Relativity and Galaxy Rotation Speed

ahnbizcad 01/27/2015. 2 answers, 279 views
general-relativity dark-matter galaxies time-dilation galaxy-rotation-curve

If time travels slower nearer gravity wells, why can't the galaxy rotation speeds being faster on the outer edges than the inner areas be explained by relativity? What necessitates dark matter?

danshawen 06/17/2017
Never mind. Problem solved. Special Relativity has no effect at all on the gravitation of a rotating spiral galaxy, Lorentz contracted on the opposite rim of the galaxy or not.

2 Answers

Rob Jeffries 05/14/2016.

The necessity of GR to solving a particular problem can be assessed by calculating $GM/Rc^2$. Here, $M$ is the mass involved in producing a gravitational field at some separation $R$.

The rule of thumb is that if $(GM/Rc^2)\ll 1$ (i.e. is close to zero) then GR effects (time dilation) can be neglected roughly at that order of precision.

So if we take an object in a galaxy orbiting at $R$ of 10 kpc with a mass interior to its orbit of say $10^{11} M_{\odot}$, then $(GM/Rc^2) \sim 5\times 10^{-7}$. The redshift implied by this is of order 150 m/s, which is small compared with galactic speeds.

An interesting comparison would be the orbit of Mercury, where very small GR (i.e. non-Newtonian) effects are noticed with extremely careful measurements over many years (many orbits). Here, $(GM/Rc^2) \sim 3\times 10^{-8}$. So GR effects certainly can be detected at this level, but whereas Mercury is nearby and can be observed over many orbits, galaxies are far away and orbital periods are hundreds of millions of years. And in any case if you wanted to estimate the mass of the Sun using the orbit of Mercury and Newtonian gravity, your answer would be correct to several decimal places.

ahnbizcad 05/14/2016
very good information. M⊙ is earth mass? solar mass?
Rob Jeffries 05/14/2016
@ahnbizcad Solar masses - Download Hi-Res Songs

1 Martin Garrix

Yottabyte flac

Martin Garrix. 2018. Writer: Martin Garrix.
2 Alan Walker

Diamond Heart flac

Alan Walker. 2018. Writer: Alan Walker;Sophia Somajo;Mood Melodies;James Njie;Thomas Troelsen;Kristoffer Haugan;Edvard Normann;Anders Froen;Gunnar Greve;Yann Bargain;Victor Verpillat;Fredrik Borch Olsen.
3 Sia

I'm Still Here flac

Sia. 2018. Writer: Sia.
4 Blinders

Breach (Walk Alone) flac

Blinders. 2018. Writer: Dewain Whitmore;Ilsey Juber;Blinders;Martin Garrix.
5 Dyro

Latency flac

Dyro. 2018. Writer: Martin Garrix;Dyro.
6 Cardi B

Taki Taki flac

Cardi B. 2018. Writer: Bava;Juan Vasquez;Vicente Saavedra;Jordan Thorpe;DJ Snake;Ozuna;Cardi B;Selena Gomez.
7 Bradley Cooper

Shallow flac

Bradley Cooper. 2018. Writer: Andrew Wyatt;Anthony Rossomando;Mark Ronson;Lady Gaga.
8 Halsey

Without Me flac

Halsey. 2018. Writer: Halsey;Delacey;Louis Bell;Amy Allen;Justin Timberlake;Timbaland;Scott Storch.
9 Lady Gaga

I'll Never Love Again flac

Lady Gaga. 2018. Writer: Benjamin Rice;Lady Gaga.
10 Kelsea Ballerini

This Feeling flac

Kelsea Ballerini. 2018. Writer: Andrew Taggart;Alex Pall;Emily Warren.
11 Mako

Rise flac

Mako. 2018. Writer: Riot Music Team;Mako;Justin Tranter.
12 Dewain Whitmore

Burn Out flac

Dewain Whitmore. 2018. Writer: Dewain Whitmore;Ilsey Juber;Emilio Behr;Martijn Garritsen.
13 Bradley Cooper

Always Remember Us This Way flac

Bradley Cooper. 2018. Writer: Lady Gaga;Dave Cobb.
14 Little Mix

Woman Like Me flac

Little Mix. 2018. Writer: Nicki Minaj;Steve Mac;Ed Sheeran;Jess Glynne.
15 Charli XCX

1999 flac

Charli XCX. 2018. Writer: Charli XCX;Troye Sivan;Leland;Oscar Holter;Noonie Bao.
16 Rita Ora

Let You Love Me flac

Rita Ora. 2018. Writer: Rita Ora.
17 Diplo

Electricity flac

Diplo. 2018. Writer: Diplo;Mark Ronson;Picard Brothers;Wynter Gordon;Romy Madley Croft;Florence Welch.
18 Jonas Blue

Polaroid flac

Jonas Blue. 2018. Writer: Jonas Blue;Liam Payne;Lennon Stella.
19 Lady Gaga

Look What I Found flac

Lady Gaga. 2018. Writer: DJ White Shadow;Nick Monson;Mark Nilan Jr;Lady Gaga.
20 Avril Lavigne

Head Above Water flac

Avril Lavigne. 2018. Writer: Stephan Moccio;Travis Clark;Avril Lavigne.

Related questions

Hot questions


Popular Tags