# Rocket Science

Let us imagine a spaceship traveling to the moon, as the Apollo 8 rocket did in 1968. Intuitively, the force of gravity on the spaceship will weaken as the rocket moves farther away from the Earth. At the same time, when the rocket is very close to the Moon it will feel the increased pull of gravity by the Moon. There is a point in the long three day journey between the Earth and Moon at which the pull of Earth’s gravity will be exactly compensated for by the pull of Moon’s gravity.

At the special transition point, a rocket would be stationary without the worry of hurtling into either the Earth or the Moon. This place of ‘zero-g’ is called a Lagrange point after the mathematician Joseph-Louis Lagrange who first found this mathematical solution in the 18th century.

If gravity was the only force operating on the Moon, Earth, and a body like a rocket or asteroid, then there would only be the one Lagrange point just mentioned. But it turns out that the Moon is also making circles around the Earth. This circular motion about a larger body introduces an additional force that pushes outward called the centrifugal force.

The centrifugal force is the one that you feel when executing a turn in a car, or when participating in any amusement park ride that turns in circles. When gravity plus the effects of centrifugal force are taken into account, then what comes out of the mathematics is that there are four additional special points in the Earth-Moon system at which a rocket could be more-or-less stationary.

Thus in total there are five Lagrangian points. Three of the points are located along a straight line drawn through the Earth and Moon, and two others are located along the circle described by the orbit of the Moon.

Although interesting, how is this information useful to us? Well, when we launch a satellite, especially of the long-term science variety, we want to maximize the lifetime, minimize the cost in terms of fuel, and be in constant radio contact with the it. Further, if the satellite is designed to do astronomy, we will want to be able to guide its view into space without having to worry about the blinding light of the sun. If the science satellite is placed at a Lagrange point, especially the one labelled “Lagrange 2” located just beyond the Earth in the direction away from the Sun, then all of these conditions are mostly satisfied.

In detail, the Lagrange 2 point is only mostly stable. Over time the satellite will wander out of this special place. In order to keep a science satellite at the Lagrange 2 point, a small amount of fuel is required to make every so minor orbital adjustments.

One famous astronomy satellite, the James Webb Space Telescope, will be launched in 2018 bound for the Lagrange 2 point of the Sun-Earth system. The only downside is that the Lagrange 2 point is 1 million miles away from Earth. There will be no way to fix this satellite once it is launched. We will have only one try to get it right.

This post raises two questions (1) will the Webb be orbiting the sun and not the earth and (2) does the sun’s gravity also affect the Lagrange point?

Thanks

If I’m reading the following page correctly, I think the short answers are “yes” and “yes”. See the sections under

A Solar OrbitandJWST at L2on this NASA page:About JWST’s Orbit