Earth has a mass of 5.97 * 1024 kg and a radius of 6.38 * 106 m, while Saturn has a mass of 5.68 * 1026 kg and a radius of 6.03 * 107 m. Find the weight of a 65.0 kg person at the following locations

Answer: mass on earth = 625.792 N, mass on saturn = 666.75 N

Explanation: weight of an object = mg

Where g = acceleration due to gravity = GM/r²

Where G = gravitational constant, M = mass of planet and r = radius of planet.

Let us start with earth.

G = gravitational constant of the earth = 6.67*10^-11 m³ / kgs²

Me = mass of earth = 5.97*10^24 kg

re = radius of earth = 6.38*10^6 m

Acceleration due to gravity on earth = (6.67*10^-11*5.97*10^24) / (6.38*10^6) ²

Acceleration due to gravity on earth = 3.98*10^14 / 4.07*10^13

Acceleration due gravity on earth = 9.778 m/s²

The mass of the person is 64 kg, hence his weight on earth is given as

W = mass * Acceleration due gravity on earth = 64 * 9.778 = 625.792 N

For saturn.

G = gravitational constant of the earth = 6.67*10^-11 m³ / kgs²

Ms = mass of saturn = 5.68*10^26kg

rs = radius of saturn = 6.03*10^7 m

Acceleration due to gravity on saturn = (6.67*10^-11*5.68*10^26 / (6.03*10^7) ²

Acceleration due to gravity on saturn = 3.788*10^16/3.636*10^15

Acceleration due gravity on saturn = 10.417 m/s²

The mass of the person is 64 kg, hence his weight on saturn is given as

W = mass * Acceleration due gravity on saturn = 64 * 10.417 = 666.75 N