# Gravitation Problem (Please check my work)

• PsychonautQQ

## Homework Statement

Two asteroids are traveling side by side, touching each other. They are both spherical and are made of pure iron. What must their diameters be in feet to exert a force of 3 lb's onto each other?

## Homework Equations

V = 4/3*∏*r^3
density of Iron = 7.63*10^3
1 lb = 4.448N
1 foot = .3048 meters
F=Gm1m2/r^2
Vp = Mass

## The Attempt at a Solution

So subtitling Vp in for m1 and m2 and then combing the terms since they are equal...
(G(p*4/3*∏*r^3)^2) / 9r^2 = F
(p*G*16*∏^2*r^6 ) / 9r^2 = F
(p*G*16*∏^2*r^4 )/ 9 = F
((F*9) / (p^2*G*16*∏^2)) ^ (1/4) = r

3 lbs = 13.344N
1 ft = .3048m

So I solved this in terms of Newtons and meters then converted the radius to feet and got 12.0 Feet and my online thing is saying it's wrong... this r would be the distance between the COM's so it would equal the diameter of one of them

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Why do you get 9r^2 in the denominator? (I assume that you mean "/(9r^2)"). Where does the 9 come from?
Edit: Ah I see. It shouldn't be there in the first line.

What happened to the density? You used the volume as mass...
Work with units, then it is easier to spot mistakes like that.

You forgot to use mass = rho * V, where rho is the density of the iron, in your force calculation.

What did you use for G?

Why do you get 9r^2 in the denominator? (I assume that you mean "/(9r^2)"). Where does the 9 come from?

The 9 comes from V = (4/3)πr2 after it is squared

I actually had p in the formula when I did it, forgot to type... screw statics I thought this class was going to be a breeze but this online homework system is stupid

The mistake was forgetting that the distance between the centers of the two spheres is a given sphere's diameter, not the radius (there are two radii between the centers of the spheres: one radius for each sphere!)

[Edit: other than that your math checks out. ]

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Oh, that and don't forget that the question is asking for the answer in terms of the spheres' diameters, not their radii. So that's another thing.