Astro Exam 1

Front 1

What is the difference between a hypothesis and a theory?

Back 1

A hypothesis is a collection of well-reasoned ideas about an observable phenomenon that can be used to make testable predictions. A theory is a hypothesis, or collection of hypotheses, that have survived repeated validation by observation and/or experiment and form a self-consistent description of some aspect of nature.

Front 2

Why are different stars overhead at 10:00 PM on a given night than two hours later at midnight?

Back 2

The Earth rotates under a seemingly fixed collection of stars at a constant rate. Some stars that were below the horizon at 10 PM are above the horizon at midnight and vice versa. .

Front 3

Why does the tilt of the Earth's axis relative to Earth's orbit cause the seasons as we orbit the Sun?

Back 3

There are two effects resulting from the tilt of the Earth's axis that combine to cause the seasons.

•The tilt causes the length of the day to vary throughout the year. Longer days allow the Sun to deposit more energy on the Earth causing it to warm more than shorter days.
•The Sun traces a different path through the sky at different times of year. When it follows its highest path then the light rays are very concentrated on the Earth's surface. The concentrated rays deposit more energy than diffuse ones leading to more warming. When the Sun traces its lowest path in the sky the light rays are spread out over a greater area of the Earth's surface resulting in less energy deposition and less warming.
The high path corresponds with the longest days leading to the most heating. This time of the year is known as the Summer.

Front 4

Why are different stars overhead at midnight on June 1 than at midnight on December 1?

Back 4

The Earth orbits about the Sun. The side facing the Sun experiences day and the side facing away experiences night. The nightside sees different areas of the sky, and hence different collections of stars, in June and December.

Front 5

What are the March and September equinoxes?

Back 5

The March and September equinoxes occur when the ecliptic crosses the celestial equator. They generally are considered the beginning of Spring and Fall, respectively, and the days and nights are of equal length then. The Sun rises due east on the equinoxes.

Front 6

What are the northern and southern solstices?

Back 6

The northern and summer solstices occur when the ecliptic is furthest north and south of the celestial equator, respectively.

Front 7

Why doesn't a lunar eclipse occur at every full moon and a solar eclipse at every new moon?

Back 7

The Moon's orbit is inclined 12° relative to the Earth's orbital plane or the ecliptic). As a result the Moon spends a great deal of its time above or below the line connecting the Sun and the Earth even when it is in the full or new position. The only way a shadow can be cast is if all three bodies fall on that connecting line known as the line of nodes.

Front 8

Which type of eclipse — lunar or solar — do you think most people on Earth have seen? Why?

Back 8

More people on Earth are likely to have seen a lunar eclipse than a solar eclipse. In a lunar eclipse the Earth is casting a shadow on the Moon. Being far larger the Earth casts a large shadow. The Moon spends a long time in the shadow and thus the eclipse is visible to entire continents at once. In solar eclipses the Moon casts a small shadow on the Earth. Only those people in the shadow's path will observe the eclipse.

Front 9

What would you tell a fellow student who said, "Stars move across the stationary celestial sphere such that each star can be seen overhead at some time of the night."

Back 9

The student is wrong, or incomplete, on a few counts in this remark. In the celestial sphere model, the stars are assumed to be fixed on the sphere. The entire sphere rotates about the Earth such that the stars pass from east to west and complete one circuit in 24 hours (23 hours 56 minutes to be precise since the stars are timed to the sidereal day). The stars that can be seen at night depend on several factors including the latitude of the observer and the time of year. Stars that are visible in the northern hemisphere are invisible year-round in the southern and vice versa because of the horizon. Stars that are visible in the summer are invisible in the winter because the Earth's nightside faces a completely different direction throughout the year.

Front 10

What would you tell a fellow student who said, "All stars have the same intensity, but a star hotter than the Sun would have a peak in the red region and its graph would be spread out more equally on both sides of the visible region of the spectrum."

Back 10

This student is wrong on pretty much all counts. Not all stars have the same intensity; that is a function of the temperature of the star (hotter stars emit more energy per unit area according to the Stefan-Boltzmann law) and the size of the star (more surface area means more area from which to radiate energy). As the temperature increases the blackbody spectrum peaks at shorter wavelengths. That would shift the peak towards the blue end of the spectrum and away from the red. The spectrum actually gets more asymmetric as the temperature increases. There is a sharp increase to peak intensity and then a long tail to longer wavelengths.

Front 11

Using Wien's law and the Stefan-Boltzmann law, explain the color and intensity changes that are observed as the temperature of a hot, glowing object increases.

Back 11

Wien's law states that the peak in the electromagnetic spectrum shifts to shorter wavelengths as its temperature increases. Short wavelengths correspond to the blue end of the spectrum so as something heats up its color would change from red to blue and on to white as the peak shifted into the wavelengths shorter than visible light. (The tail of the spectrum would lead to roughly equal amounts of all color being present causing the light to appear white.) The Stefan-Boltzmann law says that the flux of energy from a hot object increases as the temperature increases. (It goes as the fourth power of the temperature.) As the object heats up the increase in energy flux causes the object to glow more and more brightly. Combining these two effects, as an object heats up it becomes brighter and appears more blue-white.

