## Introduction to Astronomy

Time Scales

Back in the day, the POINT of astronomy was to tell time. Not necessarily the time of day, but the time of year, or how many years had passed since so-and-so was king. There are 4 interesting time scales that govern the overall appearance of the sky: 26,000 years, one year, one month, one day. We'll talk about the min order of shortest to longest, but be aware that a fraction whatever happens over the course of a month also happens over a day!
These time scales are all due to the fact that the Earth and Moon move over time, both through space and around their own axes.

• The Day:
Over the course of one day, the Earth revolves around its own axis once. This is what makes all the stars, planets, Sun, etc. appear to rise in the East and set in the West. If you've ever been on a merry-go-round, you are completely familiar with this phenomenon. The things that you can see simply depend on the direction you are facing. As the machine turns, you see different things, that all move across your view, and go out of sight again as the machine continues to turn. For the Earth, things become somewhat more complicated, because you have to decide what 'once around it's axis' means. Is that with respect to the Sun or the stars, or what? Thus, there are several different types of 'day'.
• The Earth rotates all the way around on its axis once per day. What do we mean by 'all the way'?
• Sidereal day: This is the length of time it takes for the Earth to come around to the same position relative to the stars. The sidereal day is 23 hours and 56 minutes long.
• Solar day: This is the length of time it takes for the Earth to come around to the same position relative to the Sun. The solar day is 24 hours long. The extra four minutes come from the fact that the Earth travels about 1 degree around the sun per day, so that the Earth has to turn a little bit further to present the same side to the Sun.
• Lunar day: It is also possible to define a lunar day, which is the time required for the Earth to come around to the same spot relative to the Moon. Since the Moon revolves around the Earth, this day is even longer than the solar day: about 24 hours and 48 minutes! This is why the tides do not occur at the same time every day---because the Moon is the primary cause of tides, and each day, it is 48 minutes farther East than it was the day before.
• The rotation of the Earth, combined with the gravitational pull of the moon cause the Earth to experience one full set of tides (2 highs and 2 lows) everywhere on the planet.
Aside about tides: Tides are caused by gravity. The Sun and the Moon both contribute to tides on the Earth. Newton's law of gravity looks like this:
F=GMm/(r2)
G is a constant (equal to 6.67X10-11 N*m2/kg2). M is the mass of one object, m is the mass of the other, and r is the distance between them. Even though the mass of the Sun is much larger than the mass of the Moon, the effect of the Sun on the tides is much less. This is because the Sun is so much further away, and the force of gravity drops off by r2, not just r. Because it is squared, the distance between the objects is the most important parameter. (Note: Newton, by the way, didn't "discover" gravity. People knew that apples fall out of trees before Newton. What Newton did figure out was that the thing that makes the Moon go around the Earth, and the Earth go around the Sun is the same as the thing that makes apples fall out of trees. This is a tremendous insight, and not at all obvious!) When the Sun, the Moon, and the Earth are all in a straight line, the tides are largest---the highs are highest, and the lows are lowest. These are called "spring tides". (Spring as in jump, not spring as in the season after winter.)

When the three objects form a right angle, the tides are the smallest (highs aren't very high, and the lows aren't very low). These are called "neap tides" (from Saxon neafte, meaning scarcity When the tide does not go out as far, you can't get to all the yummy tidepool creatures.).

In the above pictures, there are two tidal bulges. These two tidal bulges have been greatly exaggerated so you can see them. In actuality, the Earth's solid surface flexes by about 20 cm (about 8 inches) during the tidal cycle. The Earth's liquid surface can change much more than this, however. In the middle of the ocean, away from shore, the water may rise as much as a meter (about 3 feet). Close to land the effect is magnified, and in some cases, when storms are brewing offshore, the tides may rise by as much as 15-20 feet. There are two tidal bulges because the force exerted by the Moon is not constant over the diameter of the Earth. The side nearest the Moon is pulled on harder than the side further away. So the Earth gets "stretched" out of shape.
Tides are slowing the Earth's rotation. The frictional drag of the Earth causes the tidal bulge to be pulled slightly ahead of the moon. The Earth loses rotational energy by pulling against the moon's influence in this way, and so the rotation is slowed by about 0.0015 seconds (1.5 milliseconds) each century. (An analogy to this is to put your hand on a spinning wheel. The wheel pulls against your hand, and your hand pulls against the wheel, slowing it down.)

