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MODIFIED NEWTIONIAN DYNAMICS (MOND)

MODIFIED NEWTIONIAN DYNAMICS (MOND). Rebecca Madson AST 232 Fall 2002. MOND- an alternative to dark matter?. Mass discrepancies are observed in the universe Popular explanation is Dark Matter- based on Newton’s laws

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MODIFIED NEWTIONIAN DYNAMICS (MOND)

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  1. MODIFIED NEWTIONIAN DYNAMICS (MOND) Rebecca Madson AST 232 Fall 2002

  2. MOND- an alternative to dark matter? • Mass discrepancies are observed in the universe • Popular explanation is Dark Matter- based on Newton’s laws • An alternative idea is MOND- proposed by Mordehai Milgrom (Professor of Theoretical Physics, Weizmann Institute in Rehovot, Israel)

  3. So why Dark Matter? • The idea of dark matter comes from the observation of galactic rotation curves • Rotation curves show relationship between velocity and distance from center of system

  4. Solid body rotation e.g. Merry-go-round

  5. Our Solar System

  6. The Milky Way

  7. How we get Dark Matter • Take Newton’s gravitational law and second law and equate to get: • M=V2r/G • Differentiate mass with respect to radius and solve for mass density • (r) =V2/4Gr2 • Can be modified to • (r) =C0/(a2+r2) -where a=2.8 kpc and C0=4.6x108 solar masses/kpc

  8. What is it? • All that we really know about Dark Matter is its gravitational effects- most of it does not radiate • Candidates for Dark Matter- MACHOs, WIMPs, and axions

  9. How MOND works • Modify Newton’s Second law • F=ma(a/a0) • Introduces a new parameter a0 10-8cm/s2 cH0/6 and (x) is a function where • (x)=x when x<<1 • (x)=1 when x>>1

  10. How MOND works cont’d • This can further show the modification from Newtonian gravitational acceleration gn to true gravitational acceleration g, expressed as • g(|g|/a0)=gn­ • and at a low acceleration • g=sqrt(gna0)

  11. How MOND works cont’d • If g=V2­/r and gn=GM/r2 • then we get: V4= GMa0 • Satisfies Tully-Fisher relation that implies M  V4

  12. Observational Support

  13. Look what else it can do!

  14. Problems with MOND • Created to fit data curves of observed material • Cannot be considered a theory -Not tied to Special Relativity • Less stable because it expects physical laws to be altered without the necessary ties

  15. Want to know more? • Here are some great sources for MOND: • Bingcang, Pamela. “How to Build a Galaxy: Aesthetics, Structure, and Content.” 27 April 2001. http://www.physics.rutgers.edu/~juxian/mond.doc • Milgrom, Mordehai. “Does Dark Matter Really Exist?” Scientific American. August 2002. • Sanders, R., McGaugh, S. “Modified Newtonian Dynamics as an Alternative to Dark Matter.” 30 April 2002. http://arXiv.org/abs/astro-ph/0204521 • MOND is such a current topic, that monthly papers are published on the subject in journals such as The Astrophysical Journal.

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