Gravitational forces equal in between an object

[huronjubal]

Homework Statement

from Earth to mars, determine at what distance (from earth) the gravitation force of the Earth acting on the space probe ( mass 200kg) is equal to the gravitational force of Mars on the space probe, if the planets are aligned.
Mass of earth: 5.976 x 10 ^ 24 kg
Mass of Mars: 6.394 x 10 ^ 23 kg
Mass of probe: 200kg
Radius of Mars: 3394 km
Radius of Earth: 6371 km
distance between Earth and Mars: 7.83 x 10 ^7 km
gravitational constant: 6.673 x 10 ^ -11
surface gravitational acceleeration of mars: 3.73 m/s^2
" "of Earth: 9.81 m/s^2

Homework Equations

F= Gmm / r^2
F=mg

The Attempt at a Solution

I'm not really sure how to get this problem started. If anyone could help me get going or something I can start with. Thank you

 

[zhermes]

Well, draw a line with Earth on one end and Mars on the other, then the probe some distance (x) from earth. In terms of 'x' and the earth-mars distance, what's the distance from the probe to mars?
In terms of 'x,' what is the force of gravity on the probe from earth? What about from mars? at what distance are they equal?

Does that help?

 

[huronjubal]

That's what i needed. Thanks for the help!