Astronomy 11 - Fall 1998 (S.T. Myers)

Sample Problems for Final Exam

Last Updated 14 Dec 98

Due to time constraints, you cannot turn in this problem set for credit. The questions below are representative of the sorts of problems you will encounter on the final. It is based on your space missions, as will be the final. These problems also serve as the "data" returned by the missions. The final exam is comprehensive, so be sure to review your notes, the homework problems, and to read the book! As before, you can bring a couple of sheets of notes to the exam.

Note that no solutions will be posted for this sample set. By now you should have a pretty good idea when doing problems whether you are on the right track or not. You should be able to get sensible numbers for each of these problems! There is nothing here that you haven't calculated before in one form or another. Remember if you get something that seems way off from what we found in our own solar system or for the terrestrial planets like the Earth, then you probably did something wrong!

Problems:

  1. The second planet was a popular target for missions. It is at an orbital radius of 1.75 AU and has an albedo of A=0.35. Using the luminosity of EPS451 (0.4 Lsun), calculate the expected temperature of the planet assuming A=0.35 and also assuming A=G. Where is this planet placed within the habitable zone of EPS451?

  2. Some of the missions carried wide-field cameras which captured whole-disk images of the planet. The angular diameter of Planet 2 was seen to be 1 degree 27' 22" from a distance of 425000 km. Calculate the radius of Planet 2.

  3. A small satellite is found in an orbit with semi-major axis of 218377 km and period of 15.36 mean solar days. Compute the mass and mean density of the planet. What is the likely composition of planet 2?

  4. What is the surface gravity of Planet 2? Assuming that the height of surface features like mountains on a planets surface are inversely proportional to the surface gravity, and that the highest mountains on Mars are 30km, what altitude would you expect the highest mountains on Planet 2 to be?

  5. Assume that Planet 2 did have a thick atmosphere with a temperature determined by the equilibrium temperature for A=G. What is the minimum molecular weight of a gas that could be retained by the planet over the course of a few billion years? What gases might the atmosphere be composed of?

  6. Assume that there is significant greenhouse effect in the atmosphere of this planet, and that G=0.9. What is the expected surface temperature of the planet? What is the scale height of the atmosphere at the surface (assuming the compostion you guessed above)? What is the pressure at the top of the highest mountain that you computed in #4 in terms at the surface pressure?

  7. The planet is found to have a rotation period of 80 hours. Suppose that you wanted to place an orbiter in an equatorial orbit synchronous with the planets rotation. What is the semimajor axis of this synchronous orbit?

  8. Assume the orbiter placed in this synchronous orbit has a high-resolution camera onboard, with a telescopic diameter of 500 cm and an f-ratio of f/5.5. What is the focal length of this optical system, and what is the scale in the focal plane (arcsec per micron)? What is the resolution of the optics at a wavelength of 5000 Angstroms?

  9. In the focal plane is a CCD camera with $1024\times1024$ pixels each $1\mu$m in size. What is the angular size corresponding to one pixel, and what is the field of view of the camera? Is this camera resolution-limited at 5000 Angstroms? What is the pixel scale of an image of the planet's surface directly below the synchronous orbiter in meters? Would you be able to resolve a surface feature 1 km in size? 100 meters? 10 meters?

  10. The orbiter detects a magnetic field with strength of 10^-6 T at the synchronous orbital radius from the planet. To compare this with the field of the Earth (4 x 10^-5 T at the surface), scale the Earth's field to the same distance. What is the magnetic field strength compared to the Earth's? Is this what you would expect given the mean density and rotational period? What does this tell you about the planet?

  11. The rotation axis of the planet is inclined 30 degrees to the orbital axis. At a mid-latitude of 40 degrees, what is the minimum and maximum zenith angle that the Sun EPS451 will cross the meridian at during the Planet 2 year? If the albedo of the clouds is A=0.35, then compute the noontime solar surface flux (in W/m^2) at this latitude at mid-summer, equinox, and mid-winter. What is the temperature of a blackbody land surface (A=0.07) at these latitudes (this time, ignoring the atmospheric greenhouse, effectively setting G=0) for each of these times during the year?

  12. The orbital eccentricity of Planet 2 around EPS451 is e=0.0667. Compute the periastron and apastron orbital distances. What is the fractional change this makes on the planetary temperature? At what latitude on the planet is this variation equal to the variation introduced by the solar inclination effect?

For more sample questions, see last year's sample set.

The final is Tuesday December 15 8:30am in DRL A8 (across the hall from A7). Bring a calculator!

Index Astr11 Index --- Home Astr11 Home

smyers@nrao.edu   Steven T. Myers