Question

Please help me to calculate the weight of the moon. pleasee... Show it by step by step

Answer 1

F(g)(e) = Force of gravitation on earth 

F(g)(m) = force of gravitation on moon

F(g)(e) = GM(e)m(b)/r(e)²

where m(b) = mass of body = constant 

F(g)(m) = GM(m)m(b)/r(m)²

a(g)(e) = GM(e)/r(e)²______(1)

a(g)(m) = GM(m)/r(m)²_____(2)

Dividing 1 and 2 

a(g)(e) / a(g)(m) = GM(e)/r(e)² /  GM(m)/r(m)²

a(g)(e) / a(g)(m) = M(e)  x  r(m)²  / r(e)² x M(m) 

a(g)(m) = a(g)(e) /M(e) x  r(m)²  / r(e)² x M(m) 

a(g)(m) = a(g)(e) x r(e)² x M(m) / M(e) x  r(m)²

Putting the values of 

a(g)(e) = 9.8 m/s² 

r(e)² = (6.4 x 10⁶)² m

M(m) = 7.34 x 10²² kg

M(e) = 6.4 x 10²⁴ kg 

r(m)² = (1.7 x 10⁶)²

we get , 

a(g)(m) = 9.8 x (6.4 x 10⁶)² x 7.34 x 10²² /  6.4 x 10²⁴  x  (1.7 x 10⁶)²

a(g)(m) = 9.8 x 40.96 x 10¹² x 7.32 x 10²²/ 6.4 x 2.89 x 10¹² x 10²⁴

a(g)(m) = 2938.30 x 10³⁴ / 18.49 x 10³⁶ 

a(g)(m) = 158.91 x 10⁻²

a(g)(m) = 1.5891 m/s²

9.8/6 = 1.63 ≈ 1.5891≈ 1.59 ≈1.6 m/s²

Hence proved :)