Astronomy 100 -- Problem Set 1
Due: Tuesday 5 February 2008
Name:

Fill in the box with the correct answer (answers should be just a few words or a number).

  1. Is 0.0001 larger, smaller, or the same as 1.0x10-5 ?

  2. What is 3.0x102 x  4.0x107 ?

  3. What is 6.0x103 + 8.0x104 ?

  4. Suppose we make a scale model of the Solar System in which the model Earth is 10 centimeters in radius (about the size of a basketball). The real Earth is 6.4x108cm in radius. Jupiter is 7.1x109cm in radius. How big must the scale model version of Jupiter be in order to be the right size relative to the Earth?

    Note: Some of the problems below are meant to illustrate the level of mathematics that will accompany this course. The concepts themselves will be discussed in detail later in the semester. The problems should provide enough background information so that you need only focus on the mathematical issues.

  5. Kepler's Third Law of planetary motion relates the time, P, it takes a planet to complete one orbit about the Sun to the distance, a of that planet from the Sun via the equation P2 = a3. This equation works if P is expressed in units of years and a is in ``Astronomical Units'' (units of the Earth-Sun distance, abbreviated A.U.) You can see that this equation works for the Earth which has a=1 A.U. and P=1 year. It will also work for another solar system as long as the star at the center of that solar system has the same mass as our Sun. Suppose a planet was discovered orbiting another star and that planet takes 8 years to complete an orbit around the star. Presuming that star is the same mass as our Sun, how far does this planet orbit from its star?

  6. The total amount of energy radiated by a star each second is called its luminosity, L. The luminosity of a star which has a radius, R, and surface temperature, T, can be approximated by the equation L=4R2T4. Consider two stars which have the the same radius, R. One star has a surface temperature three times as hot as the other. How many times more luminous is the hotter star? Note that you do not need to know the value of the constant or to calculate L in order to answer this question. If you spend more than 10 minutes struggling with this question you should ask for help.

  7. What is the altitude (in degrees) of the Sun above the horizon at noon on the first day of Winter as seen from Amherst? The latitude of Amherst is 42 degrees. Remember that altitude in this context is the angle you would measure between a line drawn from your nose to Sun and a line from your nose to the horizon directly below the Sun.

    Helpful Questions: What is the altitude of the celestial pole in the sky as seen from Amherst? What is the angular distance between the celestial pole and the celestial equator? Using the previous two pieces of information...At its highest point above the horizon, what is the angular distance between the celestial equator and the horizon?

  8. Neptune (currently the most distant planet from the Sun!) lies about 4.5x109 kilometers from the Earth. If you were traveling toward Neptune at typical highway speeds (about 100 kilometers/hour) how many years would it take to reach Neptune?

  9. Although it is the Earth that orbits the Sun, it appears to us that the Sun moves around the Earth tracing a path among the stars around the sky in the course of a year. What is the name of the apparent path followed by the Sun around the sky?

  10. What is the name for the collection of constellations through which the Sun appears to pass as the Earth orbits the Sun?