All planetary orbits contain 5 unusually stable points. These points are particularly important because they allow man-made satellites to orbit the Sun with a period equal to that of Earth’s. 3 of these points are collinear. Suppose that is the distance between the centers of mass of Earth and the Sun. Find the distance from Earth’s center of mass to either one of the other stable points in the Earth-Sun system in terms of...

(I'm not looking for a full solution; I just want to know what these points are called)

What are these points it talks about, and what's their mathematical relation to Earth's orbit?

This still isn't homework; I'm just looking for the name of these points.

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    $\begingroup$ I think only two of the 5 Lagrange points support stable orbits. These are the non-co-linear ones. Asteroids trapped into such orbits are called Trojans and Greeks, respectively. $\endgroup$ – Walter Apr 12 '14 at 20:17
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    $\begingroup$ Does look a lot like homework, with that final quoted sentence there... $\endgroup$ – Rory Alsop Apr 14 '14 at 7:10
  • $\begingroup$ @Rory It isn't; it's a grab-bag problem set that I downloaded. It asks all sorts of questions ranging from Calculus to Astronomy to LaTeX to Geek Trivia. $\endgroup$ – KevinOrr Apr 18 '14 at 3:11
  • $\begingroup$ @KevinOrr 'Homework' is anything that asks us to do a question for you, not necessarily true homework. Although this question is more asking about elements of a question. $\endgroup$ – damned truths May 4 '14 at 3:32
  • $\begingroup$ @damnedtruths well, I didn't actually need a solution; once I knew what to search, I could read up on it myself and then work the problem out myself. I didn't know what to even search for in the first place, as I didn't what they were called. But I'll edit the question to be more clear. $\endgroup$ – KevinOrr Jun 17 '14 at 20:25

These are the Langrangian Points http://en.wikipedia.org/wiki/Lagrangian_point -you'll find an explanation of the maths at a variety of sources if you search using that.


As Jeremy explained, these are the Lagrangian points (see his link to the Wikipedia article). At these points, earth's gravity and the sun's gravity partially cancel each other to cause the orbital period of an object at that point to match the orbital period of the earth-sun system.

  • $\begingroup$ For the sun earth L points there are three forces that cancel. Gravity of sun, gravity of earth plus inertia in a rotating frame (what used to be called centrifugal force) $\endgroup$ – HopDavid May 19 '14 at 23:36
  • $\begingroup$ I wasn't looking at a rotating frame, but your comment is valid for a rotating frame. $\endgroup$ – NeutronStar May 20 '14 at 17:19
  • $\begingroup$ If looking at Lagrange points, a rotating frame is assumed. For two of the L points (L2 and L3) the two bodies pull in the same direction -- the gravitational pulls don't cancel. For L4 and L5, the larger body's gravity far exceeds the smaller and again the two forces don't cancel. The sun's gravity cancels the earth's gravity about 270,000 km from earth's center. But L1 is about 1,500,000 km from earth's center. $\endgroup$ – HopDavid May 20 '14 at 17:44

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