Could the Gravitational Lensing Effect Explain the Galactic Rotation Anomaly?

[meemoe_uk]

Hey, so this interest in the galactic rotation anomally I've got.
I was reading that, according to GR, black holes kinda wrap space-time around with 'em, yeah? , and really all objects that rotate wrap space time around 'em ( not that much though ). In fact NASA are testing this GR prediction right now with GravityProbe B, by observing 3 spinning gyroscopes which are in orbit around the Earth.
Now, is it possible that this wrap around thing could be having a large effect on the galaxy?
If the galaxy's wraping space time around with it, then obviosly stars would have a relatively slow orbit velocity. Really it's just a question of magnitute of this wrap around effect. Does anyone know if it could be strong enough?

 

[youtube2010]

I also have a query about galactic rotation. Apparently the rotation curve of galaxies
is more flat than Newtonian mechanics predicts. So the current theory adds dark matter
to the list of astronomical materials. My interest is how the dark matter flattens the
rotation curve of galaxies but not planetary orbits. If dark matter is everywhere how
come it only flattens large scale rotation and not all rotation?

 

[Jonathan Scott]

Hey, so this interest in the galactic rotation anomally I've got.
I was reading that, according to GR, black holes kinda wrap space-time around with 'em, yeah? , and really all objects that rotate wrap space time around 'em ( not that much though ). In fact NASA are testing this GR prediction right now with GravityProbe B, by observing 3 spinning gyroscopes which are in orbit around the Earth.
Now, is it possible that this wrap around thing could be having a large effect on the galaxy?
If the galaxy's wraping space time around with it, then obviosly stars would have a relatively slow orbit velocity. Really it's just a question of magnitute of this wrap around effect. Does anyone know if it could be strong enough?

This sort of effect is well understood, and is far too small to be relevant.

All gravitational effects on the shape of space are really tiny except very close to extremely large masses. In general, if the Newtonian gravitational acceleration is g, then the corresponding radius of curvature of space is c²/g, so for example near the surface of the Earth the radius of curvature of space due to Earth's field near the surface of the Earth is about 10¹⁶m, about a light year.

The acceleration of the sun due to the galaxy is much smaller. From the Wikipedia article on "Milky Way" I get that the sun's speed around the galaxy is about 220km/s and the radius of its galactic orbit is about 25000 light years. From those figures, I make it that the acceleration g = v²/r is something like 2*10^-10 m/s² in which case the radius of space curvature c²/g is something like 4*10²⁶m, which is something like 40,000,000,000 light years. As the Milky Way diameter is about 100,000 light years, that radius of curvature is about 400,000 times larger than the Milky Way.

 

[Jonathan Scott]

I also have a query about galactic rotation. Apparently the rotation curve of galaxies
is more flat than Newtonian mechanics predicts. So the current theory adds dark matter
to the list of astronomical materials. My interest is how the dark matter flattens the
rotation curve of galaxies but not planetary orbits. If dark matter is everywhere how
come it only flattens large scale rotation and not all rotation?

Dark matter would be very thinly distributed, unlike normal matter which is clumped into stars and planets with huge gaps in between, so it doesn't have any measurable effect locally.

Dark matter would have a significant effect overall on how star systems (such as our solar system) move around the galaxy, especially systems towards the edge of the galaxy, but within those systems all of the component objects are affected equally, so the system as a whole follows a different path, just as if the core of the galaxy was somewhat more massive, but the internal dynamics of the system are not affected.