tag:blogger.com,1999:blog-1195329121901897762.post3870480845670131822..comments2018-03-08T03:20:00.181-08:00Comments on Physics for my Mom: Galaxy rotation curvesHughhttp://www.blogger.com/profile/07207142714575405001noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-1195329121901897762.post-23507091524216687832010-05-06T14:03:22.883-07:002010-05-06T14:03:22.883-07:00Hi Hugh, nice piece of text.
Take a look at a dis...Hi Hugh, nice piece of text.<br /><br />Take a look at a disk like galaxy. Assume the mass density uniformly distributed but dependent on r: k(r). Assume the thickness of <br />the galaxy to be H. The amount of mass inside a sphere of radius r is the integral over r of k(r)*H*2pi*r. <br />If this density k(r) is constant this amount of mass would increase like r^2: K*pi*H*r^2.<br />This would result in a speed of: sqrt(G*K*pi*H*r^2 / r) = sqrt(G*K*pi*H*r).<br />This is not what we see in galaxies.<br />Is it possible that the mass density is not constant but steadily decreasing with r, like: k(r) = K / r ?<br />If that is the case the mass inside a sphere of radius r is: Integral ( K/r * H*2pi*r *dr) = 2pi*H*K*r.<br /><br />Hey, that could be something...<br /><br />Speed = sqrt (2pi*H*K*r / r) = sqrt (2pi*H*K) = constant, not dependent on r.<br />(Of course the speed is only constant at larger values of r. That is because near the center of the galaxy the mass distribution is <br /><br />different)<br /><br />What could explain that the mass density is proportional to 1/r ?<br />Suppose a uniform band of mass that is located near the center of the galaxy.<br />That means: The mass of a small ring = A*H*2pi*R*dr with A the mass density at this position R and dr the horizontal thickness of the <br /><br />ring (if the galaxy is supposed to lie on a horizontal plane).<br />Suppose for a reason that over a large number of years the radius of the ring grows from R to r.<br />This means that the original amount of mass in the original small ring is smeared out over a ring with a larger radius.<br />The total amount of mass in the larger ring is equal to the total amount in the smaller ring. <br />The new density of the expanded ring is thus: A*R/r which is proportional to 1/r.<br />If the density of rings of matter had always be nearly the same at a fixed radius R, the mass distribution over radius r is really <br /><br />proportional to 1/r if continuously new ring elements of matter keep growing their radius. <br /><br />How is it possible that the size of a mass ring could grow in time? <br />That is possible by assuming that every rotation of a piece of mass around the center causes exchange of angular momentum to and from <br /><br />the inner rings because of tidal effects (see: http://en.wikipedia.org/wiki/Tidal_acceleration). This is also the case with the moon <br /><br />that revolves around Earth. The radius of the moon orbit increases a few centimeters each year.<br /><br />If we watch a spherical rotating galaxy for a large number of years it will be flattened and stretched in horizontal direction <br /><br />because of the tidal acceleration effects. Around the outer layers of the galaxy the mass distribution is nearly uniform. This means <br /><br />that the mass density initially does not depend very much on r at large distance from the center. Because of the tidal acceleration <br /><br />the radiusses of rings of mass is growing resulting in a continuous passing of mass rings of equal density seen from a fixed radius <br /><br />R. <br />The described spherical galaxy results in a flat disc of matter uniformly distributed over the ring elements resulting in a mass <br /><br />density proportional to 1/r at larger values of r. <br /><br />When the source was an elliptically formed rotating galaxy rotating around an axis perpendicular to the long axis of the ellipse, <br /><br />i.e. the sides of the ellipse are visually rotating. Because of the same tidal accelleration effects the long axis of the ellipse <br /><br />stretches and the angular velocity decreases. This results in a spiral galaxy. <br /><br />Regards, ReneRenenoreply@blogger.comtag:blogger.com,1999:blog-1195329121901897762.post-84137448870594126882010-03-24T14:14:19.004-07:002010-03-24T14:14:19.004-07:00Dear Anonymous,
I'm not sure what you mean. T...Dear Anonymous, <br />I'm not sure what you mean. The matter contained within the arms would be included in the gravitational force felt by stars at larger radii, so that's already taken into account. To first order, the orbital velocity of an object is entirely determined by the amount of matter within the area swept out by the orbit. You can therefore approximate each location on the spiral arms as feeling the gravitational force of everything inside that location and nothing outside. <br />HughHughnoreply@blogger.comtag:blogger.com,1999:blog-1195329121901897762.post-54239517004823850472010-03-18T11:39:08.094-07:002010-03-18T11:39:08.094-07:00What would be the effect of the spiral arms spiral...What would be the effect of the spiral arms spiralling themselves (faster nearer the centre) on their rotation speed around the galaxy centre?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1195329121901897762.post-8288391192084165902009-08-09T08:26:36.722-07:002009-08-09T08:26:36.722-07:00I think your Mom would be interested know that Ver...I think your Mom would be interested know that Vera Rubin, the astronomer who pioneered the study of galactic rotation curves, took on that project because she was a pregnant post-doc and needed a short term (ha, ha) project to keep herself occupied while away from work. I know this because she lectured at the Hayden Planetarium a few years ago.Allen Everharthttp://allenev_at_hotmail.comnoreply@blogger.comtag:blogger.com,1999:blog-1195329121901897762.post-31082411500009776462009-05-13T15:41:00.000-07:002009-05-13T15:41:00.000-07:00I think I would like to know what the consequences...I think I would like to know what the consequences are of discovering or measuring dark matter. Also, does what you are doing have any relation whatsoever to things like the Hubble telescope or general space travel that people seem to be doing more and more of? Might your discoveries, for instance, give us an idea of the future of the universe as we know it?<br />xox MOMMomnoreply@blogger.com