a)Using the modern accepted value G=6.67 x 10^ -11 Nm^2/ kg^2, solve for the mas

Question

a)Using the modern accepted value G=6.67 x 10^ -11 Nm^2/ kg^2, solve for the mass of the Earth. Do this by applying the fact that near the surface of the Earth (where r is the radius of the Earth), the acceleration due to Earth's gravity is g=9.8m/s^2. Of course you check the Earth's mass in the book, so the point of this problem is to show the methodology, finding the Earth's mass using only what Cavendish knew. b) we can also weigh the sun using Cavendish's experiment. Recall that the distance between the Earth and the Sun is r=150 million km, and the Earth's orbital speed is 18.5 miles/sec=30km/s. Use Newton's equation and this data to determine the Sun's mass.

Explanation / Answer

a) a = G M/R^2

M = g R^2/G = 9.81*6.378E6^2/6.67E-11=5.98E24 kg

b) G M m/r^2 = mv^2/r

G M/r = v^2

v^2 = G M/r

(30.0E3)^2 = 6.67E-11*M/150.0E9

M=2.02E30 kg

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