5. Gravity Mass Mass of the Moon 7x 10 E 22 kg Mass of the Earth = 6 x 10 E 24 k

Question

5. Gravity Mass Mass of the Moon 7x 10 E 22 kg Mass of the Earth = 6 x 10 E 24 kg G-7 x 10 of the Sun-2 x10 E 30 kg 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 6 m 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 acceleration 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. D. What is the average orbital speed of the Earth around the sun in miles per hour? E. What is the average orbital velocity of the Moon around the Earth in

Explanation / Answer

(A) g = G M / R^2

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

g = 9.7 m/s^2

(B) a r^2 = G M = constant

( g) (R^2) = (g/2)(r^2)

r = sqrt(2) R =

and r = R + h

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

h = 2.5 x 10^6 m oR 1545 MILES

(C) g_moon = G M_moon / R_moon^2

= 1.225 m/s^2  

(D) Fg = m a_c

G M m / r^2 = m v^2 / r

v^2 = G M / r = (7 x 10^-11)(2 x 10^30) / (1.5 x 10^11)

v = 30550 m/s Or 68000 miles / hr  

(E) for moon,

v^2 = (7 x 10^-11)(6 x 10^24) / (4 x 10^8)

v = 1025 m/s

v = 2300 miles/hr

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