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
