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On Galaxies and Gravity.
On Galaxies and Gravity.
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On Galaxies and Gravity.
03/08/2016 18:14:37 »
Observations of the Andromeda galaxy in 1975 by Vera Rubin led to the unexpected finding that, within experimental error, the stars within the spiral galaxy all orbited around its central point at the same ‘constant velocity’, what ever their location was in the galaxy. The observation was totally at odds with observations of our own planetary system, where planets orbit around the Sun at different velocities, dependent upon their distance from the Sun.
The ‘orbital velocity’ of a planet in our solar system is reliant upon the balancing of two opposing forces. The first is the gravitational force of attraction, defined either by Newton or Einstein, which exists between a planet and the Sun and the second is the ‘kinetic energy’ of the planet relative to the Sun, whose magnitude enables it to counteract the gravitational force between the two bodies of matter. This velocity of the planet is called its ‘orbital escape velocity’, for if it is slowed down, the planet will spiral into the sun and if it is increased, it will propel itself out of the solar system. The fact that the planets have ‘kinetic energy’ raises the question of ‘how did they amass it in the first place’. In its own way, ‘kinetic energy’ is as big a mystery to explain as gravity.
This simple model of our solar system defines the Sun’s gravitational field as being the dominant force, with its strength being inversely proportional to the square of the distance from its surface, a factor that becomes more important when we move on to tackle galaxies. Those planets, like Mercury and Earth, being nearer to the Sun, are required to orbit with a faster velocity than those further from the Sun. The gravitational attractions between the orbiting planets are relegated to a marginal role, being confined to creating small perturbations in the orbits of other planets. And this is what we observe.
But a galaxy is a completely different animal from our planetary solar system, being comprised of around a billion stars, generally arranged in either an elliptical or spiral structure. To progress to an explanation of Vera Rubin’s finding, we need to visualise the galaxy’s beginnings from a massive cloud of hydrogen gas. Any ‘gas cloud’ located in the vastness of space has no boundaries to contain it and over time the kinetic energy incorporated within each hydrogen atom will enable it to diffuse towards a state of having an even density throughout. This is an assumption, but it seems to be a reasonable one.
The next step in the formation of a galaxy is the joining of hydrogen elements into molecules and this happens throughout the hydrogen gas cloud. The formation of molecules enables gravity to kick in and it overcomes the inherent kinetic energy of a hydrogen molecule and triggers the process of forming a star. This process does not start just in one place within the gas cloud, but at locations all over its surface area. Each star attracts the hydrogen molecules around itself, growing in size as it does. The boundary to its growth is the availability of more hydrogen molecules, but as each star is creating a vacuum around itself at the same rate, then each star becomes limited in its growth to reach a set size.
This is where the statistical ‘law of large numbers’ plays a part, for if a process is repeated many times, in this case billions of stars forming in the same environment, each star will grow to a common size, distributed as a ‘normal curve’ around a mean value. The fully formed stars are evenly spread throughout the expanse of space that was originally occupied by the ‘gas cloud’. This is the ‘young galaxy’, with no ‘black holes’ yet in existence.
Unlike our solar system, the magnitude of the gravitational field is exactly the same over the whole galaxy. Each star attracts it neighbours with equally force creating an equilibrium of forces all around itself. The reduction of the gravitational force proportionately with the ‘square of the distance’, means that individual stars are primarily affected by their immediate neighbours and largely unaffected by those stars that are light years further away. This makes the whole galaxy a stable structure, but still flexible to the movement of stars within it. If it wasn’t flexible at all, then the whole galaxy structure would rotate like a spinning plate, with the outer stars circling at the fastest speed and the centre star just rotating slowly upon its axis at a central position in space. The complete opposite of our solar system.
But gravity plays only a limited role in the rotational velocity of the stars within the galaxy. This is the preserve of their ‘kinetic energy’. The kinetic energy of each and every star comes from the original kinetic energy inherent in the hydrogen atoms that formed the original gas cloud. Energy can neither be created nor destroyed, so the kinetic energy of the hydrogen atoms is transferred to the hydrogen molecules and accumulated by each star as it grows to its mature size.
As each and every star follows the same formation process and grows to have a similar mass, so they have all incorporated the same amount of ‘kinetic energy’ and as a consequence move with the ‘same velocity’. But they are not free to travel in any direction, as they are bound together by the gravitational attraction of their neighbouring stars. This causes them to move in a circular pathway around the galaxy’s central point, but they all move with the exactly the same velocity.
