# LISA Orbits

Requires a Wolfram Notebook System

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

This Demonstration shows the approximate orbits of LISA, a space-borne gravitational wave detector. LISA consists of three satellites in a heliocentric orbit, trailing the Earth by 20 degrees. The three spacecraft form an equilateral triangle 5 million km (0.033 AU) a side. In this Demonstration, the default value for the spacecraft distance is increased by a factor of 10.

Contributed by: Oliver Jennrich (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The LISA orbits are designed to keep the distance between the spacecraft approximately constant over the course of an orbit. The triangular constellation is inclined by 60 degrees with respect to the ecliptic; the three spacecraft orbit the Sun in independent Kepler orbits with a semimajor axis of AU and a small eccentricity and inclination. To first order in the eccentricity , the coordinates of the spacecraft are

,

where the eccentricity is given by the distance between the spacecraft and , where is the initial phase.

## Permanent Citation