SOLUTION: Hello, I am having trouble with a problem regarding Newton's Synthesis. I am giving the following equations and I have to solve for "G" and I am somewhat confused. Force of Gr

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Question 1141722: Hello,
I am having trouble with a problem regarding Newton's Synthesis. I am giving the following equations and I have to solve for "G" and I am somewhat confused.
Force of Gravity is G*Mm/r^2
Centripetal Force is mv^2/r
How would I solve for "G"
Thank you!

Found 2 solutions by MathLover1, math_helper:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Force of Gravity is: F=+G%2AMm%2Fr%5E2
Centripetal Force is: +F+=+mv%5E2%2Fr
=> G%2AMm%2Fr%5E2=mv%5E2%2Fr
=> G%2AMm=mv%5E2%2Ar%5Ecross%282%29%2Fcross%28r%29
=> G%2AM%2Across%28m%29=cross%28+m%29v%5E2%2Ar
=> G%2AM=v%5E2%2Ar
=> G=v%5E2%2Ar%2FM

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Are you saying +mv%5E2%2Fr+=+GMm%2Fr%5E2+ and you need to solve for G?

It matters very little anyway, so I will just say this: if +F+=+GMm%2Fr%5E2+ you can solve for G by the following steps:
+F+=+GMm%2Fr%5E2+

Re-writing, so G will end up on the left:
+GMm%2Fr%5E2+=+F+

Multiply both sides by r^2:
+GMm+=+F%2Ar%5E2+

Divide both sides by mM:
+G+=+F%2Ar%5E2%2F%28Mm%29+

Now you can replace F with some other expression and you will likely get some cancellation of some variables, for example, if you say F = +mv%5E2%2Fr+

+G+=+v%5E2%2Ar%2FM+
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To the student: the answer to your question is yes. Sorry, just noticed you had asked for additional detail.