Anyone who has listened to a train approaching and passing on a track has been aware of the change in sound pitch that occurs. This effect is known as the Doppler Shift, and is well understood for all types of waves, including sound and light.

The image is meant to show that if the wave source is moving toward us, the waves will be compressed ahead of the source, and a high frequency is heard. Behind the source, the observed pitch is lower than that of a stationary source. The faster the source moves, the greater the change in pitch that is observed.

With light, the effect is not in pitch, but colour. If a source of light moves toward an observer, the waves will be shorter in wavelength and higher in frequency. The light will appear to be shifted toward the blue end of the spectrum. If the source is moving awat from the observer, the shift in frequency causes the colour to appear more red. As in the case of sound, the faster the source moves, the greater the change in colour that is observed. This is the red shift that is seen in all galaxies.

So, to finally answer your question, when we measure the light from more distant galaxies, we routinely note larger shifts in the colour of the light they emit. This tells us they are moving at greater speed than the galaxies that are "close by".

Until recently any body orbiting the Sun was called a planet. When Pluto was discovered it was naturally given planet status.

Curiously the asteroid Ceres was discovered it was initially given planet status. Ceres was discovered long before Pluto. It was however discovered that Ceres was one of many bodies orbiting between Mars and Jupiter. All of them, including Ceres, were designated asteroids.

More recently, other bodies such as Eris, have been discovered. The International Astronomical Union (IAU) voted on a more format classification system. There are three requirements for a body to be a planet.

First, the body must be orbiting the Sun. This excluded the larger moons such as Titan and Charon.

Second, the body must be in hydrostatic equilibrium. This means it must be spheroidal in shape due to its gravity.

Thirdly, the body must have cleared its orbit of other bodies, except for moons.

The IAU created a new classification called Dwarf Planet which meet the first two criteria but not the third. This lead to the demotion of Pluto to Dwarf Planet. Four other bodies, Ceres, Haumea, Makemake and Eris were promoted to Dwarf Planet status.

The decision was controversial. Many people, including myself, still regard Pluto as a planet.

Galaxies come in a variety of shapes and sizes. We will first talk about what gives some galaxies their spiral shape.

The most notable scientist who studied the formation spiral galaxies was Bertil Lindblad. He observed the spiral arms seen in spiral galaxies. He quickly realised that spiral arms couldn't be sustained and there must be some sort of mechanism that allowed the spiral arm to be stable. To sustain these spirals we'd have to ignore the laws of physics as the stars at the tips of the spiral arms would have to travel faster than the stars near the centre, but of course, in reality, objects move faster when they are closer to the point they are orbiting. The angular rotational speed was so great and the distance of the spiral arms with to the centre of the galaxy varied, the spiral arms would've compressed more and more each time the galaxy rotated like taffy in a taffy machine. This is called the winding problem. This problem still has not been solved, but there are two leading hypotheses:

1. The spiral arms are created from density waves in the galactic disc - one theory is that the spiral arms are created from density waves travelling through the galactic disc. Stars pass in and out of these waves filling in what we see as spiral arms. Stars accelerate when they move towards a density wave when it is headed for them and slow down as they move
2. SSPSF (Stochastic Self-Propagating Star-Formation) model - this theory suggests that in the initial star formation in a galaxy causes a shockwave which causes more star formation. So the idea is that the galaxy's rotation forms these newborn stars into the spiral arms we see, and this cycle repeats.

Courtesy Astronomy Online: This shows how the windup problem affects the shape of a galaxy.

The shape of Elliptical galaxies ranges from extremely flat to more spherical. The shape of Elliptical galaxies are created from collisions between numerous galaxies. After all these collisions in the course of a few hundred million to a few billion years the stars settle to form the featureless elliptical galaxies.

https://en.wikipedia.org/wiki/File:Andromeda_and_Milky_Way_collision.ogv
Courtesy NASA: Visit this link to see how elliptical galaxies form. At the end, we see how the collision between the Milky Way and Andromeda forms an Elliptical galaxy.

