Question

For a relatively weak gravitational field, such as that of a planet or an ordinary star, the following formula tells us the fractional amount of gravitational time dilation at a distance r from the center of an object of mass Mobject:
1c2×GMobjectr
(G=6.67×10?11m3/(kg×s2); c=3×108m/s.) For example, while 1 hour passes in deep space far from the object, the amount of time that passes at a distance r is 1 hour minus 1 hour multiplied by the factor above. (This formula does not apply to strong gravitational fields, like those near black holes.)

A) Calculate the amount of time that passes on Earth's surface while 3.0 hour passes in deep space.

Answer 1

The equation for gravitaional time dilation is:

where, is the time meassured when the observer and event are in same gravitational potential. ie. here at the surface of earth

is the time meassured from infinite distance, ie. deep space

G is the gravitational constant =

M is the mass of the object, here Earth =

r is the distance from the center of the object, here it is the radius of Earth = 6371 km

                                                                                                             

c is the velocity of ligh =

Therefore, time that passes on Earth's surface when 3 hour passes in deep space

Thus the time passes on Earth's surface when 3 hours passes on deep space is 8246.232 seconds. ie. 137.43 minutes which is equal to 2 hour 17 minutes