CEU Astronomy Homework Questions

Chapter 1: (due date given out in class)

1. If you could drive a car through space at 100 km per hour, how long would it take you to reach Pluto? (average distance is about 4 billion miles, or 6 billion km.)

2. With that same car, how long would it take you to reach the nearest star beyond our solar system? (Proxima Centauri is about 4.4 light-years from Earth and one light-year is about 6 trillion miles or about 10 trillion km.)

Hints: You are welcome to provide the answer in hours, days, weeks, months, or years. You may work with miles, if you wish, or with km, whichever is most convenient for you. Please note: this problem is actually easier to do by hand than with a calculator, if you know how to do ordinary hand division. It is especially easy if you understand scientific notation. Notice that the divisor is simply a 1 with two zeros after it, if you are working with km.

Chapter 2: (due date given out in class)

1. If a planet had an axial tilt of 35 degrees and orbited its star in a nearly circular orbit, would it have seasons?  If so, would they be more extreme than ours, or less extreme?  Why or why not?

2. How many minutes of arc are in a circle?  How many seconds of arc are in a circle?  How many seconds of arc is the diameter of the moon? (1/2 degree)

Hints: Remember what causes seasons, as we discussed in class and remember that the orbit is nearly circular. Remember that there are 360 degrees in a circle and that there are 60 minutes in each of those degrees. Remember also, that there are 60 seonds in each minute of arc, and that the moon is about 30 minutes of arc in diameter. Each of the answers to number two is computed with multiplication.

Chapter 3: (ditto)

1. The asteroid Ceres has an average distance from the sun of 2.77 A.U.   What is its year?  (how long does it take to orbit the sun one time)

Hint: for this problem you will need to remember one of Kepler's laws: A squared equals P cubed. (The orbital time squared equals the distance cubed, that is multiplied by itself twice) so you will want to find out what 2.77 cubed is, and take the square root of that number. A calculator will be very helpful here. The answer will come out as a number of Earth years- remember that because Ceres is farther from the sun that Earth, it takes longer than one Earth year for it to go around the sun one time.

Chapter 4: (ditto)

1. If the Earth were moved to 4 times its present distance from the sun, how much would the gravitational pull of the sun change?

2. If the sun were to double in mass, how much would the gravitational pull of the sun on the Earth change?

3. Compare the gravitational pull of the sun upon Jupiter with the gravitational pull of the sun on the Earth.  (How much more or less is it?) Note that the mass of Jupiter is 318 times as much as the mass of Earth, and the distance to Jupiter is 5.2 A.U.

Hints: For these problems, you will need to remember Newton's laws of gravitation: F equals G times M times M divided by D squared, where M and M are the masses of the two objects and D is the distance between them. Please note: you will not need the value of G, the gravitaional constant to do these problems. Note that this formula is an equation, which means that if you change any value on one side of the 'equals', you change the result on the other side by exactly the same proportion. Thus, for number one, if the distance D becomes 4 times as much, you must square it to 16 and thus, the value of this side is now 1/16th as much, which means that the value on the other side is now 1/16th as much. You can do number two and number three in exactly the same manner but you will find it helpful to use a calculator on number three, since you will be squaring the number 5.2 and then dividing that result into 318.

Chapter 5: (ditto)

•1. Use the formula given out in class to determine the magnification produced by the following combinations:

–A 10-inch F:10 telescope with a 1-inch eyepiece
–An 8-inch F:8 telescope with a ½ inch eyepiece
A 5-inch F:10 telescope with a 1/4 inch eyepiece
–

Hints: Remember that the 'F' numbers given here are focal ratio numbers, and you must calculate the focal length in order to answer the questions. The focal length of each optical system is the focal ratio multiplied by the diameter of the lens or mirror. Thus the focal length of the telescope in number one is 100 inches. Now you simply divide the focal length of the eyepiece (in number one, that is 1 inch) into the focal length to get the magnification. These problems can easily be done by hand if you know how to divide a fraction into a number. You simply invert the fraction and multiply instead of dividing.

Chapter 6: There is no homework assigned for chapter 6 in the book. Take a break!

Chapter 7: (due date to be announced in class)

•1. Since both Mars and Venus have atmospheres consisting almost entirely of carbon dioxide, why is there much greenhouse effect on Venus and very little on Mars?

•

2. The brightness of Venus changes considerably as it moves around the sun in its orbit.  As it rises in the western sky each time it catches up to the Earth in its orbit, it becomes much brighter before passing our planet, and sinking back down into the sunset.  A few weeks later, it appears in the morning sky, very bright, and gradually fades somewhat as it moves ahead of us in our orbit.    What are the two major reasons for this change in brightness?

