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Calculate the point between Mercury and the Sun at which an object can be placed so that the net gravitational force exerted on it by these two objects is zero. The mass of Mercury is 3.18*10^23 kg, the mass of the Sun is 1.99*10^30 kg and the distance between Mercury and the sun is 5.79*10^10 m. (Give your answer as a distance measured from the planet.
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Added Thu, 23 Jul '15
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Let distance from mercury r1 = x * 5.79*10^10 m {where 0< x<1)
Distance from sun r2 = (1-x) * 5.79*10^10 m
mass of mercury = M1
mass of sun = M2
Net force = 0
G M1 m / r1^2 = G M2 m / r2^2
(r1/r2)^2 = M1 / M2 = (3.18*10^23) / (1.99 * 10^(30))
r1 / r2 = x / (1-x) = 3.997 * 10^(-4)
x = 3.995 * 10^(-4)
Distance from mercury = 3.995 * 10^(-4) * 5.79*10^10 m

= 23131050 m
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Added Thu, 23 Jul '15
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