Answer to Question #83126 in Atomic and Nuclear Physics for Mayur

Question

The acceleration due to gravity on the earth surface of planet is 10m/s² if radius of planet is 6400km. Calculate acceleration due to gravity at height 3600km above surface

Answer 1

Use the gravity acceleration formula

g=GM/R^2

where G=6.673∙〖10〗^(-11) (N∙m^2)/〖kg〗^2 is universal gravitational constant; M is mass of the Earth; R is the distance from the center of mass of the Earth. According to the condition of the problem for R_1=6400km get g=10 m/s^2 .

g_1=GM/(R_1^2 )=10 m/s^2

If the body is at the height 3600km above surface of the Earth R_2 is equal to

R_2=R_1+3600=6400+3600=10000km.

Therefore gravity acceleration is equal to

g_2=GM/(R_2^2 )=GM/(R_1^2 ) (R_1^2)/(R_2^2 )=g_1 (R_1^2)/(R_2^2 )=10 (6400∙〖10〗^3 )^2/(10000∙〖10〗^3 )^2 =4.096 m/s^2