Why is the gravitational force component in the x-direction -Fgrav*(x/r)?

[tomkoolen]

Hello everyone,

We regard a satellite with only the gravitational force working on it.
My textbook states that the net force in the x-direction is: -Fgrav*(x/r), with r being the distance between the satellite and the Earth. Could anybody explain this to me?

Thanks in advance,
Tom Koolen

 

[gneill]

Draw a diagram with the Cartesian axes centered on the Earth. The radial vector from the origin to the satellite has length r. Now look at the satellite. What direction does the gravitational force vector act? How might you compute its x and y components?

 

[tomkoolen]

Oh yeah, of course it's the sine of that angle! Thanks :)