Astronomy - Introduction

Throughout these notes, sources and copyright information for each image are linked as "(source)".

Distance Scales and Orders of Magnitude

Many of the distance units we use are based on the travel time of light. The speed of light ("c") in vacuum is 299,792,458 meters per second (2.998 * 10⁸ m/s) and the distance in meters can then be computed using

distance = velocity * time

1 meter is a little more than a yard; the solar arrays on the International Space Station span a distance of 78 meters (source)
1 kilometer is about 0.6 miles; the ISS orbits at a distance of 400 km above Earth's surface (source)
1000 kilometers is about 1/6 of the radius of the Earth (source)
1 lightsecond is about the distance (source) to the Moon (source)
1 lightminute is about 1/8 of the distance from the Earth to the Sun (source)
(See the orbits of the outer planets (source))
1 lighthour is about the distance from the Sun to a point midway between Jupiter (source) and Saturn (source)
1 lightday is about 4 times the distance from the Sun to Pluto (source)
1 lightweek is approximately the average distance between stars in the central part of NGC 3949, a galaxy very similar to our own Milky Way (source)
1 lightmonth is approximately 2 times the average distance between stars in a globular cluster (source) like 47 Tucanae (source)
1 lightyear is about 1/4 the distance to the nearest star (after Sol), Alpha Centauri (source)
1 parsec is about 3/4 of that distance
10 parsecs is about the distance to Gliese 436b, an extrasolar planet, known to us by the wobble its orbit induces in its parent star (source)
100 (10²) parsecs is about 3/4 of the distance to Betelgeuse (source)
1000 (10³) parsecs is about 1/2 the distance to the Crab Nebula (source)
10000 (10⁴) parsecs is about the distance to the center of the Milky Way (source)
(View Cosmos DVD 6, episode 10, Milky Way Simulation.)
100000 (10⁵) parsecs is about twice the distance to Supernova 1987A in the Large Magellanic Cloud (source)
1 megaparsec (10⁶ parsecs) is about the distance to M31 in Andromeda, at the other end of the local group of galaxies (source)
10 megaparsecs is about the distance to M104 in the Virgo Cluster of galaxies (source)
100 megaparsecs is about the distance to Stephen's Quintet of interacting galaxies (source, source)
1000 megaparsecs is about 3/4 of the distance to CL 0939+4713, a remote galaxy cluster at z=0.4 (source)
the lumpy objects in this image are probably protogalaxies at z>1 (source)
Abell 2218 is a galaxy cluster containing objects up to z=7 (source)
(View Cosmos DVD 6, episode 10, Large Scale Structure Images.)

The Partial Perspective Viewer will help you find your place in the universe.

2MASS, the 2 Micron All Sky Survey, permits us to see the nearest million and a half galaxies all at once:

(source)

Portfolio Exercise 1: If we adopt a scale of 1 cm to represent 1 lightsecond, then 1 foot would represent 30.5 lightseconds and 1 mile would represent 160934 lightseconds, or 1.86 lightdays.
If we imagine the Sun to lie at mile marker zero on I-75 in Florida, how far from that point would the Earth lie? The midpoint between Jupiter and Saturn? Pluto?
I-75 is 467 miles long in Florida; 353 miles long in Georgia; 160 miles long in Tennessee; 192 miles long in Kentucky; 210 miles long in Ohio; and 394 miles long in Michigan. Where along I-75 would you locate Alpha Centauri?
To deal with the rest of the universe, we obviously need a different scale. Let us now use 1 inch to represent 1 parsec. Then 1 mile would represent 63360 parsecs. Where along I-75 (using this new scale) is Betelgeuse? The Crab Nebula? The center of the Milky Way? Supernova 1987A? M31? M104? Stephen's Quintet? Place these seven objects as accurately as possible on this map of I-75 and include it in your portfolio.

Motion in the Solar System

The Solar System Viewer will help you understand why we see the things we do. You can use it to explore the following phenomena:

