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Comparing the Effect of Gravity on Two Different Planets
A person can jump 1.5m on the Earth.  
How high could the person jump on a planet having the twice the mass of the earth and twice the radius of the earth?  
   
Let the mass of the earth be M and the radius of the earth be R.  
We are using the fact that the height to which the person will be able to jump is inversely proportional to the acceleration due to gravity. This gives us  
 
Recall that g is given by  
 
So, in this case, we have, for the earth  
 
and for the other planet  
 
Thus, we can write  
 
which, of course, reduces to the satisfyingly simple  
 
We therefore conclude that, assuming the person could launch him/her self at the same initial speed she/he would be able to jump twice as high on the other planet... this also assumes that the space-suit doesn't get in the way too much!  
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