Ch-13    Homework
1. Mars has two small satellites, Phobos and Deimos. Phobos circles Mars once every 0.31891 day at an average altitude of 5980 km above the planet's surface. The diameter of Mars is 6794 km. Using this information, calculate the mass and average density of Mars.
2.

A hypothetical spherical asteroid 2 km in diameter, and composed of rock with an average density of 2500 kg/m3, strikes the Earth with a speed of 25 km/s.
(a) What is the kinetic energy of the asteroid at the moment of impact?
(b) How does this energy compare with that released by a nuclear weapon equivalent to 20-kiloton TNT, like the device that destroyed Hiroshima, Japan, on August 6, 1945? (A kiloton TNT releases 4.2 x 1012 joules of energy.)

3.

(a) Find the speed required to escape from the surface of the asteroid described in the previous question.
(b) A typical jogging speed is 3 m/s. What would happen to an astronaut who decided to go for a jog on this asteroid?
4.

The Sun's mass is 1.989 x 1030 kg, and its radius is 6.96 x 108 m.
(a) What is the escape speed from the Sun's surface?
(b) The temperature at the surface of the Sun is 5800 K. Explain why the Sun has lost very little hydrogen over its entire 4.6-billion-year history.
5. Because of the presence of Jupiter, the Sun moves in a small orbit of radius 742000 km with a period of 11.86 years.
(a) Calculate the Sun's orbital speed in meters per second.
(b) An astronomer on a hypothetical planet orbiting the star Vega, 25 light-years from the Sun, wants to use the astrometric method to search for planets orbiting the Sun. What would be the angular diameter of the Sun's orbit as seen by this alien astronomer? Would the Sun's motion be discernible if the alien astronomer could measure positions to an accuracy of 0.001 arcsec?
(c) Repeat part (b), but now let the astronomer be located on a hypothetical planet in the Pleiades star cluster, 360 light-years from the Sun. Would the Sun's motion be discernible to this astronomer?