# Gravitation versus Curved Spacetime

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

According to Newton's law of universal gravitation, two masses and attract one another with a force varying as the inverse square of the distance between them: , where is Newton's constant of gravitation. Orbits of attracting masses, including Kepler's laws of planetary motion, can be calculated on the basis of this force law. The left-hand graphic shows some possible trajectories of a "test mass" , with around a stationary mass . The trajectories, shown as red curves, depend on the central mass and the energy of the test mass. When the test mass moves more slowly than the escape velocity, it spirals into the center. At higher energies, a stable orbit becomes possible in a progression of conic sections: circle, ellipse, parabola and hyperbola. (Hyperbolic orbits are not included here.)

[more]
Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: suborbital spiral

Snapshot 2: circular orbit

Snapshot 3: parabolic orbit

## Permanent Citation

"Gravitation versus Curved Spacetime"

http://demonstrations.wolfram.com/GravitationVersusCurvedSpacetime/

Wolfram Demonstrations Project

Published: March 7 2011