Two factors account for the composition of the cores of the inner planets of our Solar System: which elements are most abundant, and which ones are least likely to converted to volatile materials or oxidized to low-density compounds.

Let's look at abundances. According to http://www.knowledgedoor.com/2/elements_handbook/element_abundances_in_the_solar_system.html, the folleing are the top fifteen elements in abundance in our Solar System:

1. Hydrogen
2. Helium
3. Oxygen
4. Carbon
5. Neon
6. Nitrogen
7. Magnesium
8. Silicon
9. Iron
10. Sulfur
11. Argon
12. Aluminum
13. Calcium
14. Sodium
15. Nickel

This list, persented in rank order, covers most of what we see on Earth. But which ones then find their eay into planetary cores?

First a "core" element has to form nonvolatile, solid materials. This rules out hydrogen, helium (which is almost entirely within the Sun anyway), oxygen, neon (a major component of the Moon's tenuous atmosphere), nitrogen and argon. Sulfur is an intermediate case, as it can form volatile materials like sulfur dioxide but also nonvolatile ones like sulfate salts or metal sulfides, so let us keep that "in the running" for now. Ditto for carbon.

Next, a good "core" element should resist forming oxides with all that oxygen floating around. Of the fifteen elements listed above, oxygen stands out for being especially reactive, forming one type of compound or another with at least eleven out of the other fourteen and all nine that survive the nonvolatility test (above). Such compounds, where they are solid, tend to have relatively low densities and tend to float atop a heavy metal planetary core.

Which elements, among those that are not inherently volatile, are most likely to resist this reactivity and remain as heavy metals? Not magnesium, calcium or sodium. Alkali and alkaline earth elements are highly reactive towards oxygen. So are aluminum and silicon. We find these elements on Earth primarily combined with oxygen, as rocks formed from silicate minerals.

What is left? Carbon, iron, sulfur and nickel. Carbon can form metal carbides like the iron carbide that strengthens most steels. But first the metal has to be there; carbon is playing only a secondary role. Moreover, carbon also gets "lost" as other things like coal, carbon dioxide (there's that oxygen again), and carbonates (oxygen, alkaline earth metals). Likewise for sulfur, which does appear to form some metal sulfides down there.

And so, we have iron and nickel as the mahor core components, with iron being more abundant and thus tge majority.

In reality no two bodies orbit each other. They actually orbit the centre of mass of the system which is called the barycentre.

The Earth and Moon both orbit about their centre of mass called the Earth-Moon barycentre.

In the case of the solar system, the Sun and all of the planets and other bodies always orbit around the Solar System Barycentre (SSB).

So, the focus of the Earth's orbit is the SSB which is in constant motion.

The position of the SSB is constantly changing. It can be anywhere between the centre of the Sun and two solar radii from the centre of the Sun. This depends on the relative positions of the planets and other bodies.

The diagram shows the position of the SSB over a period of decades.

Electromagnetism the the force which describes the interactions between charged particle. It is mediated by the photon.

Electricity and magnetism were originally thought to be separate forces until they were unified. Maxwell's equations describe electricity and magnetism.

Quantum Electrodynamics (QED) completed the picture by describing how electrons move in atoms.

The weak nuclear force is responsible for radioactivity and aspects of nuclear fission and fusion. It is propagated by the W and Z bosons. Typical weak interactions convert a proton into a neutron, a positron and an electron neutrino or a neutron into a proton, an electron and an electron anti-neutrino.

#p -> n + W^+# then #W^+ -> e^+ + nu_e#
#n -> p + W^-# then #W^(-) -> e^(-) + bar nu_e#

The electromagnetic force and the weak nuclear force were unified by the electro-weak theory.

The strong nuclear force is not really a force. The colour force also known as Quantum Chromodynamics (QCD) describes how quarks are bound together in protons, neutrons, mesons and other baryons. It is propagated by the gluon. The strong force is a residual effect of QCD operating at distance greater than the size of protons and neutrons.

Attempts are being made to create a Grand Unified Theory (GUT). Which unifies the electro-weak theory with QCD. A GUT is going to take some time to produce and verify.

This leaves gravity which actually isn't a force. It is the result of curved space time as described by Einstein's General Relativity.

A Theory of Everything (TOE) is required to unify a GUT and gravity. This is a long term goal.

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

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.

It is impossible to know what happens after the event horizon of a black hole because no information can escape from its mighty grasp.

The physics of what happens in black holes are one of the greatest mysteries science faces. But we do have some clues as to the nature of these magnificent puzzles.

Hawking radiation: small amounts of radiation predicted to be emitted by black holes.
This picture, specifically case three, depicts how Hawking Radiation works.

The existence of Hawking radiation is crucial because without it the temperature of black holes should be absolute zero, which is not possible due to the laws of thermodynamics.

Curvature of light as it passes near the black hole
This is a result of the super-high gravitational effects of a black hole. We know that light is curved as it passes near a black hole. From this we can deduce that the mass and relative gravitational effects of black holes are massive.

Since we can detect the effects of black holes on nearby matter, we have a pretty good idea that they do indeed exist. However, understanding what happens within them after the event horizon is something that we currently do not know.