the ecliptic
From Earth, view Alpha Centauri in Heliocentric mode and press the "Animate" button twice; you will see the Sun, the Moon and the planets move along the center line: the plane of the Solar System, also called the ecliptic; pressing the "animate" button one more time stops the animation.
daily, monthly and seasonal events
In Geocentric mode, at a latitude of 39 degrees, push the "Hour" button repeatedly; observe the motion of the planets and stars as they "rise" in the East and "set" in the West.
Then, press the "Day" button repeatedly and observe the changes in the midnight sky as the days of a month progress; in Heliocentric mode, from Earth view the Earth and press the "Magnify" button; see how the phases of the Moon change as you repeatedly press the "Day" button.
Reload the page; in Geocentric mode, at a latitude of 39 degrees, push the "Magnify" button and set the hour to 12; then observe the changes in the position of the noonday Sun as you repeatedly press the "Month" button; the path over the course of a year is called an analemma.
Reload the page; from the Sun, view the Sun; set the z control to 24 and push the "Animate" button twice; observe the relative positions of the planets (through Saturn) as they orbit the Sun.
eclipses
Reload the page; in Heliocentric mode, press the "Magnify" button, then press the "Animate" button twice and watch the Moon move in and out of the plane of the ecliptic; as the Moon moves in front of or behind the Sun, we observe partial or full eclipses based on where the Moon lies relative to the ecliptic.
retrograde motion
From Earth, push the "Animate" button twice while viewing Betelgeuse on 6/1/00 (pay attention to Mercury) or 10/1/07 (Mars); or view Fomalhaut on 7/1/03 (Mars), or M48 on 8/1/05 (Mercury, then Mars, then Saturn).
Now view Mars, set the date for 8/1/07 and alternately push the "Draw Marker" and "Month" buttons until 5/1/08. Then from the Sun view the Sun and set "z" to 4; the markers show how the position of Mars changes relative to the stars as Earth "laps" Mars.
solar vs. sidereal days
Noon is defined as the time when the Sun is highest in the sky (at its zenith); a solar day is the time between two successive noons. A sidereal day is the time between two successive risings of any given star (other than the Sun).
Reload the page; from Earth, view the Sun and push the "Draw Marker" button (nothing will appear yet); then view Altair and draw a new marker; then press the day button once and again draw two markers as before; finally, from the Sun view the Sun and set "z" to 3; since the two markers pointing to Altair are parallel, but the two pointing to the Sun are not, you can see that in 24 hours, due to the change in the position of the Earth as it rotates around the Sun, the position of the Sun changes relative to the stars; this causes the sidereal day to differ from the solar day.
synodic vs. sidereal months
A synodic month is the time between two full moons.
Reload the page; from Earth, view the Earth and push the "Magnify" button; push the "Day" and "Hour" buttons until the Moon is aligned along one of the axes. Then set the time for 27.3 days (1 sidereal month) later and note the position of the Moon (the slight difference is due to the Earth's rotation around the Sun); then set the time for 2.2 days later than that (one synodic month since the first time) and note the position of the Moon, and that its phase is the same as it was 29.5 days earlier.

Here is a time-lapse sequence of the Moon through a complete lunar cycle.

The Changing Cosmos

We rarely see change as we observe the distant cosmos, supernovae being the obvious exception. This time lapse of M3 over a single night shows one of the few phenomena that are observable on human time scales: variable stars of the RR Lyrae type. And this sequence of the Cat's Eye Nebula shows the expanding nature of the nebula over a 3 year period.

Orion - What you see and where things really are

These links point to a photograph of the Eastern horizon taken in the early hours of a mid-October morning in 2002. The photo is a composite of several 8 second exposures taken with a Canon G1 (in Cincinnati, it takes a little over 10 seconds for the Earth to rotate enough to cause a star to start to become a streak):

Orion - original photograph
Orion - with star labels
Orion - a deeper view (and check out this image of Barnard's Loop)

In the second image, the red line represents the celestial equator, and the white line represents 6 hours Right Ascension.

Note the tilt of the celestial equator, which is the projection of the Earth's equatorial plane into the sky: 23.45 degrees because of the tilt of the Earth's axis of rotation. The declination measures "celestial latitude" relative to the celestial equator and is measured in degrees.
Also note that the Right Ascension increases from right to left; this is because angles increase in counterclockwise rotation, which when looking toward the South is from West to East. The Right Ascension is measured in hours (24 hours is a circle, so there are 15 degrees per hour).

The stars are labeled with Greek letters indicating their relative brightness within the constellation; their common names, celestial coordinates, visual magnitude, parallax, distance and spectral classes are given here:

Name	Common Name	RA	dec	Mag	Parallax (mas)	distance (ly)	Spectral Class
a Orionis	Betelgeuse	05 55 10.29	+07 24 25.3	0.45	7.63	427.3	M2Ib
b Orionis	Rigel	05 14 32.27	-08 12 05.9	0.18	4.22	772.5	B8Ia
g Orionis	Bellatrix	05 25 07.87	+06 20 59.0	1.64	13.42	242.9	B2III
d Orionis	Mintaka	05 32 00.40	-00 17 56.7	2.25	3.56	915.7	O9.5II+
e Orionis	Alnilam	05 36 12.81	-01 12 06.9	1.69	2.43	1341.6	B0Ia
k Orionis	Saiph	05 47 45.39	-09 40 10.6	2.07	4.52	721.2	B0.5Iavar
z Orionis	Alnitak	05 40 45.52	-01 56 33.3	1.74	3.99	817.0	O9.5Ib SB

This data comes from the Hipparcos Catalog. Note that the common names are all of Arabic origin. Alpha Orionis is a semi-regular pulsating star, gamma and kappa Orionis are variable stars, delta Orionis is an eclipsing binary and zeta Orionis is a double star.

