Collect data on the mass and radius of Earth (made of rock) & Jupiter (made of gas) and calculate the overall average density of each planet, expressed in g/cm3.

Astronomy ASTA01: The Sun and Planets

Department of Physical & Environmental Sciences,

UTSC

Fall 2018

Problem Set 3

DUE: Tuesday November 13, 2018

Where: Hand in your solutions in the mailbox marked for your tutorial, on the 5th floor corridor of the Science Wing, near office SW506C in the Physics & Astrophysics section.

Reminder: Write your name on your solutions. Also make sure you carefully read the entire problem set policy that was distributed on Quercus. It will help you avoid standard mistakes and score higher. We will assume that you have read this policy document by the time you return your solution.

How to write your solutions: Be precise and clear. Explain what you are calculating. The method of calculation you adopt and your reasoning are the most important. In case of a computational mistake, you will still get credits if your method is right, so explain it clearly.

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1. If the Solar System had formed right after the Big Bang, it would have lacked oxygen (O), and therefore water (H2O). Using the solar nebula theory, describe what would have been most different about the planet formation process and the planets formed in this alternative Solar System. [NO MORE than 15 sentences].

2. Halley’s comet is the only-naked eye comet that might appear twice in a human lifetime (since it comes back every 76 years).

(a) Based on this comet’s orbital period, would you say that it is more likely to have originated from the Kuiper belt or from the Oort cloud? [A quantitative answer is expected to justify your choice]

(b) What other orbital feature, besides the comet’s orbital period, could be used to distinguish its origin [NO MORE than 5 sen- tences]

3. (a) Collect data on the mass and radius of Earth (made of rock) & Jupiter (made of gas) and calculate the overall average density of each planet, expressed in g/cm3.

(b) The density of water that we drink is about 1 g/cm3. Use your everyday experience to describe the difference in density between rock, air, and water. [State your answers in terms of “much more/much less” or “a little more/a little less”].

(c) Is the mean density of Earth consistent with our everyday experi- ence of similar composition material? What about Jupiter (same question)?

(d) Propose a physical mechanism that might explain the discrepancy between the mean density of a planet and the density of similar composition material as we experience it in our everyday life.

4. Mean-motion resonances with Jupiter shape the Kirkwood gaps in the main asteroid belt. A resonance written as “5:2” refers to the inner body completing exactly 5 orbital revolutions when the outer body completes exactly 2.

(a) Using Kepler law, find the orbital radius in AU of the following important resonances for the Kirkwood gaps: 2:1, 3:1 and 5:2. Compare your values to those shown in the diagram on Kirkwood gaps in the class lectures (see lecture 12 slides).

(b) High-value mean-motion resonances, such as 2001:1000, are usu- ally considered as weak and thus inconsequential. Explain why you think that might be. [NO MORE than 5 sentences]

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5. A simple temperature model for the solar nebula disk is

Tdisk(a) = 20 × √

100 AU

a K, (1)

where a should be expressed in AU in this equation.

(a) Find the temperature in the solar nebula disk at the orbit of Mer- cury, Earth and Jupiter.

(b) Where is the water ice line located in this disk? [Use the conden- sation sequence values provided in the textbook]

(c) Mercury is mostly made of metal, the Earth mostly made of rock and Jupiter mostly made of gas. Are these three planetary bulk compositions consistent with the condensation sequence, if one follows the above temperature model for the Solar nebula?

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