tag:blogger.com,1999:blog-8331666102432713341.post7405632381726358081..comments2017-01-27T01:56:26.682-05:00Comments on Anomalous Readings: Lagrange Point 2: Newton's RedemptionOri Vandewallehttps://plus.google.com/107689030732454966247noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8331666102432713341.post-53412792307801069862016-03-18T10:50:31.778-04:002016-03-18T10:50:31.778-04:00Right. It's not a stable point to begin with,...Right. It's not a stable point to begin with, which is why I asked if the Moon's influence was significant.<br /><br />So you're more-or-less saying not very; probably...BUhttp://alphacentauri2.info/noreply@blogger.comtag:blogger.com,1999:blog-8331666102432713341.post-59934782144028932182016-03-12T21:10:01.495-05:002016-03-12T21:10:01.495-05:00Well, there are a couple things to consider here. ...Well, there are a couple things to consider here. When I talk about making approximations to find the L2 point, those are essentially mathematical tricks to solve the equation. They produce the correct answer, but get there by a method other than algebraic manipulation (because algebraic manipulation alone can't work here). There are other methods I could have used, such as guessing solutions, or graphing the equation and seeing where its roots are. They would all produce the correct answer.<br /><br />But... my correct answer is an approximation of the real system, because it makes some assumptions about the system. It assumes the center of mass is at the exact center of the sun, it assumes the Earth's orbit is circular, it assumes no Coriolis effect, etc. Another assumption, because this is the 3-body problem, is that no other gravitating masses are significant.<br /><br />The average distance of the moon from the Earth is 384,400 km, or 238,900 miles. And the moon's mass is small. This works out to the sun's gravity being about 1,500 times stronger at L2 than the moon's, for example. I'm sure this smudges up the numbers a bit in real life, and I'm sure the rocket scientists who keep an eye on satellites out there have to track all that, but saying L2 is at 1.5 million km (or 930,000 miles) is perfectly accurate (if not precise).<br /><br />The moon and other bodies aren't the reason why L1, L2, and L3 aren't inherently stable, though. That has to do with the shape of the potential wells that create the Lagrange points. Essentially, being at one of those points is like being in a shallow depression at the top of a hill. As long as nothing knocks you out of your little hole, you're okay. But if a slight breeze gives you any momentum, you go rolling down the hill.Ori Vandewallehttp://www.blogger.com/profile/17804391682393947159noreply@blogger.comtag:blogger.com,1999:blog-8331666102432713341.post-13560745647316675742016-03-12T18:49:59.952-05:002016-03-12T18:49:59.952-05:00What's that actual distance of the L2 point? ...What's that actual distance of the L2 point? 930,000 miles? How much does the Moon going by roughly 680,000 miles in destabilize the L2?BUhttp://alphacentauri2.info/noreply@blogger.comtag:blogger.com,1999:blog-8331666102432713341.post-20445590112671152682016-03-09T11:37:38.069-05:002016-03-09T11:37:38.069-05:00"If it were easy, everyone would do it."..."If it were easy, everyone would do it."Timothy Wallacehttp://www.blogger.com/profile/10908340222043329986noreply@blogger.com