You are here:

# Astrophysics/Lagrange points

Question
QUESTION: What way would an object at L1 progress if pushed, say, directly towards earth? I figure it's period would increase initially, and fall back behind the earth's orbit, but then what? I can't work it out...﻿

You say you 'can't work it out'. What exactly are you trying to work out?   Velocity, acceleration, direction, all the preceding? What calculation are you actually doing? (Please shown any equations, formulae etc.)

Also, what mass are you assuming for this object given that L1,along with L2 and L3 are 'unstable' Lagrangian points?

Please fill me in so I can further assist.

[an error occurred while processing this directive]---------- FOLLOW-UP ----------

QUESTION: L1 is unstable; an object of insignificant mass relative to earth (and therefore the sun) with even a slight impetus will move away from L1, as we know. Without specifying mass or acceleration, what would be the general tendency if the object was pushed directly towards Earth? That much in itself ought to have a predictable pattern, shouldn't it?
This question occurs to me as I note the launch of ESAs Lisa pathfinder spacecraft which is expected to detect gravitational waves at its new home L1.

Hello,

The "push" described (toward Earth) would effectively be a small perturbation. (Bear in mind also the LISA craft is not *at* L1 but in a 3 -dimensional, e.g. halo -type, elliptical orbit around it). Theoretically, this perturbation should change the radius of the Hill sphere (r)and lead to a shorter orbital period. However, I would think this would not yield a "predictable pattern".

Again, you have changed the basis of the 3 -body problem by your "push" (perturbation) so that new computations would need to be made for the new orbit about L1, including the new Hill sphere dimensions, stability etc.

Note also that the Hill sphere radius is based on a circular orbit while LISA is in an elliptical orbit.

Hopefully, this is of some use to you!
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Enlarging the subject and adding much

Astrophysics

Volunteer

#### Philip A. Stahl

##### Expertise

I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars – as well as the magnetohydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

##### Experience

Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

Publications
Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society. Barbados Astronomical Society award for service (1977-91) as Journal editor.

Past/Present Clients
Caribbean Examinations Council (as advisor, examiner), Barbados Astronomical Society (as Journal Editor 1977-91), Trinidad & Tobago Astronomical Society (as consultant on courses, methods of instruction, and guest speaker).