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Irregular galaxies are formed from violent collisions between two or more galaxies which redistributes interstellar matter, dust and stars e.t.c. to form a chaotic mess. This chaotic mess eventually settles to form an elliptical galaxy. Here's a picture of an Irregular galaxy if you were wondering what it looks like.

Courtesy NASA, ESA and HST

It is not actually true to say that the planets orbit the Sun and the Moon orbits the Earth. The Earth and Moon both orbit around their centre of mass which is called the Earth Moon Barycentre (EMB).

Likewise the Sun and the planets orbit around the centre of mass of the solar system. This is called the Solar System Barycentre (SSB). The SSB is in constant motion and moves between the centre of the Sun and about a solar radius outside the Sun. The diagram shows the motion of the SSB over several decades.

The Sun also orbits around the centre of the galaxy. This is even more complex. In principle all of the stars will orbit around the centre of mass of the galaxy. This will be in the galactic bulge which contains a supermassive black hole.

The motion of stars in the galaxy is complicated by the fact that some stars, particularly on the edges of the galaxy, move in a way which gravity can't describe. There isn't enough visible mass to account for their motion.

It is now thought that galaxies contain a lot of dark matter. This interacts only through gravity and is otherwise invisible. We would need to know the mass and distribution of this dark matter to define what the Sun actually orbits around.

According the Kepler's laws of planetary orbits, a planet is moving at its fastest at perihelion. It is moving at its slowest at aphelion.

Currently the Earth is at perihelion around 3 January and at aphelion around 3 July. The actual time of perihelion varies from year to year by a few days - usually between 2 and 4 January. The reason for this being that the Earth's orbit is constantly changing due to the gravitational effect of the other planets.

Also, perihelion is getting progressively later due to precession. It gets later by about a day every 70 years.

A solar day is the time between two successive solar noons - the time when the Sun is at its highest in the sky. The difference between solar noon and clock noon is defined by the equation of time. This has two components, one due to the Earth's orbit being an ellipse, the other due to the Earth's axial tilt.

The diagram shows the equation of time. The solar day is currently at its longest in December around the time of the solstice.

We might be better dealing with these the other way round - firstly it was noticed, shortly after we discovered that the many ‘clouds’ (nebulae) we noticed in the night sky were actually galaxies, that they were spinning. This was discovered by using the Doppler effect on spectroscopic images of galaxies, which showed one side of a galaxy approaching us and the opposite side receding.

So far, so happy, they spin. Then Fritz Zwicky, whilst examining the Coma cluster of galaxies in 1933, spotted that the galaxies were spinning too fast for the visible matter to generate sufficient force to hold them together. This was confirmed in the 1970’s by Vera Rubin Cooper, specifically, the outer rim of the galaxies would be expected to rotate much slower than the centre according to Newtonian mechanics. This was not observed, the rotational curves were almost “flat” in the outer reaches of galaxies.

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This allowed for two possibilities: (a) Newton’s theory of universal gravitation was wrong (b) there existed vast quantities of ‘dark’ matter. Nobody seriously believed (a) so we were left with the hypothesis that a dark matter “halo” surrounded each galaxy.

Now for the second part (your first) we have searched for the particles that might make up dark matter very hard (a Nobel prize almost certainly awaits the discoverers) but despite many year stars of searching (both in space and in particle physics labs) nothing has been found that could possible fit the bill.

Neutrinos of various sorts have been proposed, as have exotic matter, stable quarks groupings, dead stars, black holes etc etc. Martin Rees (Astronomer Royal at the time) even went so far as to suggest that it could be unread copies of the Astrophysical Journal! We genuinely have no idea and it bugs us. A lot.

It appears that this stuff outweighs visible matter by a factor of about 5:1 across the universe and you have as much idea what it is as they do. In my view this makes it an excellent time to be studying either cosmology or particle physics, because I hope major discoveries are just around the corner.