Stars, Galaxies, and the Universe Exam #1 University of Iowa

Planet Order

1. Mercury / 2. Venus / 3. Earth / 4. Mars / 5. Jupiter / 6. Saturn / 7. Uranus / 8. Neptune

Rhyme to help you remember: My Very Educated Mother Just Sold Us Narcotics.

Ecliptic

A great circle on the celestial sphere representing the sun's apparent path during the year, so called because lunar and solar eclipses can occur only when the moon crosses it.

Equator

An imaginary line drawn around the earth equally distant from both poles, dividing the Earth into northern and southern hemispheres and constituting the parallel of latitude 0°.

Celestial Equator

The projection into space of the Earth's equator; an imaginary circle equidistant from the celestial poles.

Polaris

The North Star; not true north but a close indicator for celestial navigation.

Horizon

The line at which the earth's surface and the sky appear to meet.

Zenith

The point in the sky or celestial sphere directly above an observer.

Meridian

A circle of constant longitude passing through a given place on the earth's surface and the terrestrial poles.

Vernal Equinox

0 Hours / Declination: 0° / Usual Date: March 20th / Constellation: Pisces

Summer Solstice

6 Hours / Declination: 23.5°N / Usual Date: June 21st / Constellation: Gemini

Autumnal Equinox

12 Hours / Declination: 0° / Usual Date: September 23rd / Constellation: Virgo

Winter Solstice

18 Hours / Declination: 23.5°S / Usual Date: December 22nd / Constellation: Sagittarius

Hipparchus's Stellar Magnitude System

1. Developed by Hipparchus of Rhodes, 160 - 130 BCE.

2. Consisted of 5-6 classes.

3. Brightest stars are 1st magnitude, next brightest are 2nd, and so on down to 6th magnitude (barely visible to someone with good eyes eyes in a really dark sky.)

4. Has had modifications since it was first created, but is currently still a system we use today.

Modern Stellar Magnitude System

Differences from Hipparchus's system:

1. Interesting property of magnitude system: differences correspond to ratios of power (Ex.: "10^6" = 10 the the 6th power) received from stars (not just a fixed difference subtracted to get from one magnitude to another).

2. Thinks in terms of measuring the power in starlight with a light meter (Watts/square meter).

3. Created more specific term: apparent magnitude is the magnitude of a star as it appears to us.

Apparent Magnitude

1. The magnitude (brightness) of a celestial object as it is actually measured from the Earth.

2. Depends on both the "intrinsic/natural brightness" and the distance.

3. Abbreviated as a lowercase "m"

Absolute Magnitude

1. The magnitude (brightness) of a celestial object as it would be seen at a standard distance of 10 parsecs.

2. Abbreviated as an uppercase "M"

Astronomical Unit

1. A unit of length to determine how far away are the stars. Also known as "AU"

2. 1 AU is the distance between Earth and the Sun, or 149,597,870,700 meters.

3. Shorthand can be: 1.496 x 10^11 meters

Parallax

1. The effect whereby the position or direction of an object appears to differ when viewed from different positions (e.g., through a viewfinder, or the lens of a camera.)

2. The angular amount of ____ in a particular case, especially that of a star viewed from different points in the earth's orbit.

3. The smaller the ____ (back and forth angular shift of a star), the further away it is.

Stellar Parallax

1. Parallax on an interstellar scale: the apparent shift of position of any nearby star (or other object) against the background of distant objects.

2. The fundamental way of determining stellar distances.

3. Our planet is moving back and forth in our orbital motion around the Sun. We see a (relatively) nearby star shift back and forth against very distant stars. The further away a star is, the smaller this angular shift (p) is.

"P" is shorthand for term

Arc-Minute

1. A unit of angular measurement equal to 1/60 of one degree.

2. If one degree is 1/360 of a turn (or complete rotation), then one ____ is 1/21,600 of a turn.

Arc-Second

1. A unit of angular measurement equal to 1/60 of one arc-minute.

2. One ____ is 1/3,600 of a degree , and 1/1,296,000 of a turn (or complete rotation).

3. 1 ____ is angle subtended by a dime at 1.2 miles!

