Finding the Balance Point of Gravitational Forces Between Earth and Moon

[smileandbehappy]

Homework Statement

The gravitational force due to the earth, that acts on a spaceship of mass Ms is GMeMs/d^2, where G is the gravitational constant, Me is the mass of the Earth and d is the distance between the center of the Earth and the spaceship. A similar expression can be written for the force on the spaceship due to the moon. Give an equation for the balance point of the two points of the two forces, when there would be no force afcting on the spaceship.
How derive an equation for dE in terms of D (the distance from the center of the Earth to the center of the moon).
Finally calculate the distance of this point from the Earth. The mass of the Earth is *1.4 times that of the moon, the distance between the two is 3.84*10^8m.

Homework Equations

Above in the question

The Attempt at a Solution

Well i hanvt got that far, any help would be appretiated.

 

[learningphysics]

At the balance point: The magnitude of the force the Earth exerts on the spaceship equals the magnitude of the force the moon exerts on the spaceship...

set the forces equal...

 

[chaoseverlasting]

For the DE, write a general expression for the force which will be equal to zero at the balance point.

 

[smileandbehappy]

ok i have created the first expression getting: GMeMs/De^2-GMmMs/Dm^2 is that correct? should i try and rearange this to cancel like terms etc...

I still don't get the De bit which comes next can you please help me some more?

 

[learningphysics]

ok i have created the first expression getting: GMeMs/De^2-GMmMs/Dm^2 is that correct? should i try and rearange this to cancel like terms etc...

I still don't get the De bit which comes next can you please help me some more?

Do you mean GMeMs/De^2=GMmMs/Dm^2

yes, that's correct. cancel terms G and Ms, leaves

Me/De^2 = Mm/Dm^2

where De is the distance of the ship from the earth... Dm is the distance from the ship to them moon. you also know that the mass of the Earth is 1.4 times mass of the moon... plug that in, you can get one more cancellation...

you're left with an equation with De and Dm... you need one more equation with De and Dm. Can you think of one? Look at the question... there's one piece of information we still haven't made use of.

 

[smileandbehappy]

ok but how do i derive an expression for De? Please help I am really confused? thanks

 

[learningphysics]

ok but how do i derive an expression for De? Please help I am really confused? thanks

Use De + Dm = 3.84*10^8m.

now you have two equations with two unknowns. solve for De.