What is the weight of the statue of liberty in the following cases:
1. Calculate the weight of the Statue of Liberty (205 tons) on Earth. The Earth has a mass of 6 * 10^24 kg and a radius of 6.4 × 10^6 m.
2. What would this weight be on Mars, with mass 0.11 times that of Earth and radius 0.53 times that of Earth?
The value of the universal gravitational constant is 6.67*10^-11 N*m^2/kg^2.
According to the Newton's law of universal gravitation, the force of gravitational attraction between two objects of mass M1 and M2 placed a distance R from each other is given by G*M1*M2/R^2.
Here G is the universal gravitational constant given as 6.67 × 10−11 N*m^2/kg^2.
The mass of the Statue of Liberty is 205 tons or 205*10^3 kg. The mass of the Earth is 6*10^24 kg. And the distance between the two, which is the distance between their center of mass is the radius of Earth equal to 6.4*10^6 m.
The Weight of the statue on Earth turns out to be:
6.67*10^-11*205*10^3*6.4*10^24 / (6.4*10^6)^2
=> 2.134*10^6 N
Now to find the weight of the same statue on Mars which has a mass 0.11 times that of the Earth and a radius 0.53 times that of the Earth we have:
6.67*10^-11*205*10^3**.11*6.4*10^24 / (.53*6.4*10^6)^2
=> 8.36*10^5 N.