Calculating the Critical Distance for Spaceship Gravity: A Scientific Approach

[brookbj]

Hey, I don't know how to go about and answer this question

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.

can somebody push me in the right direction.

thanks

 

[cepheid]

okay. First of all, what is the mathematical law that determines how gravitation works? In other words, the equation that tells you, given two masses and the distance between them, how much gravitational force they'll exert upon each other?

 

[brookbj]

Hey

I know Newton's Law of Universal Gravitation, but I am not given masses or distance from the Earth to the moon or the shuttle.

 

[cepheid]

That doesn't mean you can't do the problem. It just means you won't get a numerical answer. You could still set up the problem and get an algebraic answer that is *expressed in terms of* those constants you mentioned.

Example. Let the earth-moon distance be R. Let the shuttle to Earth distance be r (a variable. Then the shuttle moon distance is R - r.

Let $M_e$ be the mass of the earth, $M_m$ the mass of the moon, and m the mass of the spacecraft . Now can you do the problem?

 

[brookbj]

Is it just,

GMeMm/R2 = GMmMs/(R-r)2

thanks, this question is killing me

 

[cepheid]

close. the left hand side is the force between the Earth and the moon, which is not what you want.

you want:

force of Earth on spaceship = force of moon on spaceship

 

[brookbj]

Thanks, for your help!