ASTRON-150: CH 00 POSTLEC

If you could change the layout of the solar system, which of the following would cause a lunar eclipse to occur at least once every month in this hypothetical situation?

Change the Moon's orbital plane so it is in the same plane as Earth's orbit around the Sun. Response: Good work! You correctly visualize that the Moon's orbit has to be in line with Earth's orbit in order for a lunar eclipse to happen just about every month.

What conditions must exist for a lunar eclipse to occur?

The phase of the Moon must be full and the Moon must be passing through Earth's orbital plane. Response: The two points at which the Moon's orbit crosses the Earth's orbital plane are called the nodes of the Moon's orbit. So another way to state the conditions for a lunar eclipse is that (1) it must be full moon, and (2) the Moon must be at or quite near one of the nodes of its orbit.

What conditions must exist for a solar eclipse to occur?

The phase of the Moon must be new and the Moon must be passing through Earth's orbital plane. Response: The two points at which the Moon's orbit crosses the Earth's orbital plane are called the nodes of the Moon's orbit. So another way to state the conditions for a solar eclipse is that (1) it must be new moon, and (2) the Moon must be at or quite near one of the nodes of its orbit.

Listed following are observable characteristics of equinoxes and solstices in the continental United States (which means temperate latitudes in the Northern Hemisphere). Match each characteristic to the corresponding equinox or solstice.

spring equinox -the Sun rises due east today, but will rise slightly north of due east tomorrow summer solstice -longest day (most daylight) of the yearthe noontime -Sun reaches its highest point of the year fall equinox -the Sun has declination 0 degree today, but will have a negative declination tomorrow winter solstice -the Sun crosses the meridian 23.5 degrees lower in altitude than the celestial equator -sunset occurs at its farthest point south of due west for the year -the noontime Sun casts the longest shadows

Listed following are a series of statements that each make a claim. Classify these as either testable by accepted methods of science or non-testable by accepted methods of science. Be sure to note that this question does not ask whether a statement would pass or fail a test; it only asks whether it is testable in principle.

testable by science -Earth orbits the Sun every 365.25 days. -There will be a solar eclipse next Tuesday at 11 a.m. -People born under the sign of Sagittarius are twice as likely to be teachers as anyone else. -Mars once had liquid water on its surface. -Bacteria acquire resistance to antibiotics through changes in their DNA. not testable by science -Hurricane Katrina was an act of God. -Vince Young is the greatest quarterback of all time.

Listed following are locations and times at which different phases of the Moon are visible from Earth's Northern Hemisphere. Match these to the appropriate moon phase.

waxing crescent moon -sets 2-3 hours after the Sun sets -visible near western horizon about an hour after sunset waning crescent moon -occurs about 3 days before new moon -visible near eastern horizon just before sunrise full moon -occurs 14 days after the new moon -rises at about the time the Sun sets -visible due south at midnight

Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.

1. A solar eclipse that occurs when the new moon is too far from Earth to completely cover the Sun can be either a partial solar eclipse or a(n) annular eclipse. 2. Anyone looking from the night side of Earth can, in principle, see a(n) total lunar eclipse. 3. During some lunar eclipses, the Moon's appearance changes only slightly, because it passes only through the part of Earth's shadow called the penumbra. 4. A(n) total solar eclipsecan occur only when the Moon is new and has an angular size larger than the Sun in the sky. 5. A partial lunar eclipse begins when the Moon first touches Earth's umbra. 6. A point at which the Moon crosses Earth's orbital plane is called a(n) node.

One way to triangulate the distance to many remote objects, such as stars, is to observe the shifts in their location relative to more distant background objects. This apparent shifting of an object's location with respect to the background objects is known as parallax. Parallax is represented in the figure, where the top image shows the parallax shift that is observed along a baseline that runs from one side of Earth to the other. The bottom two images show what the observer sees from opposite sides of Earth. Using triangulation, the distance to the object can be calculated with simple trigonometric relations.