Ex.: A parallax of 1 ____ occurs when a star is 206,265 AU away! (Although no stars have a parallax that big.)

Subtend

A line, arc, or figure form an angle at a particular point when straight lines from its extremities are joined at that point.

Parsec

1. A unit of length used to measure large distances to objects outside the Solar System.

2. One ____ is the distance at which 1 AU subtends an angle of one arc-second.

3. Is the distance that would produce "p = 1 arc-second." So 1 ____ equals 206,265 AU.

3. A simpler way to remember it as an abbreviation "of the parallax of one arc-second."

5. When using the ____, there is a simple relation between the parallax and the distance, d = 1/p (d in ____, p in arc-seconds)

Light Year

1. An alternative unit of stellar distances (used by amateur astronomers).

2. Speed of light is a fundamental constant of physics, roughly 300,000 km/sec or 2.99792458 x 10^8 meter/sec, so multiplying that by 365.25 days gives us an alternative for measuring stellar distances.

Light Year & Parsec

1 Light Year: 9.460 x 10^15 meters

1 Parsec: 3.086 x 10^16 meters

Conversion: 1 parsec = 3.26 light years

Stellar Brightness: 18 Brightest Stars as seen from Earth

(Name: Distance/Apparent Mag./Absolute Mag.)

1. Sun: 93 million miles / -26.72

2. Sirius: 8.6 ly / -1.46 / 1.4

3. Canopus: 74 ly / -0.72 / -2.5

4. Rigil Kentaurus: 4.3 ly / -0.27 / 4.4

5. Arcturus: 34 ly / -0.04 / 0.2

6. Vega: 25 ly / 0.03 / 0.6

7. Capella: 41 ly / 0.08 / 0.4

8. Rigel: 1,400 ly / 0.12 / -8.1

9. Procyon: 11.4 ly / 0.38 / 2.6

10. Achernar: 69 ly / 0.46 / -1.3

11. Betelgeuse: 1,400 ly / 0.50 (varied) / -7.2

12. Hadar: 320 ly / 0.61 (varied) / -4.4

13. Acrux: 510 ly / 0.76 / -4.6

14. Altair: 16 ly / 0.77 / 2.3

15. Aldebaran: 60 ly / 0.85 (varied) / -0.3

16. Antares: 520 ly / 0.96 (varied) / -5.2

17. Spica: 220 ly / 0.98 (varied) / -3.2

18. Pollux: 40 ly / 1.14 / 0.7

Sirius

1. Brightest star in the Earth's night sky.

2. Visual Apparent Magnitude of -1.46, Absolute Magnitude of 1.42.

3. Almost twice as bright as the next brightest star, Canopus (Apparent = -0.74, Absolute = -5.74)

4. Actually a binary star system: Sirius A is a white main-sequence star (A1V), Sirius B is a faint white dwarf companion (DA2). To the naked eye they look as though they are one star.

5. Sirius A is almost twice as massive as our Sun and 25 times more luminous, but has a significantly lower luminosity compared to other bright stars Canopus and Rigel.

The Hipparchos Spacecraft

- Spacecraft active from 1989 till 1993, thanks to it:

1. We know 1% distances for over 400 stars

2. We know 5 % distances for 10,000 stars

3. We have better knowledge of our neighbors, and their properties.

The GAIA Spacecraft

- Spacecraft launched in December 2013 whose mission is to construct the largest and most precise 3D space catalog ever made of (mainly) stars but also planets, comets, asteroids, and quasars among other things. It will do this by:

1. Measuring the parallaxes of approximately one billion astronomical objects.

2. Has the angular precision of about 1:100,000 arc-seconds.

3. Roughly 10% distances 10,000 parsecs away.

4. Will produce important data to astronomy that will be crucial in advancing it further.

Luminosity

1. The total amount of energy emitted by a star, galaxy, or other astronomical object per unit time.

2. It is related to the brightness, which is the ____ of an object in a given spectral region.

Proper Motion

A gradual change in the position of a star or other celestial object on the celestial sphere that is the result of the object's intrinsic/natural motion through space rather than mere apparent motion as observed from Earth.

