Solution to Sample Problems

To help you prepare for the style of questions I ask, here are a few sample questions to solve:

Exam 1 Sample Questions and Answers

1. Give a brief definition of the Vernal equinox.

The Vernal equinox is the point on the celestial sphere where the imaginary path of the Sun (the ecliptic) intersects the celestial equator as the Sun moves northward. It marks the beginning of spring in the northern hemisphere.

2. Why did Aristarchus' theory that the earth moves around the Sun fail to gain acceptance?

Even though Aristarchus was correct, he and his contemporaries lacked the technical capability to detect stellar parallax. Without a telescope, the minute shift in a star's position due to observing it from different points in Earth's orbit is immeasurable small. The largest stellar parallax is less than a single arcsecond (less than 1/3,600 of a degree!)

3. What is the group of constellations the Sun moves through during the year?

  1. the zodiac
  2. precession
  3. autumnal equinox
  4. the ecliptic

In case you're confused, the zodiac is the group of constellations the Sun moves through during the course of the year, but the ecliptic is the actual path of the Sun.

4. Why do seasonal variations in the amount of daylight occur?

In order for the length of day and night to vary over the course of a year, a planet's rotational axis must be tilted with respect to the perpendicular of its orbital plane.

In the case of Earth, the celestial poles are not aligned with the ecliptic poles.

5. At what time of year is Earth closest to the Sun?

  1. Winter
  2. Spring
  3. Summer
  4. Fall

Although we in the northern hemisphere experience the warmest days and longest daylight in the summer months, Earth is physically closer to the Sun by about 1.5 million miles in early January.

Exam 2 Sample Problems and Solutions

1. What three laws did Kepler develop to explain planetary motion?

  1. Planet revolve about the Sun along elliptical orbits with the Sun occupying one focus of the ellipse.
  2. A radial line connecting the Sun and a planet sweeps out equal areas of space during equal areas of time.
  3. The square of the sidereal (orbital) period is proportional to the cube of the average planet-Sun distance (semimajor axis).

 

2. Sketch a diagram or describe the atmospheric layers of the Sun.

The solar atmosphere

3. Explain why sunspots are darker than the surrounding photosphere.

According to the Stephan-Boltzmann law, the total amount of energy at all wavelengths flowing through an area per second (called the flux) is related to the fourth power of the temperature:

E = σT4

From analyses of sunspots, astronomers have observed the Zeeman effect, a phenomenon that causes the splitting of spectral lines in the presence of a strong magnetic fields. Based on an understanding of gases in a plasma state, astronomers know that the speeds of ions in the presence of a strong magnetic field can be retarded. Lower ionic velocities correspond to lower kinetic energies and thus, temperature of the plasma. Since the temperature of a sunspot is typically 1,000K lower than the surrounding photosphere, the energy—and associated brightness—of the sunspot is considerably lower than the surroundings. In fact, a sunspot is blindingly bright and only appears dark in contrast to the hotter photosphere.

4. What is the triple-alpha process and when does it occur in the life of a star?

The triple-alpha process involves the nuclear fusion of helium-4 nuclei (historically called alpha particles because of the discovery of alpha rays in the early 1900s) into carbon nuclei. The reaction requires a temperature in excess of 100 million K and only occurs when a star has exhausted its core supply of hydrogen and left the main sequence. Red giant stars use the triple-alpha process to generate heat and light.

Triple-Alpha process

Final Exam Sample Problems and Solutions

1. Sketch and label a diagram of our Milky Way galaxy showing how it might appear to an observer in the Large Magellanic Cloud. Be sure to include approximate sizes and the approximate location of our Solar System.

Sketch of Milky Way

2. What significant transformation occurred about 400,000 years after the big bang? What evidence of this event do we "see" today?

At that time the temperature of the expanding (and cooling) universe dropped to approximately 3,000 K. Prior to this time the Universe consisted primarily of heavy nuclei fused at higher temperatures, protons, electrons, and electromagnetic radiation. Because of the high temperature, the electrons were zipping around so rapidly that they effectively absorbed the radiation and stopped it from traveling great distances. The Universe was essentially, a very hot, opaque fog.

At 3,000 K the electron speeds had dropped to the point that the protons could capture the electrons and form stable hydrogen atoms. This "condensation" of matter dissipated the fog permeating the Universe—just like condensing rain droplets cause a fog to lift on Earth—and allowed the radiation to "decouple" from the matter in the Universe. The Universe was transformed from a radiation-dominated phase to a matter-dominated phase.

The evidence we "see" today is the 3 K cosmic microwave background (CMB) radiation first measured by Penzias and Wilson in 1964. As the Universe continued to expand to its present size, the 3,000 K radiation emitted when the Universe was 365,000 years old experienced a red shift that changed the radiation's wavelength from the infrared to the microwave region of the electromagnetic spectrum and caused the temperature to decrease (read a discussion of Wien's law) from 3,000 K to the 3 K temperature measured today.

3. What is believed to be the source of the earth's immense magnetic field?

The earth appears to have a large molten outer core composed primarily of iron. Convection currents are believed to cause the molten iron to circulate, and as the warm, less dense iron rises, electrons are freely exchanged between iron atoms. This exchange of electrons while the atoms are circulating produces electric currents that are capable of generating a magnetic field.

4. Describe one piece of evidence indicating that a cataclysmic impact of an asteroid was at least partially responsible for the demise of the dinosaurs 65 million years ago.

Geologists have discovered a layer of shale (a metamorphic rock produced when sandstone is subjected to tremendous heat and pressure) called Burgess shale that is found under many layers of sediment and seems to date to 65 million years ago. This shale is extremely rich with the rare element iridium (16 times more than the surrounding layers). Iridium is very rare in the earth's surface but quite abundant in meteorites that have been uncovered on Earth. Also, dinosaur fossils are quite abundant below the Burgess shale but almost nonexistent above this layer.

More recently, a group of geologists working for a Mexican oil company discovered the remnant of an enormous crater buried deep below the Yucatan peninsula that dates to the same age as the Burgess shale. Additional evidence comes from the discovery of "shocked" quartz crystals that show evidence of tremendous stress and heat (presumably from a titanic impact), tiny tektites in the rock layers surrounding the Gulf of Mexico, and fossils of ocean-dwelling animals found high in the mountains of Haiti and Puerto Rico.

5. Even on a cold, but sunny winter day the temperature inside a parked car can become quite warm after the car is parked outside for a few hours. Name and describe the phenomenon responsible for this effect.

The phenomenon described is the Greenhouse effect. This effect occurs when infrared radiation (heat) is trapped beneath an opaque layer. In the case of a parked car, visible sunlight enters the passenger compartment and is absorbed by the car's seats, carpet, dash, etc. Eventually the absorbed energy causes the temperature of the materials to rise sufficiently for infrared radiation to be emitted into the passenger compartment. Infrared is incapable of penetrating glass, however, and the infrared radiation remains trapped inside the car causing the temperature to rise dramatically.

In a planetary atmosphere, carbon dioxide and water vapor form a barrier much like glass in a car that effectively traps infrared radiation emitted by the warm ground from escaping into space. The more carbon dioxide present, the more effective the atmosphere is at trapping heat.

Exam 1 Review Notes | Exam 2 Review Notes | Final Exam Review Notes