Astro C10: Astronomy on

Mon, 01 Jan 0001 00:00:00 +0000

Distances and Measurements #

How big is 1 Astronomical Unit (AU)?

1 AU is the distance from the Earth to the Sun: about 150 million km ($1.5 \times 10^8$ km)

How long does it take for light to travel from the Sun to Earth?

About 500 seconds, or 8.3 minutes

SI Unit Prefixes #

k	kilo-	$10^3$	1km = 1000m
c	centi-	$10^{-2}$	100cm = 1m
m	milli-	$10^{-3}$	10mm = 1cm
M	mega-	$10^6$	1Mm = 1000km
G	giga-	$10^9$	1Gm = 1000Mm
$\mu$	micro-	$10^{-6}$	1 $\mu$m = 1000nm
n	nano-	$10^{-9}$	1000 nm = 1 $\mu$m

Mon, 01 Jan 0001 00:00:00 +0000

Unlike other physical sciences, astronomers don’t have access to the objects they study: it’s nearly impossible with current technology to actually go to nearby stars or planets for casual observation!

Nonetheless, the universe is the ultimate astronomy laboratory, and conveys tangible information in the form of light.

What is light? #

Light is a form of electromagnetic radiation. Let’s break down what that actually means:

“Electro” = electricity: when protons (positive charge) and electrons (negative charge)
“Magnetic” = magnets: tangibly, physical magnets attract and repel each other. This is because magnets produce a magnetic field. When magnetic objects enter a magnetic field, a force gets applied to them.

It turns out that accelerating electric fields produce magnetic fields, and accelerating magnetic fields produce electric fields! This behavior can be explained by a set of four equations, known as Maxwell’s Equations:

Mon, 01 Jan 0001 00:00:00 +0000

The Spectra of Elements #

Every element on the Periodic Table has a unique configuration of electron energy states. Here are some rules, as discovered through quantum physics:

Every electron has a discrete energy level.
Electrons can exist on one of several energy levels.
If a photon (particle of light) hits an electron, the electron can absorb the photon and get excited, jumping up to a new energy level. This only occurs if the photon’s energy level exactly matches the energy difference between two discrete states.
If left undisturbed, excited electrons will emit photons, jumping down to a lower energy state. This is why certain elements appear to glow in different colors when heated.

Mon, 01 Jan 0001 00:00:00 +0000

Stars are huge, opaque, luminous balls of gas held together by gravity.

The inner parts of a star are so hot that they continuously emit radiation of all wavelengths, which is known as a continuum.

The shape of a thermal continuum is known as a Planck curve.

Stars are usually so hot that there are only slight imperfections in the continuum. Therefore, for many approximate calculations, we can pretend that they are perfect thermal emitters, otherwise known as blackbodies.

Mon, 01 Jan 0001 00:00:00 +0000

Angular Resolution #

The angular resolution of a telescope is given by

$$ \Theta = \frac{\lambda}{D} $$

Why do blue wavelengths look sharper in a telescope compared to red wavelengths?

The angular resolution θ (clarity) of a telescope is given

by θ = λ/D, where λ is the wavelength of light observed and D is the diameter of the

mirror or lens of the telescope. Blue light has a shorter wavelength than red light,

Mon, 01 Jan 0001 00:00:00 +0000

The Moon #

How do you predict where the moon will be in the sky?

What phase would an astronaut on the surface of the moon see the Earth as?

The opposite phase of the moon on Earth- for example, if observers on Earth saw a waning gibbous, the Earth would be seen as a waxing crescent from the moon.

What is earthshine?

Earthshine is sunlight that was first reflected from Earth, then from the moon back to Earth. It is most visible during the crescent phase.

How old is the Moon?

Mon, 01 Jan 0001 00:00:00 +0000

Models of the Solar System #

What is prograde and retrograde motion?

Strangely, planets seem to occasionally move backwards. In Ptolemy’s geocentric theory, retrograde motion could be explained by other planets (which are orbiting Earth) are also moving in a circular motion relative to the center of their orbit around Earth, in what is known as an epicycle:

In Copernicus’ heliocentric model (which is used today), all planets including Earth all orbit the Sun. Since Earth and the other planets orbit the Sun at different rates, retrograde motion occurs when the Earth passes the other planets in their relative orbits.
A planet can be observed to be in prograde motion if, over time, its position changes in the same direction as the rest of the stars in the sky. On the other hand, if the planet’s position changes in the opposite direction as the stars, then it must be in retrograde motion.
Prograde and retrograde motion can only be observed after many individual observations over several weeks or months.

How was Ptolemy’s model disproved?

Mon, 01 Jan 0001 00:00:00 +0000

Parsecs #

Parallax: angle subtended (covered) by 1 AU

As the distance from Earth to a star increases, the parallax decreases.

The distance for which 1AU has a one arcsecond parallax is called a parsec (pc). A parsec is about 3.26 light years.

Distance in parsecs = reciprocal of the parallax in arcseconds

Stars #

$b = \frac{L}{4\pi d^2}$: the apparent brightness of a star, by the inverse square law, decreases by the square of the distance you move away from it.

Mon, 01 Jan 0001 00:00:00 +0000

How big are galaxies?

hundreds of billions of stars, 50,000+ light years across
Most galaxies also exist in groups (clusters) of tens to thousands of galaxies.

What are some properties of the Milky Way?

All of the stars in the Milky Way orbit a supermassive black hole in the center.
Unlike the solar system, where inner planets orbit more quickly, all stars in the Milky Way orbit the center at about the same rate (flat rotation curve). This suggests the existence of dark matter propelling the outer stars.
From the rotation speed we can determine that the mass of the galaxy is about $10^{11}$ solar masses.

How do we determine how far other galaxies are from us?

Mon, 01 Jan 0001 00:00:00 +0000

Based on redshifts Vesto Slipher discovered, it appeared that many of the spiral nebulae are moving away from us.

Hubble used these redshifts to derive distances to stars: redshift is proportional to distance. The more distant the stars, the greater the redshift.
Planets, the solar system, our galaxy, etc. are not expanding because they are held together gravitationally. The expansion of empty space is a much smaller force compared to gravity.

Mon, 01 Jan 0001 00:00:00 +0000

Cosmology is the study of the structure and evolution of the universe as a whole.

Olbers’ Paradox #

Olbers’ Paradox: why is the sky dark at night if there are billions of stars? Anywhere you look in the sky there should be a star (just like trying to look through a dense forest).

By the inverse square law, distance stars look dim: $b \propto \frac{1}{d^2}$.
Distant stars have a nonzero angular size, since $A = \pi \theta^2 \propto \frac{1}{d^2}$.
By the two above equations, it appears that brightness of a star is independent of its distance… (if it’s half as bright due to distance, it must also be half the size in the sky. So it should be just as bright as the sun, just a lot smaller.)

Possible solutions to Olbers’ paradox: