Let's start by talking about Newton's First Law of Motion:

An object at rest will stay at rest unless acted upon by an unbalanced force. An object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

http://teachertech.rice.edu/Participants/louviere/Newton/law1.html

So let's look at the Moon as it orbits around the Earth.

So there's the Moon moving around the Earth (the black dot with the two arrows). Newton's First Law, if there was no other forces acting on the Moon, would follow the Forward Motion arrow - it would fly off happily, in a straight line at a constant speed, forever.

But it doesn't. Why is that?

Because there is another force acting on the Moon - which is the Pull of Gravity arrow. Earth's gravity, if there were no other forces acting on the Moon, would have it plunging down onto (and into) the Earth - resulting in the biggest collision the world has ever experienced.

Thankfully, the balance of the forces, the Moon's inertia and Earth's gravity, act on the Moon to keep it in orbit (one of my professors described it as "the Moon is continually falling towards the Earth and missing").

And so the interaction of the two forces creates accelerated movement - Earth's gravity constantly pulls on the Moon and that is the source of the acceleration (that constant change in direction).

So now to the Kepler portion of the question - it is true that orbits are slightly elliptical and not purely circular. In the case of the Moon, this ellipse is quite elongated compared to the orbit of the Earth revolving around the Sun. However, it is not the elliptical quality of the orbit that makes the orbiting motion accelerated motion.

https://www.ifa.hawaii.edu/~barnes/ASTR110L_S03/lunarorbit.html

All main sequence stars are undergoing fusion reactions in their core. The fusion reaction produces a pressure which counteracts gravity which is trying to collapse the star. When the forces are in balance the star is aid to be in hydrostatic equilibrium.

Smaller stars with masses below 8 times that of the sun are fusing hydrogen into helium during the main sequence. When the hydrogen fuel runs out the star collapses under gravity.

As the core collapses it heats up to the point when helium can start to fuse into carbon and oxygen. The outer layers of the star expand to become a red giant.

When the helium fuel runs out and the core is mainly carbon and oxygen, fusion processes stop as the core can't get hot enough to start carbon fusion. The star then collapses into a white dwarf.

Theoretically, if the universe lasts long enough the white dwarfs will cool down over billions of years to become black dwarfs.

Larger stars over 8 solar masses start by fusing hydrogen into helium. Fusion processes fusing helium into carbon and then fusing heavier elements progress almost seamlessly.

When fusion processes produce elements lighter than iron energy is released by the fusion reaction. Fusing reactions which produce elements heavier than iron require additional energy.

When the core is mainly iron no further fusion reactions can take place. The core then starts to collapse under gravity. The pressure in the core reaches the point where atoms can no longer exist and the protons get converted into neutrons. This releases vast numbers of neutrinos which cause the outer layers of the star to explode as a supernova.

The core of the star is then a neutron star. If the mass of the core is large enough the neutron star further collapses into a black hole.

When a star less than about 8 solar masses runs out of hydrogen and helium fuel, its core isn't hot enough to start carbon fusion. The core which consists of mainly carbon and oxygen collapses under gravity to form a white dwarf. Gravitational collapse is stopped by electron degeneracy pressure.

If the star is larger than about 8 solar masses it is able to fuse heavier elements up to iron. As iron fusion required energy rather than releasing it the fusion reactions stop and the stellar core collapses under gravity. It the core is more massive than the Chandrasekhar limit of 1.44 solar masses gravity overcomes electron degeneracy pressure atoms can no longer exist. Protons become neutrons and large numbers of neutrinos are emitted causing a supernova explosion. The star's core become a neutron star.

If a neutron star is spinning and has a strong magnetic field it emits radiation. As it spins at a precise rate the beam of radiation its the Earth periodically with a period of milliseconds to seconds. This is a pulsar.

If the stellar core is more than about 4 solar masses gravity overcomes neutron degeneracy pressure. Once the core collapses below its Schwarzschild radius, spacetime is curved to the point where not even light can escape. This is a black hole.