1. As the distance to the object increases, parallax decreases. 2. As the size of baseline increases, parallax increases. 3. As the distance to background objects increases, parallax remains the same. Response: Measuring the parallax of a foreground object with respect to a more distant background of objects allows for the use of geometric triangulation to determine the distance to the foreground object. The key components include the baseline over which parallax is measured, the parallax that is measured, and the distance that is determined. Astronomers have used this technique to determine distances to the Moon and planets in the solar system. Parallax has also been used to determine distances to stars, but a much larger baseline involving Earth's orbit around the Sun is necessary to accurately measure parallax.

Suppose that instead of being inclined to Earth's orbit around the Sun, the Moon's orbit was in the same plane as Earth's orbit around the Sun. (Click "Show Moon with flat orbit" to see this situation.) In this hypothetical situation, approximately how many solar eclipses would occur each year?

12 Response: If the Moon orbited Earth in the same plane that Earth orbits the Sun (the ecliptic plane), we would have a solar eclipse at every new moon. Because there are about twelve new moons in a year, we would have twelve solar eclipses. Of course, this isn't what really happens. Continue to Part B to study the real situation.

In reality, the Moon's orbit about Earth is tilted (by about 5°) with respect to Earth's orbit about the Sun. As a result, the actual number of solar eclipses that occur each year is approximately _____.

2 Response: There are generally two periods of time each year when eclipses are possible — the "eclipse seasons" — and there is a solar eclipse of some type (partial, total, or annular) during each of these eclipse seasons. (Because the time between eclipse seasons is less than six months, in some years there is a third eclipse season and hence a third solar eclipse.)

Geometric reasoning can be used to measure distances both on Earth and in space. Surveyors on Earth and astronomers both use the geometric technique of triangulation to determine the distances and sizes of remote objects. In order to determine the distance using the triangulation method, a few key geometric components must be known. Once the baseline and the sightline angles are determined, then the distance can be calculated with simple geometric reasoning.

A. Angle that decreases with increasing distance to object B. Distance to object C. Right Angle D. Baseline E. Angle that increases with increasing distance to object Response: Surveyors use triangulation to measure distances to objects on Earth. The same technique can also be used to determine the distance to nearby astronomical objects. Astronomers use Earth's diameter as the baseline in the triangulation method to measure distances to planets and other objects in our solar system.

Shown following are five different phases of the Moon as seen by an observer in the Northern Hemisphere. Imagine that tonight the Moon is in the waxing gibbous phase (as shown at the far left (labeled "first") in the following ranking box). Rank the pictured phases from left to right based on the order in which you would see them over the next four weeks, from first seen to last.

FIRST waxing gibbious third quarter waning crescent waxing crescent first quarter LAST Response: Remember that "waxing" phases mean on the way to full moon and "waning" phases mean after full moon. So if tonight is a waxing gibbous moon, then we are headed toward full moon in about three to four days. Because the full moon is not shown, we'd next see a waning gibbous moon, then a third-quarter moon, and then a waning crescent. From there we'd have new moon (which isn't shown), then the waxing crescent, and then first-quarter. Finally, a full four weeks from now (actually 29 1/2 days), we'd once again have a waxing gibbous moon.

The following figures show a top view of Earth, sunlight, and six different positions of the Moon as it orbits Earth. Note that the distances shown are not drawn to scale. Rank each of the six lunar positions from left to right based on the amount of the Moon's illuminated surface that is visible from Earth, from greatest to least. (If two diagrams have an equal amount of illumination as seen from Earth, put one on top of the other.)

GREATEST full waxing gibbious first quarter/third quarter waning gibbious new LEAST

Listed following are the declinations of five different stars. Rank these declinations from left to right based on the maximum altitude (on the meridian) each star reaches for an observer at latitude 60°N, from lowest altitude (nearest the horizon) to highest altitude (farthest above the horizon).

