Need help with number 15 Suppose the mass of the Earth were doubled, but it kept

Question

Need help with number 15

Suppose the mass of the Earth were doubled, but it kept the same density and spherical shape. How would the weight of objects at the Earth's surface change? Given that the acceleration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars' radius is 3400 km, determine the mass of Mars. At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? Determine the mass of the Sun using the known value for the period of the Earth and its distance from the Sun. Compare your answer to that obtained using Kepler's laws, Example 6-9. Two identical point masses, each of mass M, always remain separated by a distance of 2 A third mass m is then placed a distance x along the perpendicular bisector of the

Explanation / Answer

Let the distance be x

distance between centers of moon and earth is 385000 km = 3.85×10^8 m

Force will be zero where gravitational field will be zero

GMe/x^2 = GMmoon / (3.85×10^8 - x)^2

Since earth's mass is 81 times that of moon

81/x^2 = 1/(3.85×10^8 - x)^2

x^2 = 81(x^2 - 7.7×10^8x. +1.48 ×10^17)

80x^2 - 6.24 ×10^10x + 1.2 ×10^19 =0

x = 3.44 × 10^8 m = 344000 km from center of earth

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