F=Gm1m2/r^2 Solve for r

Question

Please help 

Answer 1

The most important rule in Algebra is that whatever you to to one side of an equation, you must do to the other. Starting with:

F = Gm₁m₂/R²

 

If you want to solve for R, then R definitely can't stay in the denominator. So multiply both sides of the equation by R² to get

FR² = Gm₁m₂

 

Now you want R by itself on one side of the equation, so divide both sides of the equation by F.

R² = Gm₁m₂/F

 

Now all that's left is to take the square root of both sides.

R = positive or negative √Gm₁m₂/F  where everything up till F is under the square root sign.

 

If you are going to be plugging things in to this new equation, be careful! You don't want to break the rules of the original equation, which can happen when you multiply by a variable to get your solution. You absolutely cannot set R equal to zero. Why? Because in the original equation, setting R equal to zero would cause your denominator to equal zero, which isn't allowed. 

Answer 2

F = (Gm₁m₂)) / r²

 

 

Multiply both sides of the equation by r².

 

r²F = Gm₁m₂

 

 

Divide both sides of the equation by F to isolate r².

 

r² = (Gm₁m₂) / F

 

 

Square-root both sides of the equation to undo the exponent.

 

r = √((Gm₁m₂) / F)

 

 

Fun Fact:  this formula is used by physicists when determining the gravitational force between two objects at varying distances.  If you take physics some time in the future, you will used this formula.

 

 

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