# Newton's Projectile

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This Demonstration is an animated 3D model of a projectile fired from above the Earth's equator, based on Newton's laws of motion and gravitation. According to this theory, after launch, a projectile is subject only to the Earth's gravitational attraction.

Contributed by: Erik Mahieu (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The differential equations determining the projectile's motion are .

In this Demonstration, air resistance and the effect of the Earth's rotation are not taken into account. The Earth is assumed to be a perfect sphere with diameter set to 1 and all lengths are scaled accordingly. The projectile is fired from a point directly above the equator where the escape speed is . The circular equatorial orbit is calculated using Kepler's formula, .

Snapshot 1: projectile returns to Earth

Snapshot 2: circular equatorial orbit

Snapshot 3: fired at a speed above escape velocity

Inspired by Enrique Zeleny's Demonstration "Projectile Launched around the Earth".

Graphic of the earth taken fromEd Pegg Jr's Demonstration "Geosynchronous Orbit"

## Permanent Citation