There is an underlying assumption here that the magnitude of the kinetic energy of a star counteracts the gravitational force between a star and its neighbours. This is its ‘orbital escape velocity’, for like the planets orbiting the sun, if its velocity is too fast or to slow, the star would propel itself out of the galaxy or spiral in to collide with neighbouring stars. The result would be either a scattering of the stars throughout space or the creation of one star built from a billion others!
Using the analogy of runners on an athletics track, all running at the same speed but in different lanes, the stars in the outermost layer of the galaxy take longer to travel around the outer circumference of the galaxy, whereas the stars in the inner layers take less time and so there is a constant process of overtaking by the inner stars over the outer stars. The closer the stars are to one another, the less obvious this overtaking process is, but it takes place from the outside layer through to the centre of the galaxy with stars changing locations and moving on from the gravitational influence of one set of stars to that of the next set of stars, driven by their kinetic energy.
Although this provides an explanation for Vera Rubin’s observations that all stars within the Andromeda galaxy orbit with a constant velocity, it takes no account of the galactic ageing process, whereby stars become ‘red giants’ and subsequently collapse into ‘black holes’. As Andromeda is not a young galaxy, it is reasonable to assume that black holes have minimal effect upon the gravitational field of the galaxy. This can be seen to make sense, if a black hole is created from just one star, as the constituent matter of that star can only create the same gravitational force as its younger entity, less even, if some of its matter is flung out of the confines of the galaxy during its ‘super novae’ explosion. But ‘black holes’ are rogue entities within a galaxy and their enhanced kinetic energy from a super novae explosion can set them ploughing random paths through the galaxy’s stars, but not enough to upset the gravitational status quo.
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Re: On Galaxies and Gravity.
Reply #1 on:
03/08/2016 18:47:21 »
I have only read about halfway through your post but need to point something out. Planetary orbital velocity is not as simple as you stated. If we take an arbitrary circular orbit with velocity v and reduce v then gravitational acceleration would change the orbit from circular to elliptical. Since closer orbits require an increase in speed. This will happen due to the acceleration. So you wouldn't necessarily have a planet spiral into the central star. If we increase v by some arbitrary speed we would need this increase to match the escape velocity otherwise we again end up with an elliptical orbit. I will finish reading the rest when I get time.
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Re: On Galaxies and Gravity.
Reply #2 on:
20/08/2016 14:31:31 »
Posted by: jeffreyH
« on: 03/08/2016 18:47:21 » Quote (selected)
"I have only read about halfway through your post but need to point something out. Planetary orbital velocity is not as simple as you stated. If we take an arbitrary circular orbit with velocity v and reduce v then gravitational acceleration would change the orbit from circular to elliptical. Since closer orbits require an increase in speed. This will happen due to the acceleration. So you wouldn't necessarily have a planet spiral into the central star. If we increase v by some arbitrary speed we would need this increase to match the escape velocity otherwise we again end up with an elliptical orbit.
Rockets launched from the earth's surface where our gravity is at a maximum, need to reach an 'escape velocity' in order to put satellites into orbit within the 'earth's gravitational field'.
Every planet in the solar system planets already moves at its 'solar escape velocity', as they orbit within the sun's gravitational field. Slow a planet down and the sun's gravitational pull will overwhelm the planet's reduced centrifugal force pulling it inwards in a spiralling motion, into ever increasing levels of gravitational pull from the sun, forcing it into a head on collision with the sun.
Speed the planet up and the planet's increased centrifugal force will overwhelm the sun's gravitational pull and cause it to spiral outwards into lower levels of the sun's gravitational field, eventually causing it to leave the solar system altogether, presuming it misses all the other orbiting planets on its way out.
The shape of an orbit, whether elliptical or circular is only relevant to Vera Rubin’s measurement of a star’s ‘average orbital velocity’, in so far as it affects the distance the star travels before returning to its start position within the galaxy. For Vera Rubin and her team to measure the 'average orbital velocity' of a star within the Andromeda galaxy, they only needed to measure the time taken for each star to return to its same relative position as seen from earth and then make an estimate of the distance it had travelled around the circumference of its orbit within the galaxy.
This is where there is room for experimental error, as the distance travelled is dependent upon the shape assumed for the orbit of the star. For a circular orbit the estimated perimeter distance is based upon the distance of the star from the centre of the galaxy and for an elliptical orbit, it is based upon the lengths of the major and minor axes. The ‘average orbital velocity’ of the star, which she plotted upon her graph, is measured by dividing the distance the star is estimated to have travelled around the perimeter of its orbit, by the measured time taken to traverse this orbit.
Her results showed that within experimental error, each star travelled around its orbit at the same ‘average velocity’ or as she expressed it, the same ‘constant velocity’.
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