Declination is the angle, as measured from the Earth, between the celestial equator and any given celestial object. It is equivalent to latitude on the Earth.

The local sidereal time is equal to the Right Ascension of any object on the local meridian.

A sidereal day is the time it takes the Earth to rotate on its axis once measured relative to the stars. (It is the actual time for the Earth to rotate.) Light from the stars is parallel when reaching the Earth due to the extreme distance of even the nearest star. A mean solar day is the average time for the earth to rotate measured relative to the sun. Since the Earth has moved 1/365 of the way around the sun during this time, and the sun is much closer to the Earth that even the nearest star, the Earth must rotate just a tad more than one complete revolution in order for the sun to appear to complete one circle around the Earth. This "tad" is about 4 minutes. (Actually 3m 55.9s) Thus the solar day is about 4 minutes longer than a sidereal day.

The Full Moon is directly opposite the sun, therefore if the Full Moon is transiting, it must be midnight.

A Third Quarter Moon rises 90 degrees ahead of the sun (actually 270 degrees behind, but it turns out to be the same angle.) Thus the Third Quarter Moon will rise at midnight, transit at sunrise, and set at noon. So its noon.

The altitude of Polaris is equal to your latitude, as long as you can see Polaris. (Actually, it may be up to 0.8 degrees off, but its close enough for you to use in most situations.) Thus your latitude is about 32 degrees north. If you were south of the equator, you couldn't see Polaris, so you must be north.

We do not, however, have any information about our longitude from this observation.

1: Ships sailing away from the shore disappear from the bottom up rather that just getting smaller.

2: The shadow of the Earth on the moon during a lunar eclipse is always part of a circle.

1 degree = 60" and 1' = 60", so 1 degree = (60 x 60) = 3600"

The ecliptic is the plane of the Earth's orbit around the sun. On the celestial sphere, the ecliptic is the apparent path of the sun around the Earth over the course of a year. This apparent path is just the intersection of the orbital plane with the celestial sphere, which results in a tilted circle as seen from the Earth.

Apparent solar time is time kept by the actual position of the sun. When the sun is as high up in the sky as it gets, it is apparent noon. An apparent solar day, measured noon to noon, can vary by about 15 minutes either way from the mean (average) solar day of 24 hours. Apparent solar time is what a properly set up and adjusted sundial will tell you. (Although most of the sundials you can buy in garden shops and catalogs are not adjustable, and they must be adjusted or specially made to suit your latitude if they are to tell you the correct apparent time.)

An astronomical unit is the average distance from the Earth to the sun.

(1 AU ≈ 1.5 x 10¹¹ meters, but that is not how it is defined.)

"P" is the period of the orbit (how long it takes to complete one orbit) and "a" is the semi-major axis of the orbit, (Which for practical purposes we can take to be the average distance of the orbiting object from the body that it orbits.)

We use years for P and Astronomical Units (AU) for a. If we didn't, we would have to calculate k from:

where G is the universal gravitational constant (6.67 x 10^-11 m³/kg-s²), and m2 and m1 are the masses of the orbiting body and the stationary body respectively.

See? Isn't it just easier to use P in years and a in AU?

Yes, all objects in orbit are being "pulled" in by gravity. If there were no effect of gravity on the shuttle it would fly off into space. Gravity is pulling the shuttle (or any orbiting object) down, but the object is also moving sideways, and so by the time it falls to the surface of the Earth it has moved over so far that it misses the Earth, and just keeps falling.

The Earth's axis is tilted at an angle (23.5 degrees from the vertical in reference to the plane of the ecliptic), so that in summer the hemisphere where you are is tilted toward the sun, and in winter the hemisphere where you are is tilted away from the sun. This results in the sun's rays hitting the Earth more directly in the summer, and also the sun is up for a longer time in the summer, so it gets warmer.

The radius of the circumpolar zone is equal to your latitude, so the radius at 52 degrees north latitude is 52 degrees. A star must have a declination less than 52 degrees from the pole (90 degrees) to be in the circumpolar zone, so the minimum declination that a star could have and still be circumpolar is 90 degrees- 52 degrees = 38 degrees. Therefore, a star with a declination of 35 degrees will not be circumpolar from your location.

Just like to previous question, the radius of the circumpolar zone is equal to your latitude. A star just touching your horizon just below Polaris is just barely in your circumpolar zone, so we just work the previous problem in reverse. In this case we already know the minimum declination that a star could have and still be circumpolar (62 degrees), so the question is how far is that star from Polaris? 90 degrees - 62 degrees = 28 degrees, so we are at 28 degrees North Latitude. (North because we can see Polaris.)

The sun appears to move 15 degrees an hour ( 15 degrees/ h = 360 degrees/ 24 h). If you are West of Greenwich, your time is earlier. 45 degrees is 3 X 15 degrees, so you are 3 hours earlier. Therefore, it is noon where you are.

This requires the application of the same principle as the previous question, except we're working "backwards". The sun appears to move 15 degrees an hour ( 15 degrees/ h = 360 degrees/ 24 h). If the sun transits your meridian BEFORE it transits the Greenwich meridian, you must be EAST of Greenwich, since the sun moves from east to west. There is a 6 hour time difference between when the sun transits your meridian and when it transits Greenwich, so your longitude is 6 X 15 degrees = 90 degrees, and it has to be east, so your longitude is 90 Degrees East.

Vernal Equinox: About March 21

Summer Solstice:About June 21

Autumnal Equinox:About September 23

Winter Solstice: About December 21

Vernal Equinox: When the sun crosses the Celestial Equator moving from south declination to north declination. All places on Earth have approximately an equal number of daylight and dark hours on this date.

Summer Solstice: When the sun reaches its northern-most declination, and is directly over the Tropic of Cancer. It is the day with the longest period of daylight each year in the northern hemisphere.

Autumnal Equinox: When the sun crosses the Celestial Equator moving from north declination to south declination. All places on Earth have approximately an equal number of daylight and dark hours on this date.

Winter Solstice: When the sun reaches its southern-most declination, and is directly over the Tropic of Capricorn. It is the day with the shortest period of daylight each year in the northern hemisphere.

Your local sidereal time is equal to the Right Ascension of any object on your meridian. One hour ago the star with a RA of 20 hours 15 minutes was on your meridian, so THEN your local sidereal time was 20 hours 15 minutes (20:15). NOW its 1 hour later, so your local sidereal time must be 21:15.

1-C, 2-D, 3-C, 4-B, 5-D, 6-B, 7-C, 8-B, 9-A, 10-A, 11-B, 2-B, 13-B, 14-C, 15-C, 16-C, 17-C, 18-B, 19-A, 20-C, 21-C, 22-B, 23-A, 24-E, 25-C