Hints: For number one, notice the comparison between the density of Venus' atmosphere and Earth, and the comparision between the density of Mars' atmosphere and Earth. For number two, (this is a hard question because the text book does not answer it and what they do say there is mis-leading.) Remember what we said about the intensity of light as the distance changes, and remember that since Venus is between us and the sun, we do not see all of its face at any time. (the only time the entire face is toward us is when it is behind the sun)

Chapter 8: (ditto)

1. Can Jupiter ever become a star?  Why or why not?  (a star fusing hydrogen requires a core temperature of at least 18 million degrees F.)

2. How long are the four seasons on Uranus?

Hints: Remember that the temperature in the core of a celestial body is a result of the compression of the amount of mass above it. Assume for this problem that Jupiter is not gaining any mass. For number two, simply remember how long it takes Uranus to orbit the sun one time.

Chapter 9: (ditto)

1. •How close to Pluto’s Roche limit is its moon, Charon?  (distance currently is 12,000 miles.  The Roche limit is 2 ½ times the planet’s radius.  Pluto is about 1400 miles in diameter.)

2. Assuming a constant rate of 300 tons per day, how much meteor material has been added to the Earth since it formed?

Hints: for number one, you need the difference between the present distance of Charon (12,000 miles) and the Roche limit, which you must compute (2 1/2 times the planet's radius). Remember that the radius is one half of the diameter. For number two, simply figure out how many days have passed since the Earth formed (use 4.6 billion years as its age) and multiply that by 300 tons. The answer is a very big number.

Chapter 10: (ditto)

1. Why were most of the first extrasolar planets discovered, large Jupiter-like planets?
2. Why are we most interested in knowing the size of an extrasolar planet?

Chapter 11: No homework!

Chapter 12: (due date to be announced in class)

1. What is the absolute magnitude of the star Sirius?  (about 8 light-years distant and has a visual magnitude of about -1.5)

2. •Why are there relatively few massive stars? (stars much more massive than our sun)

Hints: Number one might be the most difficult problem you are given in this class this semester. You must use the magnitude scale I discussed in class and figure out how many magnitudes would change from its current visual of -1.5 to compute its absolute magnitude if it were moved from its present distance of 8 light-years to 32 light-years, which is 4 times as far away. This means that it will be much dimmer and the answer will be a positive number. Remember that each magnitude represents a factor of 2 1/2 times or one over 2 1/2 times its neighbor. In this case, you will be working with fractions of 1 over 2 1/2, and you will find it very convenient to use a calculator to determine how many of these fractions multiplied by each other, equals the fraction of light coming from Sirius when it is moved 4 times farther away. An approximation is just fine here- The answer will be to move about ? number of magnitudes to the right, giving you a magnitude that is between two positive whole numbers. Sorry about the complexity of this problem, but you needed to have one real challenge this term.

Chapter 13: (ditto)

1. •In what year did the Crab Nebula (M1) actually explode?  (the distance is about 2000 parsecs and it was seen here on Earth in the year 1054 a.d.)

Hint: You need to calculate how many years have passed since the Crab blew up and that means calculating how many light-years are in 2000 parsecs. Then subtract that number from 1054 a.d. The answer will be a particular year B.C. Remember that subtracting a larger number from a smaller number is simply a matter of reversing the process. You will subtract 1054 from the actual number of years that have passed, and instead of making that a negative number, it will just be a B.C. number.

Chapter 14: (ditto)

1. •About how big is the event horizon of a 100-solar-mass black hole?  (remember the formula of the radius of an event horizon:  Radius = 2 times G times Mass divided by the speed of light squared)  (hint:  you do not need to use the value of G or the speed of light in computing this value- just remember that the event horizon of a 5-solar-mass black hole is 18 miles in diameter.) And remember that since this is an equation, if you change the value of one side, you change the value of the other side by the same proportion. You can give the answer as the new radius, or as the new diameter, whichever you wish, but be sure to specify which.

Chapter 15: (ditto)

1. How many times has our solar system orbited the core of the Milky Way Galaxy since it was formed?  ( it takes 230 million years to go once around)

Hint: remember that the solar system is about 4.6 billion years old. You can do this one easily by hand, especially if you know scientific notation.

Chapter 16: (ditto)

1. •About how fast is the Coma cluster of galaxies receding from us?  (It is about 300 million light-years from Earth)  (You will need Hubble’s Law for this:  V = H times D, where H is Hubble’s constant-   71 Km per second )

Hint: Remember that the value of 'D' here, is given in MegaParsecs, or millions of parsecs. So you must figure out how many millions of parsecs there are in 300 million light-years. Remember that there are 3.26 light-years in one parsec, so there are 3,260,000 light-years in one million parsecs. Once you have that result, you simply multiply it times 71 to get the speed in Km per second.

Bad News: there is no more homework assigned for this class this semester. So sue me.......

Rich Erwin, Physics Dept., CEU