These are problems that you should be able to do. Similar problems
to these will appear on the midterm. I do not guarantee all of these
will be on it, nor that all that are on the test are like these.
However, if you can do these you will be in good shape for the test!
Note that some of these questions use the results of previous questions.
Be sure to show your work so that if you make a mistake in one question,
we can see that you knew how to do the next one and not penalize you twice
for one error! If you can't get one at all, pick a plausible number and
then follow through on the calculation (be sure you write down that you
are doing this!).
I may not give as many hints on the midterm as I give here after the
question.
You will need a calculator for this and for the midterm!
- The Synodic period of Saturn is 1.03513 years. What is
the Sidereal period of its orbit? (Use the formula relating sidereal
to synodic periods. Be sure to choose the correct version - is Saturn
an inferior or superior planet?)
- Using the sidereal period of Saturn just derived, calculate
the semi-major axis of its orbit in AU. (Use Kepler's 3rd law)
- Assuming the orbit is close to circular, what is the average
orbital velocity of Saturn in km/s? Compare this value to the velocity
of the Earth in its orbit at 1 AU. Note 1 AU = 1.496 x 10^8 km.
(Find circumference of orbit compared to its sidereal period)
- From the Earth at Saturn's closest approach (distance is
approximately the difference between Saturn's orbital radius and
the Earths = 1 AU) the disk of Saturn is
observed to have an angular diameter of 19.5 arcseconds. What is its
physical diameter in kilometers? (use small angle formula)
- The apparent visual magnitude of the brightest star in the
sky, Sirius, is -1.47. The 20th brightest star, Beta Crucis, has
a magnitude of 1.28. How many times brighter is Sirius than
Beta Crucis? (find intensity ratio)
- The greatest elongation of the planet Mercury is observed
to be about 22 degrees, 30 minutes. What is the semi-major axis of its
orbit in AU, assuming a nearly circular orbit? (use the triginometric
relation to find the ratio of orbital radius to that of Earth)
I will work through these problems on Monday. Remember, the midterm is
Wednesday Feb 14 in class.