# Calculus

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Okay so I have the following question and I am totally stuck:

Newton's Law of Gravitation says that the magnitude F or the force exerted by a body of mass m on a body of mass M given by
F=(GmM)/r^2
where G is the gravitational constant and r the distance between the bodies. A cosmonaut insde a spaceship is approahing a newly disvoered Planet Htrea. Looking at his instruments, he notices that at a distance of 20000km from the planet, its gravitational pull is increasing at 1N/km as he approaches the planet. Compute the gravitational force that the planet will exert on the spaceship at a distance of 10000km from it.

I don't see how I can do this without the mass of the plants or anything, theres to many variables. I don't know, in great need of help, please.

A note on distances: The distance in the law of gravitation is distance to the center of mass, normally the geometric center of the body.

F=(GmM)/r^2 Let M be the new Planet.

F/M= Gm/r^2 This quantity is called gravitational field, in N/kg units.

The gravitation field is dependent on distance squared from the center of the planet. So at half the distance, it ought to be four times as great. Think that out. You can get the new gravitational pull from that, in N/kg.

Now you are correct, the actual force will require the mass of the space ship.
Force= g * massspaceship where g is the field value of gravitational pull, in N/kg

Wow I am still totally lost. At half the distance it will be 4 times as great, this means that the new gravitational pull will be 4N/kg?

But I still don't know how that will let me find the gravitational force on the spaceship if we don't have the mass of the spaceship. I was thinking filling in the equation based on the first information given and find the mass, but I don't think I'm sure we have all the numbers, so that still wouldnt work. G=1N/km, m=?, M=? r=20000km. So it still can't work..

Yes, at half the distance..

g= 1N/kg (2E7/r )^2 so as r becomes 1E7, then g is 4N/kg.

You cant get the Force without the mass of the spaceship.

F=ma= mg you have to have m.

Okay that's what I was thinking and what was confusing me, but I thought maybe there was a way around that since they didn't give us one. Thanks = )

Well actually,what that guy got is wrong.The answer would e the recipicol of that.By the way Hello,I'm Keira.

Hello Keira.
I still can't get the answer from that though can I?

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