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December 18, 2014

December 18, 2014

Posted by **Jennifer2008** on Sunday, November 19, 2006 at 7:54pm.

We are given a chart with information on the mass, etc. of planetary objects. I know to use law of universal gravitation but how do I manipulate the equations and what am I solving for?

At some arbitrary point inbetween Mars and the Sun the force in the direction of the sun is:

M_{sun} m G/r^2 -

M_{mars} m G/(R_{mars} - r)^2

Here r is the distance from the object to the sun and R_{mars} is the distance from the Sun to Mars, and m is the mass of the object. If you equate this to zero you get:

M_{sun}/r^2 = M_{mars}/(R_{mars} - r)^2

Take the reciprocal of both sides, and you have a quadratic equation.

You must then solve for r...

I am having trouble getting the right equation. After I take the reciprocal he numerator and denominator should be flipped, correct? Than do I multiply both sides by the masses?

That's right:

M_{sun}/r^2 = M_{mars}/(R_{mars} - r)^2

becomes:

r^2/M_{sun} = (R_{mars} - r)^2 /M_{mars}

and then you get:

r^2 =(M_{sun}/M_{mars})*(R_{mars} - r)^2

Take the squate root of bith sides:

r=sqrt[M_{sun}/M_{mars}]})*(R_{mars}-r)

This is a linear equation for r.

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