Wednesday 28 September 2011

The Celestial Sphere. The sky can be thought of as the inside of a sphere of very large radius with us in the middle. The rotation of the Earth makes the celestial sphere appear to rotate every 23hr and 56min on an axis from the north celestial pole to the south celestial pole. These poles are the points on the celestial sphere where an extension of the Earth's rotational axis would intersect the celestial sphere.

Celestial Equator and Ecliptic. The ecliptic is the great circle on the celestial sphere that the Sun appears to follow as the Earth revolves around the Sun. The ecliptic is tilted by 23.5 degrees with respect to the celestial equator. The solstices mark the points where the Sun is farthest north or south of the equator, and the equinoxs mark the two points when the Sun is exactly on the equator.

Path of Sun in sky. As the Earth revolves around the Sun, it appears to us that the *Sun* moves on a great circle on the celestial sphere. (of course, it is us that is doing the moving.) This great circle line is called the ecliptic. A related word is zodiac. The zodiac is a band of sky above and below the ecliptic- an ecliptic belt. The planets appear always near the ecliptic (but not exactly on the ecliptic due to slight tilts of their orbital planes w.r.t. the Earth's). The zodiac is the belt that emcompasses the paths of all the planets.

Constellations of the Zodiac. If you could see the stars in the daytime, the Sun would appear "in" different constellations as it moves around the ecliptic. We say the Sun is "in" the constellation it appears in front of.

Constellations of the Zodiac visible at night At night, of course, we see best the constellations that are 180 degrees away from the constellation the sun is "in".

**The Zodiacal Light and the Gegenschein**

The Sun is centered in a disk of very diffuse dust and gas. The dust particles are continually being ejected from the solar system by the Sun's radiation pressure, but new dust particles arrive as comets pass by the Sun and shed dust in their tails. This dust disk is brightest near the Sun, but extends all the way around the sky, as we are *IN* the dust disk.

Seeing the dust disk is difficult because of the overwhelming brillance of the Sun. If you could see the dust disk in the daytime, it would form a huge flattened belt across the sky (along the ecliptic) with the Sun in the middle of a large "belt buckle". Of course, we can't see the dust disk in the daytime because of sunlight scattered in the Earth's atmosphere utterly overpowers the sunlight scattered from the dust particles.

We can see part of one side of the dust disk *if* we look at just the right time after sunset or before sunrise. We see the disk as a large pyramid shaped glow called the zodiacal light (ZL). Seeing the ZL is a bit tricky- one first needs a VERY dark , very clear sky, far away from city lights, with no moonlight. One does *NOT* need any optical aid- just your (dark adapted) eyeballs. (The zodical light covers such a large angle that not even binoculars are useful in seeing it.) Then one must look at the right time- too close to sunset (or sunrise) and the dusk or dawn light will blot out the ZL- too far (in time) from sundown/rise and the brighter part of the ZL will be below the horizon. The best time to see the ZL is during about a 1/2 hour period after the end of astronomical twilight (AT) in the evening (or 1/2 hour before AT in the morning). The begining (or end) of astronomical twilight is defined as the time when the Sun is 18 degrees below the horizon. At our latitude, the time between sunset/rise and AT in September/October is about 1 hour and 25 minutes. The best time of year to see ZL is when the ecliptic (and hence long axis of the dust disk) is most perpendicular to horizon. This happens (for our latitude) in Sep/Oct in *morning* sky and Feb/Mar in *evening* sky. So the best time to see ZL this Fall would be 2 to 1.5 hour before sunrise in next month or so. In mid-October AT starts at about 6:15AM, so the best time to see ZL would be about 5:45AM- 6:15AM. One book describes the ZL thusly: "The zodiacal light appears as a huge, softly radiant pyramid of white light with its base near the horizon and its axis centered on the zodiac."

Dust disk around Sun An artists conception of the dust disk around the Sun, as seen from near Pluto (with no atmosphere). From Earth, we can see this dust disk only when the Sun is below the horizon, as scattered Sunlight in Earth's atmosphere completely overwhelms it in the daytime.

Zodiacal light from New Mexico

Zodiacal light from an "all sky" camera The zodiacal light starts almost due E in this picture and can be traced about half way up to the zenith (in center of this "fisheye lens" image.

Zodiacal light from Chile

Zodiacal light and Milky Way Portions of two of the three "great circles" on the celestial sphere (ecliptic or zodiac and plane of Milky Way) can be seen in this image. The zodiacal light traces out part of the ecliptic.

Another Zodiacal light and Milky Way picture

Zodiacal light and Milky Way The ecliptic and galactic plane (Milky Way plane) cross near the horizon on this stunning picture from Paranal, the 2600 meter high Chilean mountain where the ESO has a major observatory.

Gegenschein If you look directly opposite the Sun, there is a very faint patch (around 10 degrees across) of glow called the gegenschein (or counterglow). This is due to light which is preferentially backscattered off of interplanetary dust grains back towards the Sun. (The same effect causes the full moon to be much brighter than twice the brightness of 2 "quarter moons". A "quarter moon" is one where we see 1/2 of the moon lit up- the quarter has to do with where the moon is in its orbit, not the lit up fraction). The gegenschein is MUCH harder to see than the zodiacal light. You need an extremely dark clear sky when the antisolar point is away from the Milky Way or bright stars or planets. I have never seen the gegenschein, but have seen the zodiacal light dozens of times.

