Help me please

Question

The moon has an average radius of 1.74x10^6 m. A 68.kg person on the moon's surface weighs only 110 N. What is the mass of the moon? 

 

 

Answer 1

Hi Hannah,

 

The general gravitation equation is   g = G m M / r²   If we take your data, then we can apply this to both the Earth and the Moon. So on Earth:

 

(9.8 * 68) = G m_E 68 / (6371000²)

 

And on the Moon:

 

110 = G m_m 68 / (1740000²)

 

If we re-arrange these in terms of G (the gravitational constant), we get:

 

G = 110 (1740000²) / m_m 68  =  (9.8 * 68) (6371000²) / m_E 68

 

So we can drop G, and also the 68 kg from both denominators. A little algebraic re-arrangement and we obtain:

 

m_m = m_E 110 (1740000²) / (9.8 * 68) (6371000²) = 0.0123 m_E

 

If we know the mass of the Earth (5.972 * 10²⁴ kg), then the mass of the Moon is:

 

mm = 0.0123 * 5.972 * 10²⁴ kg = 7.35 * 10²² kg.

 

(This is the currently accepted value, to 3 s.f.)

 

We could also just say that the mass of the Moon was 1.23% of the Earth's, an easy-to-remember figure.