WEBVTT FILE 1 00:00:00.300 --> 00:00:02.933 Lagrange points. Named after Italian mathematician 2 00:00:02.933 --> 00:00:04.600 Joseph-Louis Lagrange. 3 00:00:04.600 --> 00:00:07.600 Lagrange points are a solution to what's called the "three-body" problem. 4 00:00:07.833 --> 00:00:11.966 Two massive objects like the Earth and the Sun create points in space 5 00:00:11.966 --> 00:00:15.533 where their gravitational forces balance with the centripetal force 6 00:00:15.533 --> 00:00:18.600 of the motion of a smaller third object - like a spacecraft. 7 00:00:19.300 --> 00:00:24.200 There are five different points where these forces balance named L1 through L5, 8 00:00:24.700 --> 00:00:28.333 L4 and L5 are known as stable points, and they attract objects, 9 00:00:28.333 --> 00:00:31.800 like space debris, which can easily stay in orbit around these points. 10 00:00:32.366 --> 00:00:35.400 L1, L2, and L3 are known as semi-stable. 11 00:00:35.666 --> 00:00:38.266 To stay put here, an object, like a spacecraft, 12 00:00:38.266 --> 00:00:40.300 would have to use some fuel so it doesn't drift off. 13 00:00:41.166 --> 00:00:44.000 We use L1 and L2 between the Earth and the Sun 14 00:00:44.200 --> 00:00:47.700 to host satellites and telescopes without needing an excessive amount of fuel. 15 00:00:48.066 --> 00:00:50.300 For example, the James Webb Telescope orbits 16 00:00:50.300 --> 00:00:53.100 in L2 on the opposite side of the Earth from the Sun. 17 00:00:53.900 --> 00:00:58.033 Lagrange points are a helpful resource in furthering space exploration.