Letter | Published:

Third Integral of Motion for High-velocity Stars

Nature volume 212, pages 5758 (01 October 1966) | Download Citation



SEVERAL attempts have been made in recent years to establish whether models of the galactic mass distribution admit a third isolating integral of motion for stellar orbits in addition to the well-known integrals of energy and angular momentum1–4. Although the various investigators concerned are in agreement that orbits of the solar type are non-ergodic, the issue is not so clear-cut for the high-velocity stars. The current lively interest in violent events connected with galactic nuclei has given rise to the idea5 that stars in almost radial orbits may have been expelled from the central region of the Galaxy, and the present investigation was undertaken in order to study the behaviour of such orbits. It will later be argued that this special case does not restrict the validity of the results as applied to the high-velocity stars so long as one is considering orbits or very low angular momentum.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , Stockholms Obs. Ann., 20, No. 5 (1958).

  2. 2.

    , Bull. Astron. Inst. Neth., 16, 241 (1962).

  3. 3.

    , and , Astron. J., 69, 73 (1964).

  4. 4.

    , and , Astrophys. J., 140, 1106 (1964).

  5. 5.

    , and , Proc. Roy. Soc., A, 290, 177 (1966).

  6. 6.

    , Stars and Stellar Systems, 5, 513 (University of Chicago Press, 1965).

  7. 7.

    , Bull. Astron. Inst. Neth., 13, 15 (1956).

  8. 8.

    , Mon. Not. Roy. Astro. Soc., 132, 35 (1966).

  9. 9.

    , , and , Astrophys. J., 136, 748 (1962).

Download references

Author information


  1. Institute of Theoretical Astronomy, University of Cambridge.

    • S. J. AARSETH


  1. Search for S. J. AARSETH in:

About this article

Publication history




Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.