Most large galaxies have a supermassive black hole at their centres. These are in excess on hundreds of thousands of solar masses. If there is a good supply of gas and dust in the vicinity of a supermassive black hole it forms an accretion disc of material falling into the black hole. Material falling into the accretion disc gets superheated by friction and gravity to the point where it emits huge amounts of energy. This is a quasar.

So, all are similar in that they are formed from the remains of dying stars. Pulsars are a type of neutron star. Neutron stars and black holes behave similarly. The main difference between these objects is mass.

First of all the radius of a black hole is defined by its Schwarzschild radius #r_s#:

#r_s=(2GM)/c^2#

Where G is the gravitational constant, M is the mass of the black hole and c is the speed of light.

Curiously the radius of a block hole is directly proportional to its mass.

The first way a black hole can change over time involves Hawking radiation. In space, even in a vacuum, particle - anti particle pairs are constantly being produced. They usually quickly annihilate each other. Stephen Hawking predicted that if a particle - anti particle pair forms close to a black hole one particle can fall into the black hole and the other can escape. This process, known as Hawking radiation, causes the black hole to lose mass and it can ultimately evaporate.

If material falls into a black hole it will add to the black hole's mass and hence make it bigger.

Also, black holes can collide to form bigger black holes.

There are three types of black hole, each of which is likely to change differently over time.

Very small black hole were thought to have been created soon after the Big Bang. These are most likely to evaporate due to Hawking radiation.

Stellar black holes are formed by the death of a large star. It would take a very long time for them to evaporate by Hawking radiation and they are likely to gain material from their surroundings.

Supermassive black holes exist at the centres of galaxies. They are so massive that they are more likely to grow by consuming material or colliding with other black holes.

The electromagnetic force describes the interactions between charged particles. The photon mediates the force and is responsible for creating electric and magnetic fields. Electricity and magnetism were thought to be separate forces until Maxwell showed that they were related.

The weak nuclear force is responsible for radioactive beta decay. For example it can convert a neutron into a proton, an electron and an electron antineutrino. The weak nuclear force is mediated by the W and Z bosons.

The electromagnetic and weak forces have been unified into the electroweak force. It has been proved that at very high energies the photon and the Z boson are indistinguishable. It was the discovery of the W and Z bosons which confirmed the electroweak theory.

The residual strong nuclear force is responsible for binding protons and neutrons together to form an atomic nucleus. The force is mediated by gluons. The residual strong nuclear force is actually a residual effect of the colour force which binds quarks into mesons and baryons.

We don't yet have a Grand Unified Theory (GUT) which unifies the electroweak force with the strong nuclear force. There have been a number of GUT candidate theories. They require the discovery of new particles to confirm the theories. One problem is that the unification will happen at very high energies which would require particle accelerators which we don't have the technology to build.

The electromagnetic, weak and strong forces are described by quantum theories. There is no quantum theory of gravity. In fact Einstein showed that gravity is the result of the curvature of 4 dimensional spacetime by masses.

The unification of all four forces requires a Theory of Everything. This can't happen until we have a GUT and have a quantum gravity theory.

The problem with defining the length of a day is that there are several definitions.

The length of a day as measured by clocks is the mean solar day. It is exactly 24 hours long.

The sidereal day is the time it takes for the Earth to complete one rotation with respect to the fixed stars. It is about 23 hours 56 minutes.

The solar day is the period between two successive high noons. High noon being the moment the Sun is at its highest in the sky. It varies continuously from day to day due to the Earth's orbit being elliptical and due to the #23^@# axial tilt. Successive days vary in length by up to 20-30 seconds.

Solar days were traditionally measured using sun dials. When clocks were invented a correction factor needed to be added to sundial time to make it agree with clocks. The time difference is called the equation of time and the difference between clock noon and solar noon can be as much as 18 minutes.

The graph shows the equation of time. The orange curve is the difference due to the Earth's orbital eccentricity. The green curve shows the difference due to the axial tilt. The blue curve is the sum of the other two curves which is the equation of time.