There are two planets called Alpha and Beta.
mass of alpha=M
mass of beta=0.01M
They are distance R apart.
At what distance, expressed in terms of R, from the planet Alpha, along a straight line joining the centres of Alpha and Beta, will the ratio of [force alpha : force beta] on an asteroid be equal to 8100?
I avoided the use of newtons universal theory of gravity since there are no actual numbers. i used ratios instead.
The Attempt at a Solution
[mass (alpha)/distance (alpha)] / [mass (beta)/distance (beta)]=8100
let x be the distance between alpha and the asteroid.
[M/xR] / [0.01M/(R-xR)]=8100
Solve for x:
but the answer is 0.909R!!!
Thanks for your help.