Astronomy 23/223 In-Class Exercise:

Density and Temperature

 1 What is a typical density (in grams per cubic centimeter g cm-1) for a) Ice b) rock c) iron? If you don’t know, make a wild guess. When we converge on the “right” answers, save these numbers — we will refer to them again! If I have a planet with a mean density of 1.5, can it have a rocky surface? What would a mean density of 16 suggest? 2 How would you expect the mean density of the Earth and Moon to compare? 3 In small groups, list ways that a planet can warm up and ways that a planet can cool off. What properties of the planet are most influential in each of these mechanisms? 4 The temperature of an object in equilibrium is understood by a balance of incoming and outgoing energy. Given that the radiation from the sun decreases by the square of the distance (D-2), this means that the equilibrium temperature of an object depends in part on its distance from the sun. What is the total energy radiated by the sun? Divide this quantity by the volume of the sphere of radius D. This is the “solar flux” at that distance. If you multiply by the area of the planet, this is the amount of energy received. Now, what is the energy emitted by the planet? Set these equal to one another, and solve for the temperature. What does it depend on? Discuss how it is that some planets are colder or hotter than their equilibrium temperature. 5 Mercury is at a distance of 0.387 AU from the Sun, with an orbital period of 87.97 days. Use this information to compute its orbital speed. Let Mercury “run into” a 100-m rock at this speed, and compute the kinetic energy of the collision (kinetic energy is one-half the mass multiplied by the square of the velocity: 0.5 m v2). Compare this energy to the energy it takes for a typical rock to a) crush: 108 erg g-1; b) melt: 1010 erg g-1; c) vaporize: 1011 erg g-1. (For the units: erg = g cm2 s-2).

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