Question
You throw a rock with an initial horizontal velocity and it hits the ground at x meters away from your feet. What if:
(a) You throw the same stone with the same initial conditions but instead you do this on a another planet with a mass 4 times the mass of the earth. With what factor will x change?
(b) You throw the same stone with the same initial conditions but instead you do this on a another planet with a radius 6 times the radius of the earth. With what factor will x change?
(a) You throw the same stone with the same initial conditions but instead you do this on a another planet with a mass 4 times the mass of the earth. With what factor will x change?
(b) You throw the same stone with the same initial conditions but instead you do this on a another planet with a radius 6 times the radius of the earth. With what factor will x change?
Answers
Since the force is GmM/r^2, it varies directly with the mass of the planet, and inversely with the radius-squared.
4*mass = 4 * acceleration
6*radius = 1/36 * acceleration
Then just plug in your equations of motion with the new acceleration value.
4*mass = 4 * acceleration
6*radius = 1/36 * acceleration
Then just plug in your equations of motion with the new acceleration value.