December 16th, 2007, 06:15 PM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Circular Motion
1. Suppose a spacecraft was in between the Earth and the Moon. At what distance from the Earth would the Moon's gravity balance Earth's gravity? 2. What would be the acceleration due to gravity on the surface of the Sun? (The Sun has a radius of about 700000 km.) These problems are hard for me, and I have an final exam on Tuesday, so if anyone will help me out on these problems, it'll be much helpful to me. Thanks, J. 
December 16th, 2007, 06:38 PM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Circular Motion
For both problems all the physics you need is that the gravitational force between two objects of mass M and m at distance d is GMm/d^2, where G is the gravitational constant. Quote:
GEs/d^2 = GMs/d'^2 Ed'^2 = Md^2 Let D = d + d' be the distance from the earth's center to the moon's center. Then E(Dd)^2 = Md^2 (Dd)^2 = Md^2/E D^22dD+d^2 = Md^2/E (1  M/E)d^2  2Dd + D^2 = 0 You can use the quadratic formula to get d. Quote:
 
December 16th, 2007, 06:55 PM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Thanks for the help. I'm having a final this coming tuesday, so are there any more equations or anything that I should brush up on besides the two examples that I've just gave?

December 16th, 2007, 07:36 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I don't know. I've not taken any physics since my freshman year of undergrad. Most formulas are pretty easy at that level  dimensional analysis gives you just about everything you need.


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