There are five sweet spots where a spacecraft can keep pace with Earth as both orbit the Sun. They are called the Lagrange points, after the brilliant French mathematician Joseph-Louis Lagrange who found special solutions to what is called the “three-body problem”.
To locate the second Lagrange point, L2, draw a line 150 million km from Sun to Earth and extend it by about one per cent.
Normally an object orbiting the Sun farther out than Earth takes longer than a year to complete a cycle. But at L2 the gravitational forces of Sun and Earth combine to speed things up, so a spacecraft placed there moves in synchrony with the Earth, all three objects remaining in a straight line. Keeping the object close to Earth allows for faster communications and higher data volumes.
Space telescopes
The Hubble Space Telescope has been orbiting Earth for 35 years and continues to provide remarkable images of space. Hubble has led to major breakthroughs in astronomy. It has enabled us to determine the accelerating expansion rate of the universe and pin down its age to about 13.7 billion years. Hubble should continue to operate for at least another decade.
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It orbits at about 550km above the Earth’s surface and much of the sky is eclipsed by the planet as the telescope moves in and out of Earth shadow every 90 minutes. On Christmas Day, 2021, a successor to Hubble, the James Webb Space Telescope (JWST or Webb), was launched. Unlike Hubble, Webb orbits the Sun about 1.5 million km beyond Earth at L2, providing an unimpeded view of the sky.
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Webb observes in the infrared spectrum and can detect objects 100 times fainter than Hubble. Its main objectives are to study how the first galaxies formed and evolved after the Big Bang, the birth of stars and planetary systems and the origins of life.
Its mirror, with 18 hexagonal gold-plated segments, has a 6.5-metre diameter, considerably larger than that of the Hubble Space Telescope. The first image from Webb was revealed by US president Joe Biden in July 2022.
Location and orbit
An object placed exactly at the L2 Lagrange point would be permanently in the shadow of the Earth, cutting off the Sun as a source of power. So Webb has been placed in a halo orbit, following an elliptical path of width about 830,000km around the line from the Sun through L2, so that it avoids being eclipsed by either the Earth or Moon.
This ensures uninterrupted solar power and Earth communications on its sun-facing side. Its sun-shield is oriented so that the temperature of the spacecraft remains constant at a cool 50 Kelvin (minus 223 degrees), crucial for observation in the infrared spectrum.
Launching Webb to L2 was like cycling to the top of a hill by pedalling furiously at the beginning of the climb, generating enough speed to coast uphill and come to a halt near the top. Although an object placed at L2 is in equilibrium, the balance of forces is metastable and a small disturbance will cause it to gradually drift away into its own solar orbit and lose contact with Earth.
However, a spacecraft can be kept near L2 with minimal energy, remaining in line with Earth as it orbits the Sun. The telescope is not intended to be serviced in space but, with relatively little rocket thrust needed to keep it on station at L2, Webb should remain operational for 20 years or more.
Peter Lynch is emeritus professor at the School of Mathematics & Statistics, University College Dublin. He blogs at thatsmaths.com
