Simulation · Physics · Class 11
Build a planet
From the lesson Acceleration due to gravity in Gravitation. Change the values and watch what happens.
Build a planetPhysics · Class 11
The idea behind it
NCERT §7.5
- Think of the earth as many concentric shells. A point outside is outside every shell, so the whole earth pulls as if its mass M_E were at the centre.
- On the surface the force on a mass m is F = G M_E m / R_E², and since F = mg, g = G M_E / R_E².
- g does not depend on the mass of the falling body; it depends only on the mass and radius of the earth.
- Knowing g, R_E and G gives the earth's mass: M_E = g R_E² / G. With g = 9.81 m/s² and R_E = 6.37 × 10⁶ m this is 5.97 × 10²⁴ kg, hence the phrase 'Cavendish weighed the earth'.
- The Moon's orbit gives the same mass another way, M_E = 4π²R³/(G T²) ≈ 6.02 × 10²⁴ kg, within 1% of the first value.
- Inside a uniform earth, at distance r from the centre, only the mass within radius r pulls, and the force is F = G M_E m r / R_E³, proportional to r.