Proper Motion Equation

tan A=(V,T)/d

Inverse Square Law of Brightness

1. This relates the Apparent Brightness of a star (or other light source) to its Luminosity (Intrinsic Brightness) through the Inverse Square Law of Brightness:

2. At a particular Luminosity, the more distant an object is, the fainter its apparent brightness becomes as the square of the distance.

Inverse Square Law of Brightness Equation

- Let F be the flux of luminous energy we receive from a star (Watts/Square-meter)

- Let L be the luminosity (units are Watts)

- Let r be distance to a star

- Surface area of a sphere

Equation: F=L/(4πr^2 )

Answer would be in the form of L = ______ Watts

Absolute Magnitude "M"

- The apparent magnitude a star would have if it were 10 parsecs away.

1. We can always know the apparent magnitude of a star, if we know the distance (d), we can calculate how much brighter (or fainter) a star would be if it were 10 parsecs distant instead.

2. If we know how much brighter/fainter it would be at 10 parsecs, we can calculate how many magnitudes bright/fainter it would be.

Differences between Apparent Magnitude "m" & Absolute Magnitude "M"

1. If a star is at a distance d < 10 parsecs, it would be fainter if it were at 10 parsecs. So M is a bigger number (fainter) than m. The number (m-M) is negative.

2. If a star is at a distance d > 10 parsecs, it would be brighter if it were at 10 parsecs. So M is a smaller number (brighter) than m. The number (m-M) is positive.

3. Since (m-M) is directly related to the distance to a star, it is called the distance modulus.

Telescopes

1. Collect "Big Piles" of light.

2. Magnify object (it looks a lot closer than it is).

Types of Telescopes

Refractors, Reflectors, Radio____

Refractor Telescope

1. Also known as the "dioptric" telescope, this type of optical telescope uses a large lens (the "objective") to form an image that you can see through the smaller lens (the "eyepiece").

2. This design was originally used in spy glasses and astronomical telescopes, but is also used for long focus camera lenses.

3. Suffered from severe chromatic aberration.

4. Its magnification is calculated by dividing the focal length of the objective lens by that of the eyepiece lens.

Reflector Telescope

1. Also know as the "catoptric" telescope, this type of optical telescope uses a single or combination of curved mirrors that reflect light to form images.

2. Almost all major telescopes used in astronomy research are of this type as their design allows for many variations, like employ extra optical elements to improve image quality or place the image in a mechanically advantageous position.

3. Made as an alternative to the refractor telescope as it negated the effects of chromatic aberration and because it allows larger apertures.

Radio Telescope

1. This telescope has a specialized antenna and radio receiver used to receive radio waves from astronomical radio sources in the sky.

2. They are the main observing instrument used in radio astronomy, which studies the radio frequency portion of the electromagnetic spectrum emitted by astronomical objects, just as optical telescopes are the main observing instrument used in traditional optical astronomy studies the light wave portion of the spectrum coming from astronomical objects.

3. They are typically large parabolic ("dish") antennas similar to those employed in tracking and communicating with satellites and space probes.

4. Unlike conventional optical telescopes which work best only at night, these telescopes can operate in day & night.

5. Wavelength capability is large (1 cm to 1 meter typically) so the diameter has to be HUGE.

Focal Length of the Objective Lens Equation

Equation: 1/s1 + 1/s2 = 1/f => f=s1

Optical Telescope Magnification

The longer the focal length, the higher the magnification.

Angular Resolution

- How small a detail can you see with a telescope?

- Smallest angle measurable

Equation: B = w/D

- B is angle of resolution

- w is wavelength of light

- D is the diameter of the telescope

Radio Interferometers

The ultimate in angular resolution.

