1. A body orbiting the earth just above the atmosphere (like a cellular phone satellite) has an orbital radius about the same as the radius of the earth- about 6.4 million meters, and an orbital period of about 1.5 hours.
Communication satellites, on the other hand, orbit above the equator with a period the same as the rotational period of the earth. Thus they stay over the same spot on earth all the time. If you lived at the equator, how far overhead would a communications satellite be?2. On page 97 of Moons and Planets, Problem 18 reads as follows:
Two optically thick infrared stars are at the same distance. Star A has peak radiation at 2.0 micrometers, and B at 4.0 micrometers. Star A is 16 times as bright as B. What physical conclusions can you draw about these stars if they both radiate as blackbodies?
Do this problem. You will need to use Wien's law (p. 85) to find out the ratio of the (absolute) temperatures of the two stars. You also need to know that the total power radiated per unit area of a blackbody is proportional to the fourth power of the temperature, that is:
(Power Radiated)/(Unit Area) = (sigma)*(Absolute Temperature)4
where sigma is a constant called the Stefan-Boltzmann Constant. The value of sigma is in the table on p. 41, though you don't actually need to know it for this problem.
Then, knowing the surface area of a star of a given radius, you can calculate the total radiation emitted (luminosity), then find the associated brightness at a given distance from the star, and finally find the relative radii of the two stars.