Lagrange Point (L1) Calculation

A Lagrange point is a point in close proximity to the Earth's orbit around the sun at which placing a satellite would allow it to orbit the sun with the same exact time period as the Earth, namely 365 days per revolution (orbit). As we mentioned in the previous lecture, five such points exist. Let us suppose that we want to calculate one of these points known as L1 that lies on a horizontal axis connecting the Earth and the Sun. We would like to calculate the distance from the Earth to the Lagrange point on which we can place the satellite. There are two steps in this problem: first we must find all the forces acting on the satellite (two forces, one due to the gravitational pull of the Sun and the second one due to the pull of the Earth) and then we must find all the forces acting on the Earth (we assume that only one force acts on the Earth and this is the force due to the Sun). We do a tad bit of mathematics to obtain a formula for the distance. We plug in our known values and calculate the distance from L1 to the Earth.

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