Portfolio Exercise 2: Use SIMBAD to find the celestial coordinates of the five brightest stars in the constellation Cassiopeia. On a piece of graph paper, set up a coordinate system where the horizontal axis runs from 0 to 2 hours of Right Ascension, and the vertical axis runs from 55 to 65 degrees of declination. Plot the locations of the five stars. Find the constellation in the night sky and use your graph to identify the stars. How do you have to orient your graph so that it looks correct? Why did you have to orient it that way?

Parallax

Consider the image on the left. The two blue-green circles represent the Earth at opposing points in its orbit. The large yellow circle between them of course represents Sol (our Sun). Suppose we want to measure the distances to the red and gold stars. As the Earth moves over half its orbit, each star appears to change position. This is called parallax and the change in position is twice the parallax angle. The parallax angle for the red star is a and that for the gold star is b. Note that b is less than a because the gold star is farther away.

If we know the radius r of the Earth's orbit we can compute the distances R_i to the stars:

R_red = r cot (a) and R_gold = r cot (b)

Since for large distances cot(q) is very close to 1/q (if q is measured in radians!), we have

R_red = r / a and R_gold = r / b

A parallax angle of 1 arcsecond (there are 60 minutes of arc in a degree and 60 seconds of arc in a minute) yields a distance of 1 parsec. Therefore to find the distance in parsecs of a star whose parallax is measured in milliarcseconds, simply divide 1000 by the parallax.

Gravity and Planetary Motion - Timeline

This timeline illustrates the changing rates of progress in our understanding of gravity and planetary motion.

(View Cosmos DVD 2, episode 3, Kepler's life.)

Some particularly interesting dates:

October 22, 2136 B.C. - first record of a solar eclipse

July 4, 1054 - Crab Nebula Supernova

January 7, 13, 1610 - Galileo discovers Callisto, Europa, Io and Ganymede
March 25, 1655 - Christiaan Huygens discovers Titan

March 13, 1781 - William Herschel discovers Uranus

September 23, 1846 - G. J. Galle discovers Neptune
October 10, 1846 - William Lassell discovers Triton
August 18, 1868 - Norman Lockyer discovers Helium in the Sun
August 11, 17, 1877 - Asaph Hall discovers Deimos and Phobos

June 30, 1908 - Tunguska Event
May 29, 1919 - General Relativity tested during solar eclipse
February 18, 1930 - Clyde Tombaugh discovers Pluto
February 16, 1948 - Gerard Kuiper discovers Miranda
October 4, 1957 - Sputnik 1 orbits Earth
January 2, 1959 - Luna 1 arrives at the Moon

December 14, 1962 - Mariner 2 arrives at Venus
July 14, 1965 - Mariner 4 arrives at Mars
January 31, 1966 - Luna 9 lands on the Moon
October 18, 1967 - Venera 4 enters Venus' atmosphere
February 24, 1968 - Jocelyn Bell discovers pulsar in the Crab Nebula
July 20, 1969 - Apollo 11 lands on the Moon

December 15, 1970 - Venera 7 lands on Venus
February 15, 1973 - Pioneer 10 passes through asteroid belt
December 3, 1973 - Pioneer 10 arrives at Jupiter
March 29, 1974 - Mariner 10 arrives at Mercury
July 20, 1976 - Viking 1 lands on Mars
March 10, 1977 - Uranus' rings discovered
March 4, 1979 - Jupiter's ring (source) discovered by Voyager 1
September 1, 1979 - Pioneer 11 arrives at Saturn

June 13, 1983 - Pioneer 10 becomes first spacecraft to leave the Solar System
September 11, 1985 - International Cometary Explorer arrives at Giacobini-Zinner
January 24, 1986 - Voyager 2 arrives at Uranus
August 25, 1989 - Voyager 2 arrives at Neptune

December 7, 1995 - Galileo enters Jupiter's atmosphere

February 22, 2000 - Stardust collects coma material from P/Wild 2
February 12, 2001 - NEAR lands on Eros
December 3, 2001 - Genesis collects solar wind particles
January 14, 2005 - Huygens probe lands on Titan

These dates represent first successes; for a more complete picture see NASA's Chronology of Lunar and Planetary Exploration.

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