Question 1

What is escape velocity?

Accepted Answer

Escape velocity is the minimum launch speed at which a body leaves a planet's gravitational field without further propulsion. It equals √(2GM/r), where M and r are the planet's mass and the launch distance from its centre. At Earth's surface this works out to about 11.2 km/s.

Question 2

Does escape velocity depend on the mass of the object?

Accepted Answer

No. The projectile's mass cancels out of v_e = √(2GM/r) entirely. A feather and a rocket need the same 11.2 km/s from Earth's surface. Mass does appear in the energy quantities (KE, PE, total energy), but not in the trajectory or the required speed.

Question 3

Why do astronauts float in orbit if gravity still acts?

Accepted Answer

At low Earth orbit altitudes gravity is still roughly 90% of its surface value (at 400 km it is about 89%; even at 1600 km it remains about 64%). Astronauts float because they and their spacecraft are in continuous free fall — falling towards Earth while moving forward so fast that the ground keeps curving away. This is weightlessness, not absence of gravity.

Question 4

What is Kepler's third law?

Accepted Answer

Kepler's third law states that the square of a planet's orbital period is proportional to the cube of its orbital radius: T² = 4π²r³/GM, i.e. T² ∝ r³. It lets you compare periods of satellites or planets by ratio without knowing G or M individually.

Question 5

What is the total energy of a satellite in a circular orbit?

Accepted Answer

For a circular orbit, total energy E = −GMm/2r, kinetic energy KE = +GMm/2r and potential energy PE = −GMm/r. Hence E = −KE and PE = 2E. The negative sign means the satellite is bound; the magnitude GMm/2r is the binding energy needed to free it.

Escape Velocity & Orbits — Newton's Cannonball in 3D

Practice

Learned it? Now prove it under the clock.