Gravity Ratios using pronumerals

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    Gravity Ratios
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The discussion revolves around calculating the distance from planet Alpha where the gravitational force ratio between Alpha and Beta equals 8100. The user initially set up the ratio using the masses of the planets and distances to an asteroid, leading to an equation that simplifies to x = 0.012R. However, the user later acknowledges that the correct answer according to the book is 0.1R. The conversation highlights the importance of correctly applying gravitational ratios in problem-solving. Ultimately, the user resolves the issue after clarification.
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Homework Statement


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?


Homework Equations


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


here goes...

[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

Simplify:
[1-x/0.01x]=8100

Solve for x:
x=0.012R

but the answer is 0.909R!

Thanks for your help.
 
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sorry, quick correction to the answer to the above question.

the book says the answer is 0.1R.
 
dont worry, did it
 

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