Question

A planet has a mass of 5.97 x 1024 kg and a radius of 6.38 x 106 m. Find the weight of a 65.0 kg person at 1000 km above the surface of this planet.

Answer 1

Answer: The weight of the person above the surface of a planet is 635.83N.

Explanation:

To calculate the weight of a person, we use the formula:

$w=mg$     ....(1)

where,

w = weight of an object

m = mass of the person = 65kg

g = acceleration due to the gravity of the planet

For the calculation of weight, we need to first find the acceleration due to gravity and for that we use the formula:

$g=\frac{GM}{r^2}$

where, g = acceleration due to gravity = $?m/s^2$

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

M = mass of the planet = $5.97\times 10^{24}kg$

r = distance of the person from the planet = $6.38\times 10^6m$

Putting values in above equation, we get:

$g=\frac{(6.67\times 10^{-11}kgm/s^2.m^2/kg^2)(5.97\times 10^{24}kg)}{(6.38\times 10^6m)^2}\\\\g=9.782m/s^2$

Putting this value in equation 1, we get:

$w=65kg\times 9.782m/s^2=635.83N$

Hence, the weight of the person above the surface of a planet is 635.83N.