NEAREST dec = -20 degrees dec = -5 degrees dec = +0 degrees dec = +10 degrees dec = +30 degrees FARTHEST Response: For latitude 60°N, the celestial equator extends from due east on the horizon to due west on the horizon, crossing the meridian at an altitude of 90° - 60° = 30° (in the south). Because the star with dec = +30° lies 30° to the north of the celestial equator on the celestial sphere, it must cross the meridian at a point 30° to the north of where the celestial equator crosses, which means at an altitude of 60°. The same reasoning explains the rest of the rankings. For example, the star with dec = -20° lies 20° to the south of the celestial equator on the celestial sphere, so it must cross the meridian at a point 20° to the south of where the celestial equator crosses, which means at an altitude of 10°.

Listed following are the latitudes of several locations on Earth. Rank these latitudes from left to right based on the maximum altitude (on the meridian) at which you would see a star with a declination of 0°, from lowest altitude (nearest the horizon) to highest altitude (farthest above the horizon).

NEAREST latitude 70 degrees N latitude 50 degrees N latitude 40 degrees N latitude 30 degrees N latitude 10 degrees N FARTHEST Response: A declination of 0° means the star is on the celestial equator. The star therefore follows the path of celestial equator across the local sky, which means it rises due east, crosses the meridian at an altitude of 90° minus your latitude, and sets due west.

Listed following are the latitudes of several locations on Earth. Rank these latitudes from left to right based on the maximum altitude (on the meridian) at which the celestial equator passes through the local sky, from lowest altitude (nearest the horizon) to highest altitude (farthest above the horizon).

NEAREST latitude 70 degrees N latitude 50 degrees N latitude 40 degrees N latitude 30 degrees N latitude 10 degrees N FARTHEST Response: The celestial equator always makes a half-circle across your sky (except at the North and South Poles), extending from due east on your horizon to due west on your horizon and crossing the meridian at an altitude of 90° minus your latitude. Therefore, the celestial equator passes directly overhead (altitude 90°) at Earth's equator (latitude 0°). As you move northward to higher latitudes, the celestial equator drops downward toward the southern horizon. (For latitudes south of the equator, the celestial equator drops toward the northern horizon as you move to more southerly latitudes.)

Each item following represents an amount of time. Recall from your reading that "sidereal" refers to events that are timed with respect to the distant stars, and "synodic" refers to special alignments of astronomical bodies, such as the Earth, Moon, and Sun. Rank the items from left to right in order of the amount of time they represent, from shortest time to longest time. If two items represent equal amounts of time, show this equality by dragging one on top of the other.

SHORTEST TIME sidereal day/one rotation of Earth on its axis solar day sidereal month/one Moon orbit around Earth synodic month/one full cycle of moon phase LONGEST TIME Response: The first three times relate to Earth's rotation: A sidereal day is equal to Earth's rotation period of about 23 hours and 56 minutes; our 24-hour solar day is slightly longer because Earth is moving around its orbit at the same time that it rotates. The last four items are related to the Moon's orbit around Earth, The Moon's true orbital period is the sidereal month, which is about 27 1/2 days. The synodic month, which is equal to the time from one new moon to the next, is longer (about 29 1/2 days) because Earth and the Moon are moving around the Sun at the same time that the Moon orbits Earth.

Once the distance to a remote object is determined via triangulation, one can measure the angular diameter of the object and convert that to an actual diameter. For relatively small angular diameters of a few degrees or less, the corresponding linear diameter can be approximated using the following expression: Diameter=Distance×(Angular Diameter)(57.3 degrees). Consider the Moon and Sun. Their angular diameters are both equal to about .5 degree. If the Sun is roughly 400 times more distant than the Moon, how much bigger is the Sun's diameter than the Moon's?

about 400 times bigger Response: Proportional reasoning shows that the Sun, being about 400 times more distant than the Moon, must be about 400 times larger in order to have the same angular diameter as the Moon, because angular distance is proportional to diameter divided by distance: (Diameter×(57.3 degrees))Distance=Angular Diameter