7 m
h = 1,000,000 m
Gh = 7.33 m/s^2