Question

On the surface of the Moon an astronaut has a weight of Fg = 160 N. The radius of the Moon is Rm = 1.74 × 106 m, the gravitational constant is G = 6.67 × 10-11 N (m/kg)2 and the mass of the Moon is Mm = 7.35 × 1022 kg. calculate the mass of astronout in kilogram?

Answer 1

Given,

The weight of the astronaut on the surface of the moon, Fg=160 N

The radius of the moon, Rm=1.74 × 10⁶ m

The gravitational constant, G=6.67 × 10⁻¹¹ Nkg⁻²m²

The mass of the moon Mm=7.35 × 10²² kg

The weight is the force with which the moon pulls the astronaut towards its center. That is, weight is the gravitational force acting on the astronaut.

From Newton's universal law of gravitation, this gravitational force is given by

`F_g=(GM_mm)/(R^2_m)`

Where m is the mass of the astronaut.

On rearranging the above equation,

`m=(F_gR^2_m)/(GM_m)`

On substituting the known values in the above equation,

`\begin{gathered} m=(160*(1.74*10^6)^2)/(6.67*10^(-11)*7.35*10^(22)) \\ =(4.84*10^(14))/(4.9*10^(12)) \\ =98.8\text{ kg} \end{gathered}`

Thus the mass of the astronaut is 98.8 kg