Eventually the Moon and the Earth will become tidally locked, and as the Earth always appears now in the same position in the Moon's sky, so the Moon will appear always in the same position in the Earth's sky. For example, if the Moon winds up over Asia, people in North America would never see it, unless they travelled around the Earth. At this time, the "day" will be 47 of our current days long!
Different celestial objects have days of different length, depending on how fast they rotate around their axis.
• One month (29 days):
• The Earth orbits the Sun roughly 1/12 of the way.
• The tilt of the axis causes us to travel through 1/3 of a season.
• Different stars are visible at night, due to the change of location of the Earth relative to the Sun. The stars rise earlier and earlier each night, a total of about 2 hours per month. If a star rises at 6:00 pm on January 1, it will rise at approximately 4:00 pm on February 1.
• The Earth and the other planets change their relative positions, so that the planets appear to move generally eastward over the course of the month.
• The moon goes through one cycle of phases in 29 days. The view of the entire cycle from where astronaut Spiff stands (far North of the Earth's North pole) looks like this:

The Moon is in synchronous rotation with the Earth, so that the same side of the Moon always faces the Earth (the man in the moon, or the energizer bunny in the moon). This is because the moon is literally heavier on the near side! This does NOT mean that the Moon does not spin on it's own axis (recall the demo in class), it's just that the rotation period exactly matches the revolution period, or the amount of time it takes to go around its own axis is the same as the amount of time it takes to go around the Earth.
Eclipses
There are two types of eclipses: lunar eclipses, and solar eclipses. In a solar eclipse, the moon comes between the Earth and the Sun, and blocks the Sun's light from reaching us. Here is a view as astronaut Spiff would see it:

In a lunar eclipse, the Earth comes between the Sun and the Moon, and blocks the Sun's light from reaching the Moon. Here is a view as astronaut Spiff would see it:

Lunar eclipses are quite common, but solar eclipses are rare. For both types of eclipses you need to be in the right place at the right time to see one.

Eclipses do not happen during each lunar cycle because the plane of the Moon's orbit is inclined with respect to the line between the Earth and the Sun. Here is a view 'from the side':

Only at some times of year will the Moon be on the line between the Sun and the Earth at the same time that it is in new or full phase.

Solar eclipses are possible because the Sun and the Moon are nearly the same angular size in the sky (about 0.5 degrees). We are fortunate to live in a time when we can see solar eclipses. The moon is getting further from us all the time (about 3 cm per year). As it moves further from us, its angular size decreases, and it looks smaller relative to the Sun. It will take a long time for this to add up to a significant effect...

• One year (365.25 days):
• The key thing that happens over one year is that the Earth orbits the Sun, once, relative to the fixed stars.
• The tilt of the axis causes the seasons.
• Different stars are visible at night, due to the Earth being in a different location relative to the Sun.
• The moon moves away from us a little bit (about 3 cm).
• 26,000 years: The key thing that happens over this time period is precession. Precession is most easily observed in tops. As a top spins on its axis, the axis itself turns around, and points in different directions. The axis of the Earth behaves in a similar manner, pointing at different stars at different times. So, for example, Polaris has not always been the North star! About 12,000 years ago, Vega was the pole star. It takes about 26,000 years for the pole to precess completely around to point in the same direction in the sky.
As the axis points in different directions, the plane of the celestial equator moves, so that the equinoxes (the points where the celestial equator cross the ecliptic) also move. This is often called the "precession of the equinoxes", and is really the same thing as the precession of the pole. What does this mean? It means that every 50 years or so, we have to recalculate all of our RA's and Decs for all the objects in the sky, since the origin of RA changes its location! A pain in the neck, no? Thank goodness we invented the computer to keep track of this for us!

Concept Question 1:
If the Earth orbited the Sun twice as fast as it does now (1 orbit=182.5 days), what would be the length of the SOLAR day?

1. 23 h 56 m
2. 48 h
3. 12 h
4. 24 h 4 m

Concept Question 2:
If the moon rotated around its own axis half as fast as it does now, we would still never see the 'far' side.

1. T
2. F

Concept Question 3:
You observe the first quarter moon on the Eastern horizon. What time is it?

1. midnight
2. 6 am
3. noon
4. 6 pm

Concept Question 4:
Solar eclipses occur because

1. the shadow of the Earth falls on the Sun.
2. the shadow of the Moon falls on the Earth.
3. The shadow of the Moon falls on the Sun.
4. The shadow of the Sun falls on the Earth.