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**Solution**: The gravitational attraction between two objects with masses m1 and
m2, separated by distance
x, is
F=Gm1m2/x2, where G is the
gravitational constant.How much work is done by gravity when the separation changes from x1 to
x2? Assume
x2&lt;x1.If one mass is much greater than the other, the larger mass
stays essentially at rest while the smaller mass moves toward
it. Suppose a 1.5kg1013 kg
comet is passing the orbit of Mars,
heading straight for the 1.99kg1030 kg sun at a speed of
3.7
m/s104 G. What will its speed be when it crosses the orbit of Mercury?
The orbit of Mars is 2.28m/s108
m km, the orbit of Mercury is 5.79km107
m km, and
G = 6.67km10-11
m Ncdot m^2/kg^2.

###### Problem

The gravitational attraction between two objects with masses m_{1} and
m_{2}, separated by distance
x, is
F=Gm_{1}m_{2}/x^{2}, where G is the
*gravitational constant*.

How much work is done by gravity when the separation changes from x_{1} to
x_{2}? Assume
x_{2}<x_{1}.

If one mass is much greater than the other, the larger mass
stays essentially at rest while the smaller mass moves toward
it. Suppose a 1.5kg10^{13} kg
comet is passing the orbit of Mars,
heading straight for the 1.99kg10^{30} kg sun at a speed of
3.7
m/s10^{4} G. What will its speed be when it crosses the orbit of Mercury?
The orbit of Mars is 2.28m/s10^{8}
m km, the orbit of Mercury is 5.79km10^{7}
m km, and
G = 6.67km10^{-11}
m Ncdot m^2/kg^2.