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Physics Problem 3 - Gravitation, Newton's Law of Gravity

 
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dumperdery



Joined: 23 May 2010
Posts: 4
Location: Canada

PostPosted: Tue Jun 01, 2010 5:56 pm    Post subject: Physics Problem 3 - Gravitation, Newton's Law of Gravity Reply with quote

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.
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hepcj
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Tue Jun 01, 2010 8:57 pm    Post subject: Reply with quote

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/(d-r)^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/(d-x)^2 = G M_Earth m/x^2

cancelling G and m, we are left with:

M_moon / (d-x)^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.
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