Radius of the Earth 1.5 x 10E 11 m of the Earth =6x10E6m 5. Gravity Mass of the

Question

Radius of the Earth 1.5 x 10E 11 m of the Earth =6x10E6m 5. Gravity Mass of the Sun 2 x10 E 30 Orbital Radius of the Moo n-4x 10 E 8 m Radius Orbital Mass of the Earth = 6 x 10 E 24 kg G=7x10-11 oftheparth=7x10E22kg Radius of the Moon 2 x 10E6 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 alitude above the surface of the Earth where the acceleration is half that at the surface. = 5.9 m/s* 2. 2 C. Calculate the acceleration due to gravity on the surface of the Moon. What is it compared to "g" on Earth. Mo en (2x10m) =1,2 m/ 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

(D) Orbital radius of the earth, R = 1.5 x 10^11 m

So, circumference of the path = 2*pi*R = 2*3.141*1.5 x 10^11 = 9.423 x 10^11 m

The earth completes one revolution around the sun in 365.26 days.

Convert this in second.

t = 365.26 x 24 x 3600 s

So, orbital speed of the earth around the sun = (2*pi*R) / t

= (9.423 x 10^11) / (365.26 x 24 x 3600)

= 2.986 x 10^4 m/s

= (2.986 x 10^4) x (3600 / 1600) miles / hr

= 6.72 x 10^4 miles/hr

(E) As calculated above -

Circumference of the orbit = 2*pi*4.0 x 10^8 = 2.513 x 10^9 m

Moon completes one revolution around the earth in 27.3 days.

So, t = 27.3 x 24 x 3600 s

So, orbital speed of the moon around earth = (2.513 x 10^9) / (27.3 x 24 x 3600)

= 1.065 x 10^3 s

= (1.065 x 10^3) x (3600 / 1600) = 2.40 x 10^3 miles / hr.

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