Ch. 2 HW

How many degrees is the angle from the horizon to the zenith? Does your answer depend on what point on the horizon you choose?

90 degrees

When is the next leap year? Was 2000 a leap year? Will 2100 be a leap year?

According to Gregorian calendar, leap years occur in years exactly divisible by 4. Yes 2000 was a leap year. No, 2100 will not be a leap year.

Imagine that someone suggests sending a spacecraft to land on the surface of the celestial sphere. How would you respond to such a suggestion?

Astronomers now recognize that the celestial sphere is an imaginary object that has no basis in physical reality.

How do the stars appear to move over the course of the night as seen from the north pole? As seen from the equator? Why are these two motions different?

At the north pole, all the stars are circumpolar, circling around the celestial pole but never going below the horizon. Stars on the celestial equator would make a 360◦ path, following the horizon. From the equator, all the stars rise and set. The 90◦ difference in latitude is responsible for the difference in appearance.

Where on Earth do you have to be in order to see the north celestial pole directly overhead? What is the maximum possible elevation of the Sun above the horizon at that location? On what date can this maximum elevation be observed?

At the north pole. Since the horizon coincides with the celestial equator as seen at the north pole, the maximum possible elevation of the sun is equal to obliquity of the ecliptic (the angle of tilt of the equator with respect to the ecliptic), namely 23½°. This elevation can be observed on the date of the summer solstice, that is on or about June 21.

How does the daily path of the Sun across the sky change with the seasons? Why does it change?

Because the Sun's position on the celestial sphere varies slowly over the course of a year, its daily path across the sky (due to Earth's rotation) also varies with the seasons. On the first day of spring or fall, when the Sun is at one of the equinoxes, the Sun rises directly in the east and sets directly in the west.

What is the celestial equator? How is it related to Earth's equator? How are the north and south celestial poles related to Earth's axis of rotation?

Celestial equator= a great circle on the celestial sphere 90 degrees from the celestial poles If we project Earth's equator out into space, we obtain the celestial equator. The celestial equator divides the sky into northern and southern hemispheres, just as the Earth's equator divides Earth into two hemispheres. If we project Earth's north and south poles into space, we obtain the north celestial pole and the south celestial pole. Thus, the two celestial poles are where Earth's axis of rotation intersects the celestial sphere. The celestial equator is the great circle on the celestial sphere that is midway between the celestial poles. The plane of the celestial equator is the same as the plane of the Earth's equator. The north and south celestial poles are at the intersection of the celestial sphere with the extension of the Earth's axis of rotation.

What is the celestial sphere? Why is this ancient concept still useful today?

Celestial sphere= an imaginary sphere of very large radius centered on an observer; the apparent sphere of the sky Astronomers now recognize that the celestial sphere is an imaginary object that has no basis in physical reality. Nonetheless, the celestial sphere remains a useful tool of positional astronomy. If we imagine, as did the ancients, that Earth is stationary and that the celestial sphere rotates around us, nit is relatively easy to specify the directions to different objects in the sky and to visualize the motions of these objects.

Why is a particular star overhead at 10 PM on a given night rather than two hours later at midnight; how does this relate to Earth's orbit? Why are different stars overhead at midnight on June 1 rather than at midnight on December 1?

Earth rotates once a day around an axis from the north pole to the south pole (diurnal motion); Earth also revolves once a year around the Sun

Using a diagram, explain why the tilt of Earth's axis relative to Earth's orbit causes the seasons as we orbit the Sun.

Earth's axis of rotation is inclined 23.5 degrees away from the perpendicular to the plan of Earth's orbit. The north pole points in the same direction as it orbits the Sun, near the star Polaris. Consequently, the amount of solar illumination and the number of daylight hours at any location on Earth vary in a regular pattern throughout the year. This is the origin of the seasons.

What is the ecliptic plane? What is the ecliptic?

