"How far above the Earth's surface will the acceleration due to gravity be a quarter of what it is on the surface?"

I tried to use the g' = (G * m) / r^2 equation (with the mass of the earth as "m") because it was used with a somewhat similar problem in my book about the value of g on the top of Mount Everest, but I came up with a ridiculous number.

Can you tell me how to do this problem correctly?

Solution Preview

Hi,
To begin with, I'd like to say you were on the right track when you used g=G*m/r^2 but I guess something went wrong in your calculation. I'm going to suggest 2 approaches: one of them quick and intuitive, the other a more brute force method that will succeed if the first way doesn't occur to you.

Method 1
since G and m are constants regardless of your height above the earth, the only variable here is "r", ie distance to the centre of ...

Solution Summary

The acceleration due to gravity above the Earth is determined. How far above the earth's surface will the acceleration due to gravity be a quarter of what it is on the surface is computed.

...Acceleration due to gravity on earth = g = GM/R2 (2). g'/g = [R/(R+h)]2 Dividing (1) by (2): ... Answer: Acceleration due to gravity on earth = g = GM/R2. ...

... to gravity at the surface of the earth is given by g = W/m = 10.78/1.1 = 9.8 m/s2 Now as the acceleration due to gravity at the surface of earth is given by. ...

... where m is the mass of the object, g is the acceleration due to gravity at the Earth's surface, is the angular velocity of the Earth's rotation, and R is the ...

... 5. Many people mistakenly believe that astronauts that orbit the Earth are "above gravity." Calculate the acceleration due to gravity (g) for space shuttle ...

... and g = G*M/(Re)2. Or, g`/g = Re2/D2. Or, the acceleration due to gravity at an altitude D from the center of earth is given by. g` = g [Re2/D2]. ...

Simple Pendulum Gravity is responsible for an object falling toward Earth. ... increases by a constant amount, called the acceleration due to gravity, denoted g ...

... GmM/r2, which does depend on the mass, but that the acceleration due to gravity (which is ... 1. The object is SO massive that it pulls the Earth towards itself ...

... that gravity on moon is 1/6 of the gravity on earth. ... This is due to Newton's second law ... It shows that acceleration is inversely proportional to the mass of the ...

... The completed table is given below for EARTH ( g = 9.8 m/s2 ) t2 (2s/t2)= g s (distance, m) t (time, s ... The last column gives acceleration due to gravity. ...