Front 12

If you double the Kelvin temperature of a hot piece of steel, how much more energy will it radiate per second?

Back 12

The Stefan-Boltzmann law states that the energy flux of a hot blackbody goes as the temperature (in Kelvin) raised to the 4th power. If the temperature is doubled, then the energy output would increase by a factor of 2^4 = 16.

Front 13

Why do different elements display different patterns of lines in their spectra?

Back 13

The different spectral lines are determined by the atomic orbitals available to the electrons in the atom. A spectral line corresponds to a transition between different orbitals as an electron absorbs or emits a photon of just the right energy/wavelength. The available orbitals are set by the number of protons in the nucleus and the electrons orbiting about the nucleus (the number of electrons and protons is the same). Different elements have different numbers of protons (that's how you tell them apart) so they have different spectral line patterns.

Front 14

If you see a blue star, what does its color tell you about how the star is moving through space?

Back 14

The fact that a star is blue does not necessarily tell you anything about the motion of a star. A motionless star can appear blue because its temperature is such that it emits a lot of energy at blue wavelengths due to Wien's law. It could indicate that the star is moving towards you; a cool, reddish star moving towards you could exhibit a Doppler shift that would cause it to appear blue. It's also possible that is a high-temperature star moving away whose light is red-shifted so it appears blue. It's really necessary to look at spectral lines to determine the motion of a star using Doppler shift.

Front 15

Why can radio astronomers make observations at any time during the day, whereas optical astronomers are mostly limited to observing at night?

Back 15

Radio astronomers can work day or night because our atmosphere is mostly transparent to radio wavelengths of electromagnetic radiation. It is also transparent to visible light but the scattering of the Sun's light by the atmosphere washes out our view of stars other than our own during the day.

Front 16

What would you tell a fellow student who said, "Planets move fastest when farthest from the Sun because there is more gravity at great distances."

Back 16

Planets actually move fastest when they are close to the Sun. Kepler's second law states that planets sweep out equal areas in equal times. When the planet is close to the Sun it has to travel a greater distance to sweep out an equal area compared to when it is far from the Sun. The second statement is false as well. The gravitational attraction between objects falls off with distance. It is this reduced gravitational attraction that leads to planets traveling slowly when distant from their primary.

Front 17

How is an astronomical unit (AU) defined? Give an example of a situation in which this unit of measure would be convenient to use.

Back 17

The astronomical unit is defined to be the average distance between the Earth and the Sun. It is a useful unit to use when dealing with interplanetary distances, that is distances between objects inside our Solar System. The furthest planet away in our Solar System, Neptune, orbits at a distance of 4498 million kilometers or a mere 30 AU.

Front 18

A reporter once described described a light-year as "the time it takes light to reach us traveling at the speed of light." How would you correct this statement?

Back 18

A light-year is the distance through space that light travels in one year. It is a unit of distance, not time like the reporter seems to suggest. Since all light travels at a uniform speed this works out to be a uniform distance of 9.46 million-million kilometers.

Front 19

In what direction does a planet move relative to the horizon over the course of one night?

Back 19

Planets move in the same direction as every other natural body in the night sky - from east to west.

Front 20

A planet moves in the same direction relative to the horizon whether the planet is in retrograde motion or not. What does this tell you about the speed at which planets move on the celestial sphere?

Back 20

Clearly the planets do not move that rapidly across the celestial sphere otherwise we would see them travel from west to east over the course of one night when they were in retrograde motion. As usual, the motion of objects in our night sky is dominated by the 24 hour rotation period of the Earth.

Front 21

What is Kepler's first law?

Back 21

The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

Front 22

What is Kepler's second law?

Back 22

A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

Front 23

What is Kepler's third law?

Back 23

The square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of the orbit.

Front 24

Why are Kepler's laws important?

Back 24

Kepler's laws can be used to predict the future positions of orbiting bodies and they paved the way for Newton's laws and the law of universal gravitation.

Front 25

What observations did Galileo make that reinforced the heliocentric model?

Back 25

Galileo made two main observations that reinforced the heliocentric model. He directly observed objects orbiting an object other than the Earth - he observed several moons orbiting Jupiter. This was anathema to the geocentric model that stated everything circled the Earth. He also saw that Venus exhibited all the same phases as the Moon and that the apparent size of the planet was correlated with its phase. It would be impossible for Venus to exhibit the full phase unless it was on the far side of the illuminating object, the Sun, from us. It would be impossible for it to exhibit the new phase unless it was on the near side. Since Venus exhibits both it must orbit the Sun.

Front 26

Why couldn't Galileo's observations backing up the heliocentric model have been made before his time?

Back 26

These observations could not have been made previously because they all required a telescope. Venus and Jupiter appear as nothing more than points of light in the night sky unless viewed through a telescope.

Front 27

What is Newton's first law?

Back 27

An object remains at rest, or moves in a straight line at a constant speed, unless acted on by a net outside force.

Front 28

What is Newton's second law?

Back 28

The net force exerted on an object is equal to its mass times its acceleration.

Front 29

What is Newton's third law?

Back 29

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.