How to place a satellite permanently behind the Earth

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

23 January 2022

There was a lot of excitement on 24th December 2021 after the successful launch of the James Webb Telescope. what is special about this telescope is that it will be orbiting the sun from “behind the Earth” permanently. In other words, it will always be in the shadow of the Earth and so it will be able to observe outer space with great clarity since it is hidden from the glare of the sun.

Placing a telescope permanently in the Earth’s shadow is a great idea but it is not easy to achieve in practice. The challenge is that the law of gravity dictates that the farther away from the sun an object is, the slower it needs to move in order to remain in an orbit.

Mercury, the planet closest to the Sun revolves completes one orbital revolution in just 88 days (less than 3 months); Venus, the second in line, does it in 255 days; and Earth take 365 days. This progressive increment of the orbital periods continues as we go farther and farther away from the Sun. By the time we reach Neptune, it is over 60,000 days or 165 years.

Thus, it follows that, if an object is placed “behind the Earth” in relation to the Sun, it will be farther away than Earth and so it should require a slower orbital speed in order to remain in orbit. So, the question is: how will the James Webb Telescope be able to stay in its orbit?

The orbital speed of an object depends only on the strength of the gravitational field at the orbit. The stronger the gravity, the faster the orbiting object needs to move. Furthermore, the closer to the source of gravity, the stronger the field.

Now, an object that is relatively near the Earth will “feel” two forces of gravity – from the Earth and also from the Sun. However, the Earth’s gravity at this distance from the Sun is much greater than that of the Sun. Thus, the tendency is to orbit the Earth.

As we go farther from the Earth, the planet’s gravitational strength reduces. Soon we reach a distance where it is no longer the predominant force. The object now reacts to the combined Sun and Earth gravity.

We continue moving outward and we come to a point where the combined Earth plus Sun gravity is now exactly equal to the Sun’s gravity at Earths orbit. This means that an object orbiting the Sun from this distance will need to move at exactly the same speed as the Earth in order to remain in that orbit. Therefore, it can permanently stay “behind” the Earth as it goes around the Sun.

This is what is planned for the James Webb Telescope. That special point is about 1.5 million km from the Earth and the telescope will take about 30 days to get there. That is, it should get there any time between yesterday and today.