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Astronomy Problems (Homework) 2 Solutions

# Astronomy Problems (Homework) 2 Solutions - Homework 2...

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Homework 2 University Astronomy 4/1/10 1 University Astronomy 1017-301 Homework Assignment 2 Instructor: Dr Andrew Robinson Due Date: 9 am Friday, 9 April 2009. To tackle some of the following problems you will need to do some research, using either the textbook or other resources, to find various pieces astronomical data and the values of certain physical constants. For calculations, show all your workings in order to receive full credit . 1. It is believed that, were it not for Jupiter’s strong gravity, a 5 th terrestrial planet would probably have formed out of the material now occupying the asteroid belt between Mars and Jupiter. Let us suppose that somehow, such a planet did form at this location. Let’s call it Phoenix . Astronomers have accumulated some basic data on Phoenix. It is a terrestrial-type planet, with an albedo and rotation period about the same as those of Mars but has a radius 1.5 × that of Earth. It has a nearly circular orbit and is 3 AU from the sun. It also has a small moon, which has a circular orbit around Phoenix with a radius of 2.83 × 10 5 km and a period of 10 d. Calculate or deduce the following properties of Phoenix. a. The length of a year on Phoenix (in Earth days). b. Its orbital speed. c. Its mass. Length of year = period of orbit around sun. Since we know the radius of Phoenix’s orbit, we can find the period from Kepler’s 3 rd law: P = 2 " a 3 2 GM ! (see Lecture 5). With a=3 AU 4.5x10 11 m and M =2x10 30 kg (mass of sun), P 1900 d 5.2 y Mass: Phoenix has a moon, whose orbital period and radius we know. We again apply Kepler’s 3 rd law, but this time it is the moon orbiting Phoenix, so the relevant mass (M ph ) is that of Phoenix: P = 2 " a 3 2 GM Ph . Solving for M ph , with the orbital period and radius given for the moon, we find M ph 1.79x10 25 kg 3xEarth’s mass. Phoenix has a nearly circular orbit, so knowing the radius and period, the mean orbital speed is v orb = 2 π a/P 17.2 km s -1

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Homework 2 University Astronomy 4/1/10 2 d. Its escape speed. e. Its average surface temperature. f. Given the escape speed and surface temperature, what is the likely composition of Phoenix’s atmosphere? (Refer to the graph in Lecture 8.) 2. Tidal evolution. As discussed in Lecture 6, frictional coupling causes a misalignment between Earth’s tidal bulges and the Earth-Moon direction. The resulting torque (off- center force) slows Earth’s rotation and hence decreases its angular momentum.
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