Gegenschein Wow! The best picture of the gegenschein I have ever seen. This is an ESO (European Southern Observatory) image taken at the site in Chile of the VLT (Very Large Telescope) which is 4 separate 8 meter scopes. If you look at this image on a good monitor, you see that the light band extends almost from top to bottom of the image, flanking the gegenschein patch. As we are *in* the flattened dust distribution the zodiacal light *should* extend as a band *completely* around the sky. The brightness should peak near the Sun (where it is hard to see due to sunlight) then get fainter farther in angle from Sun, then peak opposite the Sun where we get the backscattering gegenschein.

Sizes of particles responsible for zodical light This shows the range of sizes of the particles that reflect the sunlight we see as the zodiacal light. Above the graph are some approximate sizes of some common objects for comparison.

Zodiacal thermal infrared emission The blue band is the infrared thermal emission from the dust particles in the zodiacal dust band. The zodiacal light we see with our eyes is *reflected* sunlight. The infrared seen in this all sky image from a satellite telescope is thermal radiation *emitted* by the dust. The blue band is, of course, a great circle around the celestial sphere. In this projection of the clestial sphere, the center of the image is the center of the Milky Way.


Inner Planets- basic length of "day"

Doppler shift. When a source of a wave (sound or electromagnetic radiation) is moving towards you, the waves are "bunched up" and the wave you detect has a shorter wavelength (higher frequency) than the emitted wave. If the source is moving away from you, the waves are "stretched out" and the wavelength is longer (frequency lower).

For low speeds (compared to speed of light, c) the fractional change in wavelength is just equal to the fraction the speed is compared to c. The DS only measures the RADIAL component of speed (see next slide).

Doppler shift and radial velocity. Uusually, the DS only measures the radial component ("towards or away from") of the motion between source and observer. (At high speeds - compared to c -, there is a second order effect called the "transverse Dopple Effect")

Primitive Radar Astronomy basics Radar astronomy has greatly enriched our knowledge of the Solar System over the past few decades. The most basic data we can derive from radar astronomy is the distance, and rotational speed (spin period) of a planet, as well as an estimate of its radius. The rotational speeds of Mercury and Venus were not known until the advent of radar astronomy in the 1960s.

Using the fact that different parts of a planet have different speeds relative to Earth (due to planet rotation) - plus the Doppler shift - it is now possible to use Earth-based radar to map certain aspects of a planet's surface.

Rotation of Moon.. The fact that we always see the same side of Moon means that it must rotate on its axis once for every orbit around the Earth. This is called synchronous rotation and is due to tidal locking.

Synodic and sidereal months. Relative to a fixed coordinate system , the Moon orbits the Earth in one sidereal month (sidereal= "relative to stars"), which is equal to 27.32 days. However, the time between full moons (or new moons) is a time period called the synodic month (29.53 days).

Bizarre "day" on Mercury. Only after radar was used to study Mercury was its true sidereal rotational period measured- 58.646 days. This period is 2/3 of the orbital period of mercury around the Sun- which is 87.969 day. Thus, the planet rotates (relative to the stars) exactly 1.5 times each "year". However, the solar day - say time from noon to noon- is equal to *TWO "YEARS"* (~176 day). (To convince yourself of this, follow the red dot around in the right most figure.)

Bizarre "day" on Venus. Radar reveals that the sidereal day on Venus is 243.01 day. This is longer than the "year" on Venus, which is 224.7 day. Venus also rotates in the opposite sense as the other planets (retrograde). This combination result in a "solar day" on Venus that is 116.8 day long. On Venus, the Sun rises in the west!

"Day" on Earth You all "know" that the Earth rotates in exactly 24 hours, right? Well, wrong! Now that you have seen the enormous difference between "day" with respect to the stars and "day" with respect to the Sun on Mercury, lets come back to the Earth. The *sidereal* rotational period of the Earth is 23 hr 56 min 4.091 sec. This is the rotation rate w.r.t. the rest of the Universe. This is how long it takes the Earth to rotate, not 24 hours! The *solar day* (average time from noon to noon- i.e. time from when Sun is highest in sky to when it again highest in sky) *is* 24h 0min 0 sec. But that does not mean the Earth rotates in 24 hours! Of course, since (except for some weird astronomers!) people care about where the Sun is in the sky, rather than the stars, we base our time system on *solar* time. (Now, of course, we actually base our time on quantum mechanics.)

The angle in the diagram is marked as 1 degree, but it is certainly not drawn as 1 degree- looks more like 30 degrees. Its the thought that counts. The Earth goes around the Sun in 366.25... sidereal days (or, as we usually think of it, 365.25... solar days), so the angular speed is 360 / 365 or just a little under 1 degree per solar day. Because the Earth's orbit is not a perfect circle, its orbital speed varies slighly, so the angular seed around the Sun also varies over the course of a year.