ASTR330 Homework #3

HOMEWORK COMPLETE!

Homework hint: All problems in the text have answers at the back of the book! Some problems require just a written response, while others ask you to calculate something. Please write up all answers clearly, completely, and as succinctly as possible. You can work with others, but your final answers must be written up on your own.

Chapter 4

Question 1. This is the last problem with the Solar System Collisons program. The energy contained in the motion of an object of mass m moving at speed v is m*v*v/2. In this problem, you will test how well this formula fits the energy released a high speed impact with Earth.
a) Go back to the table that you created in HW#1. How much does the impact energy increase for each factor of ten increase in diameter? Is this consistent with the formula? Why or why not?
b) Now run several simulations for a 1km object hitting Earth at different velocities: 15, 30 and 60 km/s. Record the impact energies and show how well they match the predictions of the equation. Use ratios as you did in problem 1 of HW#2.

Chapter 5

Question 2. Find the error on page 160.

Question 3. Solar heating drives Hadley cell circulation on Earth and on other planets. This circulation pattern leads to prevailing easterly or westerly winds. Read page 190 (especially box 5.7) carefully to see how this works.
a) As an air parcel at the top of a Hadley cell moves north from the equator on Earth, high altitude winds move more quickly to the East (relative to Earth's surface) for two reasons. State them. Which is more important?
b) Repeat the calculation for a near-surface air parcel moving from 30 degrees to 60 degrees North latitude. Start by assuming that the air is motionless with respect to the Earth's surface at 30 degrees latitude. These are the Westerly trade winds - how fast do you predict them to be? Are they faster or slower than the calculation done in the book for the zero to 30 degree Hadley cell?
c) Convert your answer to a more familiar unit: miles per hour. Does the answer surprise you? Discuss factors that will slow these speeds. Based on your experience, do you think that these factors are fairly weak or fairly strong?

Chapter 6

Question 4. a) What is the suspected reason for the yellow and brown colors of Jupiter's cloud layer?
b) Uranus and Neptune probably have similar colors in their deep cloud layers, but above these clouds, these planets have a thick global layer of methane clouds that should be white. Why then, are Uranus and Neptune blue in color? The answer lies in much thicker layer of gaseous methane and other hydrocarbons above the methane clouds. Given that methane is an extremely good greenhouse gas (due to its 3D shape), can you guess why Uranus and Neptune look blue? Hint - think about what greenhouse gases do and what a very efficient one might do, and consider what happens to sunlight bouncing off the methane clouds.

Question 5. a) Look at question 6.4 in the text and its answer in the back of the book. Repeat this calculation for Earth: work out how much heat flux (in Watts) is produced by Earth's entire surface and then how much heat is produced by a square meter of surface. Compare your answer to the average amount of the Sun's energy received by a square meter of Earth's surface, 342 W/m², and form a ratio as in question 6.4. Which energy source primarily determines Earth's surface temperature?
b) The strength of solar heating decreases with the inverse square of distance (the same amount of energy from the Sun is divided up into ever larger spherical shells). How much farther would the Earth have to be from the Sun for the solar heating rate to equal the heat from radioactive decay?
c) From your answer in b), speculate on which objects in the solar system might have their surface temperatures determined by radioactive decay rather than by the intensity of intercepted sunlight.

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