Ecliptic plane= the plane of Earth's orbit around the Sun -all planets orbit on/near the ecliptic -orbit is nearly aligned with the ecliptic Ecliptic= the apparent annual path of the Sun on the celestial sphere -plane of this path is the same as the ecliptic plane -sun moves from west to east - opposite of celestial sphere motion -sun takes a year to go around the ecliptic

Where on Earth do you have to be in order to see the Sun at the zenith? As seen from such a location, will the Sun be at the zenith every day? Explain reasoning.

On the Summer and the Winter Solstice (around June 21 and December 21 respectively), the Sun reaches its most northern and southern declinations. People who live at a latitude of 23.5º north (Tropic of Cancer) and south (Tropic of Capricorn) of the equator will have the Sun at their zenith at noon only on that day of the year (June 21 or December 21 depending upon whether they live at 23.5º north or south).

Is there any place on Earth where all the visible stars are circumpolar? If so, where? Is there any place on Earth where none of the visible stars is circumpolar? If so, where? Explain answers.

Since at either pole the celestial equator coincides with the horizon, and since the diurnal circles of all stars are parallel to the celestial equator, it follows that at either the north or the south pole all visible stars are circumpolar. Since the sky seen from the equator would have both celestial poles on its horizon, it follows that at the equator there are no circumpolar stars.

Why can't a person in Antarctica use the Big Dipper to find the north direction?

The Big Dipper is on the northern hemisphere of the celestial sphere, close to the north celestial pole. A person near Earth's south pole can only see things in the southern celestial hemisphere because the Earth (the horizon) blocks the view of everything else.

Why is the ecliptic tilted with respect to the celestial equator? Does the Sun appear to move along the ecliptic, the celestial equator, or neither? By about how many degrees does the Sun appear to move on the celestial sphere each day?

The ecliptic is inclined to the celestial equator by 23.5 degrees because of the tilt of Earth's axis of rotation. As seen from Earth, the Sun appears to move around the celestial sphere along a circular path called the ecliptic; move along the ecliptic at a rate of about 1 degree per day.

Where would you have to look to see your zenith? Where on Earth would you have to be for the celestial equator to pass through your zenith? Where on Earth would you have to be for the south celestial pole to be at your zenith?

The point in the sky directly overhead an observer anywhere on Earth is called that observer's zenith. If you were at the Earth's equator, the celestial equator would pass through your zenith. If you were at the South Pole Station, the celestial pole would be at your zenith.

What is the difference between the sidereal year and the tropical year? Why are these two kinds of year slightly different in length? Why are calendars based on the tropical year?

The sidereal year is defined to be the time required for the Sun to return to the same position with respect to the stars. It is equal to 365.2564 mean solar days. The sidereal year is the orbital period of Earth around the Sun, but it is not the year on which we base our calendar. But most people want annual events to fall on the same date each year. Therefore, to set up a calendar we use the tropical year, which is equal to the time needed for the Sun to return to the vernal equinox. This period is equal to 365.2422 mean solar days. Because of precession, the tropical year is 20 mins and 24 secs shorter than the sidereal year.

Give two reasons why it is warmer in summer than in winter.

The sun is high in the midday summer sky, so a shaft of sunlight is concentrated onto a small area, which heats the ground effectively and makes the days warm. Northern hemisphere spends more than 12 hours in sunlight, longer days.

What are the vernal and autumnal equinoxes? What are the summer and winter solstices? How are those four points related to the ecliptic and the celestial equator?

Vernal equinox= the point on the ecliptic where the Sun crosses the celestial equator from south to north; marks beginning of Spring in northern hemisphere Autumnal equinox= the intersection of the ecliptic and the celestial equator where the Sun crosses the equator from north to south; fall begins Summer solstice= the point on the ecliptic where the Sun is farthest north of the celestial equator; beginning of summer Winter solstice= Sun reaches greatest distance south of the celestial equator; Winter begins

Is there any place on Earth where you could see the north celestial pole on the northern horizon? If so, where? Is there any place on Earth where you could see the north celestial pole on the western horizon? If so, where? Explain answers.

Yes, the north celestial pole is visible from the northern horizon. No, not visible from western horizon.