# General Astronomy/Basic Astrophysics

## Newtonian Physics

Isaac Newton formulated the Universal Law of Gravitation, the Laws of Motion, and calculus. The Universal Law of Gravitation is summed up in the formula

$F=\frac{GM_1M_2}{D^2}$

where $M_1$ and $M_2$ are two masses, in kilograms, and $G$ is the gravitational constant $6.67\cdot10^{-11}\frac{Nm^2}{kg^2}$. $D$ is the distance between the centers of the two masses, in meters. $F$ is measured in Newtons.

Work is calculated with the formula

$W=FD$

where $W$ is work (measured in Joules), $F$ is force (measured in Newtons), and $D$ is distance (in meters).

Kinetic energy (energy of motion) is calculated by the formula

$K=\frac{1}{2}MV^2$

where $M$ is mass (in grams), and $V$ is velocity.

Newtonian relativity: A man is walking at 1 km/h, and he throws a ball at 3 km/h. To get the speed of the ball, simply add speeds: $1 km/h + 3 km/h$.

The First Law of Thermodynamics states that energy can be neither created nor destroyed, only transformed into one of its two forms: energy and matter.

## The Four Forces

There are four forces in the universe: gravity, which holds together galaxies and other massive structures; the electromagnetic force, which holds atoms together; the nuclear force, which holds atomic nuclei together; and the weak force, which is concerned with the transmutation of elements and radioactive decay. The nuclear force is the strongest, and gravity is the weakest. Without these forces, the universe would disintegrate.

The gravitational force causes mass to attract mass. More massive objects have a stronger gravitational field.

The electromagnetic force can be summed up by the phrase "opposites attract" and allows atoms to bond with each other creating the great variety of compounds that make our experience possible. The nucleus, with its positive charge, attracts negatively charged electrons. The electro- static force is calculated according to Coulomb's Law.

The power of the nuclear force depends on distance. At a distance of between one and 2*10-15 meters, the force is attractive. However, if distance is too close (less than 10-15 meters), the force is repulsive; and at distances greater than 2*10-15 meters, the force diminishes to zero.

## Atoms

The atom was first postulated by the Greek philosopher Democritus. He believed that matter could not be split indefinitely. He believed that all matter was composed of connected particles which could be split apart, but could not be split themselves. These indestructible pieces are called atoms. The word comes from the Greek atomos, which means "uncuttable"---a (not) + tomos (to cut). [1]

The Periodic Table of Elements was created by Dmitri Mendeleev in 1869 (revised in 1871). The manmade elements are radioactive and have short half-lives.

Nuclear reactions are categorized as critical or supercritical. A critical reaction is one neutron in, one neutron out. A supercritical reaction is one neutron in, three neutrons out---releasing a terrific amount of energy. Supercritical reactions are used in atomic weaponry.

Nuclear fusion is a great source of energy, but requires temperatures of 1,000,000 Kelvins.

## Particles

All atoms are composed of particles. Particles are characterized by mass, charge, and spin. A particle's spin is right-handed (counter-clockwise) or left-handed (clockwise).

At the center of the atom is the nucleus, which contains a number of protons and neutrons about which the Electrons orbit. The force that keeps the electrons in orbit is the electric force; the force that keeps the nucleus together is the nuclear force.

In a neutral atom, there are equal amounts of protons and electrons. For example, Helium has two protons in its nucleus and two electrons orbiting its nucleus. It also has two neutrons in its nucleus. When there is more electrons than protons, or vice versa, then the atom is called an ion and it is more reactive with other ions and atoms because it has an overall net charge associated with it.

An electron has a negative (-) charge, a proton has a positive (+) charge. Neutrons, neutrinos, and photons have no charge. The most massive of these is the neutron; it can decay into a proton, electron, and a neutrino. Particles are made up of quarks. The six types of quarks are up, down, strange, charmed, top, and bottom.

Antimatter was predicted by Paul Dirac. Every particle has an anti-particle, with the same mass, but an opposite charge and spin. There are anti-electrons/positron, anti-protons, anti-neutrinos, and anti-photons. (The anti-photon has the same spin as the photon.) When a particle meets its anti-particle, the result is mutual annihilation, and the creation of energy. The opposite is also true: when two photons meet, matter is created. This creation of matter is called "pair production".

If there are antimatter stars; their light would be identical to that of matter stars, because the anti-photon is the same as the photon.

Astronomy studies the flow of energy, and forces. Energy comes primarily from two sources: gravity from gaseous clouds collapsing to form stars and planets; and nuclear energy. The fusion that makes stars burn is one type of nuclear energy; another is the radioactive decay that heats the cores of planets.

Earth has a magnetic field. The core has a current. This field causes the Aurora Borealis.

The relationship of frequency and wavelength to the speed of light is shown in the formula

$f\lambda=C$

where $f$ is frequency, $\lambda$ is wavelength, and $C$ is the speed of light.

A photon is a discrete packet of light energy. To calculate the energy of a photon, use the formula

$E=hf$

$h$ is Planck's constant:

$6.63\cdot10^{-34}J\cdot sec$

$f$ is frequency, which is in units of $\frac{1}{sec}$

Einstein's famous equation, $E=MC^2$, demonstrates that mass and energy can be converted into each other. $E$ is energy, $M$ is mass, and $C$ is the speed of light, $3\cdot10^8m/s$.

