Abstract
The James Webb Space Telescope will hover in an orbit not around the Earth, as does the Hubble Space Telescope, but around the Sun. It will mimic Earth’s orbit, but be farther out, orbiting at the so-called second Lagrangian point, or the L2 point. The telescope will maintain a stable temperature, unaffected by passing in and out of the Earth’s shadow. Yet the reader may ask: how may an object orbiting the Sun farther out from the Earth, in a larger orbit, keep up with us? Bodies in more distant orbits move more slowly; we continually overtake the slower, outer planets as we whirl around the Sun, and the inner planets outpace us. Won’t the JWST fall behind? The answer is no, and to know why requires understanding the Lagrangian points.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This can be readily calculated from the Newtonian equation for gravitational acceleration, f = GM/r 2.
- 2.
An animation of the Lagrangian points can be found at the European Space Agency website, at http://www.esa.int/esaSC/SEMM17XJD1E_index_0.html.
- 3.
If one is sitting in a circular frame of reference, though, there appears to be no particular thing acting on the object that accounts for this outward force except the rotation of the reference frame itself. So in a merry-go-round, one would not necessarily know why coins spilled on the ground would all move outward from the center. As noted earlier, physicists often refer to the centrifugal force as a “fictitious” force. It effectively cancels the accelerative effects of the reference frame itself to make it an “inertial” reference frame – that is, without its own acceleration, and where Newton’s laws remain valid.
- 4.
Length A is r .cos(30°). The cosine of 30° is equivalent to √3/2.
- 5.
The law of cosines is allows one to calculate the third side of a triangle when we know the other two and the angle between them. It is usually written this way: c 2 = a 2 + b 2 − 2ab cosθ. Its use is shown in the problem.
- 6.
See http://www.astro.uwo.ca/~wiegert/3753/3753.html for an interesting discussion of this moon.
- 7.
Chaisson and McMillan [1].
- 8.
For a readable discussion of this problem with references to further reading, see Szebehely and Mark [2].
References
Chaisson E, McMillan S (2005) Astronomy today, 5th edn. Pearson Prentice Hall, Upper Saddle River, pp 324–324
Szebehely VG, Mark H (1998) Adventures in celestial mechanics, 2nd edn. Wiley, New York, Chapter 13
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
MacDougal, D.W. (2012). Hovering in Space: Those Mysterious Lagrangian Points. In: Newton's Gravity. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5444-1_19
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5444-1_19
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5443-4
Online ISBN: 978-1-4614-5444-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)