Question

Physics HELP!!!!! On the surface of the Moon an astronaut has a weight of Fg = 140 N. The radius of the Moon is Rm = 1.74 x 106 m, the gravitational constant is G = 6.67 x 10-11 N m2kg2 and the mass of the Moon is Mm = 7.35 x 1022 kg. Solve numerically for the mass of the astronaut ma in kg.

Answer 1

Well, you have the formula 

F = GMm/r^2 

So, plug in the numbers. What do you get? 

Oh, OK. The astronaut's mass is thus 

m = Fr^2/GM

Answer 2

Answer:

Mass of the astronaut is 86.45 kg

Explanation:

It is given that,

Weight on the surface of astronaut, $F_g=140\ N$

The radius of the moon is, $R_m=1.74\times 10^6\ m$

The gravitational constant is,  $G=6.67\times 10^{-11}\ Nm^2/kg^2$  

Mass of the moon,  $m_1=7.35\times 10^{22}\ kg$

We need to find the mass of the astronaut. It can be calculated using the formula as :

$F=G\dfrac{m_1m_2}{R^2}$

m₂ = mass of the astronaut

$m_2=\dfrac{FR^2}{Gm_1}$

$m_2=\dfrac{140\ N\times (1.74\times 10^6\ m)^2}{6.67\times 10^{-11}\ Nm^2/kg^2\times 7.35\times 10^{22}\ kg}$

m₂ = 86.45 kg

So, the mass of the astronaut is 86.45 kg. Hence, this is the required solution.