5. Gravity Mass of the Sun 2 x10 E 30 kg Mass of the Moon = 7x 10 E 22 kg Mass o

Question

5. Gravity Mass of the Sun 2 x10 E 30 kg Mass of the Moon = 7x 10 E 22 kg Mass of the Earth 6 x 10 E 24 kg G-7 x 10-11 Orbital Radius of the Earth 1.5 x 10 E 11 m Orbital Radius of the Moon = 4 x 10 E 8 m Radius of the Earth = 6 x 10 E 6 m Radius of the Moon 2 x 10 E 6m 1600 meters 1 mile A. Calculate, using the Given quantities for the mass of the Earth and its radius, the acceleration of gravity at the surface of the Earth ? B. Determine, in miles, the altitude above the surface of the Earth where the acceeration is half that at the surface. C. Calculate the acceleration due to gravity on the surface of the Moon. What is it compared to "g" on Earth. 2x10

Explanation / Answer

(A) g = G M / R^2
  

g = (7 x 10^-11)(6 x 10^24) / (6 x 10^6)^2

g = 11.7 m/s^2

(B) a = G M / r^2 = g / 2

G M / r^2 = G M / 2 R^2

r = sqrt(2) R and r = R + h

h = (sqrt(2) - 1) R = 0.414 R

h = 2.5 x 10^6 m Or 1600 miles .....Ans

(C) g_moon = G M_moon / R_moon^2 = 1.225 m/s^2

Ratio = g_moon / g = 0.105 times of acceleration on earth's surface

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