Question

What is the acceleration of gravity from the Earth when you are one full Earth radius height above the surface of the earth?

Select the answer below in terms of the acceleration at the surface, g.


A.2g
B.g
C. g/2
D. g/4

Answer 1

The acceleration of gravity decreases as you move away from the surface of the Earth. The acceleration of gravity at a height of one Earth radius above the surface can be found using the formula:

g' = (R/(R+h))^2 * g

where R is the radius of the Earth, h is the height above the surface, and g is the acceleration due to gravity at the Earth's surface.

If we plug in R = 6,371 km (the radius of the Earth) and h = 6,371 km (one Earth radius above the surface), we get:

g' = ((6,371 km)/(2*6,371 km))^2 * g

g' = (1/2)^2 * g

g' = g/4

Therefore, the answer is D. g/4.

Answer 2

Explanation:The acceleration due to gravity at a distance equal to one full Earth radius above the surface of the Earth is given by:

g' = g/(1 + R/E)^2

Where g is the acceleration due to gravity at the surface of the Earth, R is the radius of the Earth, and E is the distance of the object from the center of the Earth.

Substituting R for E+R, we get:

g' = g/[1 + (E+R)/R]^2

g' = g/[1 + (1+E/R)]^2

g' = g/[1 + (1+1)]^2 (Since E/R is very small compared to 1)

g' = g/16

Therefore, the acceleration due to gravity at a distance equal to one full Earth radius above the surface of the Earth is g/16. Answer: D. g/4.