Calculating the Critical Distance for Spaceship Gravity: A Scientific Approach

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To determine the distance from Earth where the moon's gravitational pull on a spaceship exceeds that of Earth, one must apply Newton's Law of Universal Gravitation. The problem can be set up algebraically using variables for the distances and masses involved, specifically letting R represent the Earth-moon distance and r the distance from the spaceship to Earth. The gravitational forces can be expressed as GMe*m/r^2 for Earth and GMm/(R-r)^2 for the moon. The goal is to find the point where these two forces are equal, focusing on the forces acting on the spaceship. This approach allows for a theoretical solution without needing specific numerical values.
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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
 
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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?
 


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.
 


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?
 


Is it just,

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

thanks, this question is killing me
 


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
 


Thanks, for your help!
 
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