Problem set 1 for ASTR 221: Stars and Planets

Due 5pm, Friday Sept 5.

(1) Using ADS and/or the astronomy library, find the oldest article you can written in an astronomical journal, or the oldest book (or chapter in a book) (preferably written for a non-general audience) which discusses a theory for the formation of the solar system, or of the Earth/giant planets/asteroids/comets in the context of solar system formation.
The articles or books should be pre-1960 at least. You may talk with each other about your searches, but each student should hand in a discussion of a different book or article. (Email me to check you have chosen a suitable article and that nobody else has it, once you have found your article or chapter. You should choose your article by Sept 3 at the latest.) Include a copy of the article or chapter with your handed-in work. (Apart from the Kant/Laplace theories from the 18th century, I have found interesting articles as early as 1905 in the astronomical literature.) I'll give a prize for the most interesting paper.
(a) Describe the theory that is put forward in the article or book in 2-3 paragraphs. Your target audience should be other physics and astronomy students at your level. NB: Clearly describe the important physics that is used in this theory.
(b) Contrast this theory with currently popular theories on your chosen topic. If we have not discussed this yet in class, come talk to me or email me.
(c) Discuss the evidence that is used to bolster the theory, and any problematic facts mentioned by the author. Remember that confronting the theory and the evidence is at the heart of science.
(d) Is the theory still a viable one, in the light of new evidence that has come to light in the last 50 or more years?
In total, you should write about 2-3 typed pages.

(2) In class, we saw that the rate of growth of a planet can be written as

where M is the mass, t is time, ρ and ρs are the densities of the solid planet and the planetesimal swarm, G is the gravitational constant, R is the planet radius and v is the relative velocity.
a) Using the relationship between mass and density for a solid body and the chain rule, rewrite the above equation in terms of dR/dt.
b) Explain in words what style of accretion is represented by each of the two terms in the brackets, what controls which style of accretion dominates at a particular time, and how the density of the planetismal swarm and the relative velocities of the objects affect the growth of the planet.

(3) Using the plots in notes which show (a) the temperature variation in models of the planetary disk (use the solid lines) and (b) the equilibrium condensation temperatures for atomic elements and selected molecules, along with the diagram of solar system abundances which is also in class notes (to work out the most common atoms and molecules in the protoplanetary cloud), calculate the range of likely locations of the ice line in the Solar System as it formed. Compare this with the position of the planets today.