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michealjohnson michealjohnson
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11 years ago
Titan is the largest moon of Saturn and the only moon in the solar system known to have a substantial atmosphere. Find the acceleration due to gravity on Titan's surface, given that its mass is 1.35 x 10^23 kg and its radius is 2570 km.
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wrote...
11 years ago
The gravitational force is GMm/(r^2), where G = the gravitational constant = 6.67*10^-11, M = the mass of the attracting object = 1.35*10^23 kg, m = the mass of the attracted object, and r = the distance from the center of gravity of the attracting object, which on the surface of Titan is 2.570*10^6 m.

You know that for any force, F=ma, where F = the force, m = the mass of the object subject to the force, and a = the acceleration due to the force.

So for gravity, you can say ma = GMm/(r^2). m is on both sides of the equation, therefore you can remove it. The equation becomes
a = GM/(r^2).
And that's what you needed. Filling it in gives
a = 1.36 m/s^2


The trick is realizing you can say
ma = F = GMm/r^2
and that you can then remove the unknown m on both sides of the equation.
wrote...
11 years ago
ga= GM/r^2
G is newtons constant, 6.673 x 10^-11
M is the mass of the object in kg
r is the radius of the object in meters

ga= 6.673 x 10^-11 x 1.35 x 10^23/2,570,000^2
ga= 1.363 m/s²
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