General Astronomy, 29:61
Fall, 2004
Tenth Homework Set...December 1, 2004.
Due December 8, 2004

(1): How close could a planet like the Earth come to the Sun before being tidally disrupted? Express your answer in both kilometers and solar radii. You will need data from the Appendix.

(2) An object called a neutron star (you'll learn about them next semester) has the mass of the Sun, but a radius of 10 kilometers. Calculate how close a terrestrial planet could come to a neutron star before it is tidally disrupted.

For the questions 3-6, use this description of a hypothetical planetary system. A planet has a radius of $10^4$ km and a mass of $2.3 \times 10^{25}$kg. It also has a ring, like Saturn's ring, which extends from an inner radius of $r=1.5 \times 10^4$ km to $r=2.5 \times 10^4$ km. There is a satellite orbiting beyond the ring, in a circular orbit with a radius of $3.74 \times 10^4$ km

(3) Calculate the orbital period of the satellite.

(4) At what distance from the planet would an object in a circular orbit be in a 3:1 resonance with the satellite? Is it in the ring?

(5) At what distance from the planet would an object in a circular orbit be in a 2:1 resonance with the satellite? Is it in the ring?

(6) Based on your results from questions (4) and (5), draw a sketch of the appearance of the ring. Do a half-decent job of drawing it carefully.

(7) Refer to Table 7-1 of the book for data on comets. Calculate the aphelion distance (distance at which the comet is furthest from the Sun) of Comet Donati. Show your work.

(8) A comet has a period of 5000 years and an eccentricity of 0.9970.

• What is the semimajor axis?
• What is the perihelion distance of the cometary orbit?
• What is the aphelion distance?
• Would this comet be visible from Earth? Explain why or why not.