Universal Gravitation - Example Problem 1.4-3

 

Considering that the earth has a mass of 5.97 x 10²⁴ kg and an average radius of 6371 km, derive the average acceleration due to gravity experienced at the earth's surface.

 

Given:

• m_earth = 5.97 x 10²⁴ kg
• r_earth = 6371 km

 

 

Find: g

 

Start with the law of universal gravitation. The force of gravity on an object of mass m at the earth's surface is equal to mg, where g is the acceleration due to gravity.

 

F = G m_Am_B /d ²

 

Equating the afore mentioned equations, g is given by

 

g = G m_earth / r_earth
g = G m m_earth / r²_earth
g = G m_earth / r²_earth
g = G m_earth / m r²_earth