
Splung.com Physics Forum Discuss physics or ask questions. Part of the Splung.com physics web site.

View previous topic :: View next topic 
Author 
Message 
dumperdery
Joined: 23 May 2010 Posts: 4 Location: Canada

Posted: Tue Jun 01, 2010 5:56 pm Post subject: Physics Problem 3  Gravitation, Newton's Law of Gravity 


A spaceship is launched and starts moving directly towards the Moon. At what
distance from the Earth will the pull of the Moon on the spaceship exceed the
pull of the Earth? Ignore the effect of the Sun in this calculation. 

Back to top 


hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Tue Jun 01, 2010 8:57 pm Post subject: 


This a one dimensional problem in which you must calculate the force due to the Earth and the force due to the moon. Using Newton's law of gravity, we have:
F(r)_Earth = (G M_Earth m)/ (r)^2
and for the moon:
F(r)_Moon = G M_moon m/(dr)^2
We are using the distance d to be distance from the centre of the Earth to the centre of the moon.
Obviously, as the ship moves away from the Earth, it moves closer to the moon and at any time so the equations are linked.
Since we want the forces to be equal we can equate them,
G M_moon m/(dx)^2 = G M_Earth m/x^2
cancelling G and m, we are left with:
M_moon / (dx)^2 = M_Earth/ x^2.
Solve for x and take away the radius of the Earth as the question asks for the distance from the Earth. 

Back to top 




You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

© Copyright 2010 Splung.com