Light

1. One of the most important pieces of information we can get from most astronomical objects.

2. Is a wave in the electromagnetic spectrum.

3. Without it, we wouldn't even be able to see.

4. To understand it, we must understand the physics of it.

Wavelength

The distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave. (w)

Frequency

The rate at which a vibration occurs that constitutes a wave, either in a material (as in sound waves), or in an electromagnetic field (as in radio waves and light), usually measured per second. (f)

Amplitude

The maximum extent of a vibration or oscillation, measured from the position of equilibrium. (how strong)

Speed in waves

In the case of a wave, the ____ is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. (c)

Electromagnetic Radiation

Also known as the "EM Spectrum," this kind of radiation includes gamma rays, x-rays, ultraviolet, light, infrared, microwave, & radio, through which electric and magnetic fields vary simultaneously.

Electromagnetic Spectrum

1. Gamma Rays (highest energy, lowest wavelength)

2. X-Rays

3. Ultraviolet

4. Visible (light)

5. Infrared

6. Microwaves

7. Radio (lowest energy, highest wavelength)

Units

1. Our standard unit of length is the meter (a long yard, 39 inches)

2. The metric, or SI system of units

3. Sometimes it is hand to have a secondary, more convenient unit

made up from meters (e.g. 1 light year = 9.461 X 1015 meters)

4. The wavelength of light is tiny compared to a meter; use nanometers

5. 1 nanometer = 1 billionth of a meter 10-9 meters

6. Visible light consists of electromagnetic waves with wavelengths from 400 - 700 nanometers (nm)

Spectrum

1. A fundamental measurement to extract more information from starlight.

2. The ____ of an object is the variation in the intensity of its radiation at different wavelengths.

3. Spread out light according to wavelength

Kirchoff's Laws

- Objects with different temperatures & compositions emit different types of spectra. By observing an object's spectrum, then, astronomers can deduce its temperature, composition, & physical conditions, among other things.

1. A hot solid, liquid or gas, under high pressure, gives off a continuous spectrum.

2. A hot gas under low pressure produces a bright-line or emission line spectrum.

3. A dark line or absorption line spectrum is seen when a source of a continuous spectrum is viewed behind a cool gas under pressure.

Wien's Law

1. Wien's Law tells us that objects of different temperature emit spectra that peak at different wavelengths.

2. The wavelength at which a hot (opaque) object is brightest depends only on the temperature.

3. Hotter objects emit most of their radiation at shorter wavelengths; hence they will appear to be bluer.

4. Cooler objects emit most of their radiation at longer wavelengths; hence they will appear to be redder.

5. Furthermore, at any wavelength, a hotter object radiates more (is more luminous) than a cooler one.

Equation: λpeak= (0.0029 K)/T

- λpeak is the Wavelength of Maximum Intensity (nm)

- T is temperature (in Kelvin)

The Planck Function

1. Called one of the great intellectual triumphs of physics.

2. You can derive mathematically an equation describing the spectrum of light from a hot object.

3. Describes how the light emitted by a hot object changes as the temperature & wavelength are changed.

4. Describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Equation: Look up, it is rather large and cannot be pasted on here.

A hot object of a certain size

1. ...is brighter (emits more power in the form of light) at all

wavelengths than a cooler object of the same size.

2. ...is brightest at a shorter wavelength than a cooler object.

3. The spectra of stars are often very similar to Planck Function spectra; we can apply this theory to stars to get their temperatures (and other properties).

Spectral Classes O, G, & M

1. An O star is really

hot and bright. Surface temp of 35,000 degrees Celsius, color: blue-white, strong lines: ionized helium.

2. A G star is like the Sun. Surface temp of 6,000 degrees Celsius, color: yellow, strong lines: calcium.

3. An M star is relatively cool. Surface temp of 3,000 degrees Celsius, color: red, strong lines: titanium oxide.

Hertzsprung-Russell Diagram

1. Highest quality data from the Hipparchus spacecraft.

2. Gave us types of stars (important terms): Main Sequence (luminosity class V), Giants (luminosity class III), Supergiants (luminosity class I), White dwarfs