## Spectroscopy

"The one thing that man will never know is the chemical composition of the stars." ---Auguste Comte, 19th century philosopher

He was wrong!

Kirchoff & Bunsen discovered that individual elements burn with different colors. Different colors correspond to different wavelengths of light. The colors given off can be recorded on a photographic plate. This is called the elements' emission spectrum and it is unique to each and every known element. Therefore, any known element in the laboratory can be determined by investigation of its "spectra".

An explanation of why different elements give off different wavelengths of light is needed to explain how the composition of stars can be determined. An individual element has a unique number of protons. If you were to follow the periodic table from left to right, you would find that for the first few lines the atomic number increases by one each time. Hydrogen is the smallest element as it has one proton. Helium is the next smallest, as it has two protons, and so on.

Each of these elements therefore has a different amount of electrons and protons. Assuming these elements are all neutral, each successive element consists of one more electron than the previous element. i.e. helium has two electrons, and hydrogen has one.

Electrons orbit the nucleus of an atom. They can be described as having an energy level associated with them. The electrons in a particular element can only occupy a specific energy level or shell. When elements are heated, there is an input of energy, which is distributed to these electrons and they therefore move to a higher energy level. When this electron falls back to its original energy level, the energy gained by heat must be lost. The electron loses this energy by emitting a photon(a packet of light).

This photon will have exactly the right amount of energy needed to enable the electron to fall to its exact original state. This energy can be calculated using E=hf, where E is the energy, h is Planck's constant, and f is the frequency of the individual photon. While it seems odd that a particle would have a frequency, it does due to wave-particle duality.

From above, it can be seen that each element, because each has electrons that only occupy certain energy levels, that the frequency of the photon emitted can only have certain values.

From the equation c = f * lambda, where c is the speed of light, which is nearly always the same, f is the frequency and lambda is the wavelength, it can be seen that because c is constant, each element, by only emiting photons with certain frequencies, gives off photons with certain wavelengths and therefore colors.

It is impossible to use the laboratory technique of defining elements by using their emission spectrum because the light that we receive from the stars is a combination of colors. There is however, another way. If we were to view the emission spectra of the sun, for example, there would be no signature "barcodes" of individual elements, rather, there would appear a continuous spectrum, like a rainbow on paper. This "continuous" spectrum will have a few black lines, where the wavelength of light has been absorbed rather than been emitted by the Sun's photosphere. It is from these, that we can deduce a stars chemical composition.

It was discovered that the black lines in the continuous spectrum of a star corresponded exactly to the emission lines of certain elements. Their presence in the star is suggested because those elements emit light of the same wavelength that is absorbed and hence, shows as a telltale black line. It receives this light in a concentrated beam but emits it in all directions. If you imagine the light rays as a 20 pack of javelins hitting an element in a certain place, the element will throw these javelins back out individually, into the surroundings so that the amount of light emitted in the direction of Earth is minute or non-existent, and hence we observe dark lines in the emission spectrum.

## The Quantum Model of the Atom

Quantum physics is a relatively new branch of physics that deals with very small objects, such as atoms and quarks. It follows different rules than classical (or "Newtonian") physics. While Newtonian physics assumes that energy can be continually divided and holds that an object can have an arbitrarily small amount of energy energy, quantum physics deals with objects that emit or absorb discrete packets of energy known as quanta that cannot be further divided. Classical physics assumes a continuum whereas quantum physics assumes the universe is discrete.

Max Planck is considered the "father of Quantum Theory".

In 1913, Danish physicist Niels Bohr used Ernest Rutherford's research on the atomic nucleus and Max Planck's quantum hypothesis to create a quantum theory of atoms. This theory stated that an atom's electrons move only in definite orbits. When a hydrogen atom emits an Hα photon, the electron drops to a lower orbit. When a hydrogen atom receives a photon, it jumps to a higher orbit.

Niels Bohr's model of an atom.

The hydrogen spectrum has been studied for ultraviolet (the Lyman series) and visible light (Balmer series). In the Lyman emission series, the electron drops from a higher orbital to the n=1 orbit. In the Balmer emission series, it drops from a higher orbital to the n=2 orbit. (n=1 is the lowest energy state, or orbit, of an electron, called the principal quantum number.) The energy change produced as an electron moves from n=2 to n=1, results in the emission by the electron of a photon of energy 10.2 eV and appears in the ultra-violet part of the spectrum. The energy change produced as an electron moves from n=3 to n=2, results in the emission (H-alpha) by the electron of a photon of energy 1.89 eV and appears in the red part of the spectrum.

The energy levels in a hydrogen atom, can be calculated by: $E_n = \frac {-13.6eV}{n^2}$

where $n$ is the electron's orbit.

In 1929, Prince Louis de Broglie won the Nobel Prize for his theory of matter waves.

## Albert Einstein and the Theory of Relativity

Einstein's Principle of Equivalence demonstrated that gravity causes space to curve. He discovered that the curvature of space determines how matter will move. Thus gravity can be thought of as a consequence of the "shape" of the universe rather than a force vector. This is Einstein's Law of Motion. Under the theory of General relativity light should also be affected by gravity. This phenomenon has been observed by studies of gravitational lensing.