• gravitational force exerted on each mass = Gm₁m₂ / D²

    • gravitational potential energy of system = -Gm₁m₂ / D

    • kinetic energy of a mass = ½ mv²

    • acceleration of rock = gravitational force / m₂

    • max. displacement = ((1/Q) - (v₁² / 2Gm₁))⁻¹ - Q

    • displacement = ((1/Q) - ((v₁² - v²) / 2Gm₁))⁻¹ - Q

    • time = ((Q)^3/2 tan^-1((Q/R)-1)^1/2) + (RQ(Q-R))^1/2)) / (2Gm₁)^1/2)

     • m₁ = mass of planet (kg)

     • m₂ = mass of rock (kg)

     • D  = separation of centers of planet and rock (m)

     • R = radius of planet (m)

     • r = radius of rock (m)

     • Q = R + r

     • v = speed (m/s)

     • v₁ = initial speed (m/s)

• There are no other masses in the universe.

• The velocity of the planet is zero all the time.

• A picture can include infinity.

• G has the same value everywhere in the universe.

It is said that:

"What goes up must comes down."

What if you could throw really fast?

This simulation works best if you are using a device that uses a keyboard that has arrow keys.

The left and right arrow keys can be used to make small changes to the values of the two velocity sliders.

Small changes can make a big difference when the rock's position approaches infinity.

EscapeVelocitySim

Download, free, from kirbyx.com