Scientific Classification of our Sun

1. Is a class G2V star.

2. Is a main sequence, spectral class G star.

3. The Galaxy probably has a billion of them.

Chemical Composition of the Sun

Elements: Percentage

1. Hydrogen: 73%

2. Helium: 25%

3. Oxygen: 0.80%

4. Carbon: 0.36%

5. Iron: 0.16%

Summary of Basic Properties of the Sun

1. Mass: 2X10^30 kg (330,000 mass of Earth)

2. Radius: 696,000 km (109 times than of Earth)

3. Density: 1.5 g/cc

4. Surface temperature 5800K

5. Luminosity: 3.848x10^26 Watts

Color of Hottest & Coldest Stars (with star class)

1. Blue (Hottest): O,B,A, & F

2. White: F & G

3. Yellow: G

4. Orange: K

5. Red (Coldest): K & M

Main Sequence Star

1. Also known as "dwarf stars," this is a type of star that is fusing hydrogen in its core and has a stable balance of outward pressure from core nuclear fusion and gravitational forces pushing inward.

2. About 90% of the stars in the Universe (including our Sun) are of this type.

3. They can range from a tenth of the mass of our Sun to up to 200 times as massive.

4. Luminosity class V in the Yerkes Luminosity Classes Scale

Giants

1. A star with substantially larger radius and luminosity than a main-sequence (or dwarf) star of the same surface temperature.

2. They lie above the main sequence on the Hertzsprung-Russell diagram and correspond to luminosity classes II and III on the Yerkes Luminosity Classes Scale

Supergiants

1. The largest stars in the universe. They can be thousands of times bigger than our Sun and have a mass up to 100 times greater.

2. Is larger, brighter, and more massive than a giant star, being thousands of times brighter than the Sun and having a relatively short lifespan—only about 10 to 50 million years as opposed to around 5 billion years for the Sun.

3. The largest known example, VY Canis Majoris, is up to 2,100 times the size of the Sun (based on upper estimates).

4. Luminosity class I in the Yerkes Luminosity Classes Scale

White Dwarf

1. Also known as a "degenerate ____," is a small very dense star that is typically the size of a planet, formed when a low-mass, Main Sequence star has exhausted all its central nuclear fuel and lost its outer layers as a planetary nebula.

2. This star is a stellar core remnant composed mostly of electron-degenerate matter.

Binary Star

A system of two stars in which one star revolves around the other, or both revolve around a common center.

Speed

(m/sec): how fast you are moving; doesn't depend on direction. Mathematical symbol: v

Position

(m): where you are in some coordinate system (x,y,z). Mathematical symbol: r

Velocity

(m/sec): how fast you are moving and your direction. Does depend on direction of motion.

Mathematical symbol: v

Acceleration

(m/sec/sec): rate of change of the velocity with time. Depends on change in direction of the velocity as well as the magnitude. Mathematical symbol: a

Equation: acceleration=a= change in velocity divided over change in time= V2-V1 divided over t1-t2

Newton's Laws of Motion

1. 3 physical laws that, together, laid the foundation for classical mechanics.

2. Acceleration occurs if the speed of an object changes while the direction of motion stays the same, if the speed stays constant while the direction of motion changes, or if both the speed and the direction changes.

Newton's 1st Law

1. An object that is at rest will stay at rest unless a force acts upon it.

2. An object that is in motion will not change its velocity unless a force acts upon it.

Newton's 2nd Law

If an object with a mass (m) is acted upon by an external net force (F), it accelerates (a) according to the law: (Equations) F=(m)(a) or a=F/(m)

Newton's 3rd Law

1. "To every action, there is an opposite & equal reaction."

2. That definition sounds neat, but a more useful definition is: "If an object A exerts a force on object B, object B also exerts a force on A, which is equal in magnitude, but opposite in direction to the first force."

Gravity

An attractive force between two objects because they have mass.

The Mass-Luminosity Relation

1. Obeyed only for Main Sequence stars.

2. Shows a very strong dependence of the luminosity on the mass of the star.

3. Shows that it is the mass

of a star that determines its position on the main sequence, its surface temperature, etc.

Easy Equations To Know

1. Luminosity: power=energy/time

2. Energy=power X time (watts X seconds=joules)

3. Time=energy/power

The Einstein Energy-Mass Equivalence Relation

E=mc^2

c=speed of light