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A100 -- Dan Swearingen
Homework 4 -- Due by the beginning of class on Tuesday October 22
Chapter 5, page 167
Questions for review 10: Why does the Moon form two tidal bulges on the Earth?
This was a tough one. The point to the book's explanation given on page 163 is that what causes the tidal bulges is the difference in force on the different areas of the oceans, and that the oceans are fluid and will move in response to this difference in force.
Chapter 5: Additional question: If it is sunrise and the moon is high in the sky, what phase must the moon be? Show why.
If it is sunrise you must be standing at location (A). The New moon is rising, the Full moon is setting, the First Quarter moon cannot be seen but the Third Quarter moon at location (B) would be high in the sky. So when the moon is high in the sky at sunrise it is third quarter.
Essay 4, page E4-8, Questions for review
2. Why do the sidereal and the solar day differ in length?
A sidereal day is one rotation of the Earth on it's axis: and this takes about 23 hours and 56 minutes. This is less than the 24 hour length of the solar day because the solar day is how long it takes for the sun to go from noon to the next noon.
As the earth turns, it is also going around the Sun. If we start at noon and wait for the earth to turn once (23 hours and 56 minutes), the sun will not be in the noon position because the earth also went around the sun 23 hours and 56 minutes worth of distance. The earth must turn a little past, something like four minutes past, where it was the day before so that the sun will again be in the noon position.
4. Why isn't the solar day always exactly 24 hours long?
As discussed in number 2, the solar day is a combination of two motions. The Earth's 23 hour 56 minute rotation coupled to the Earth's annual motion around the Sun. The Earth's rotation is almost perfectly constant but it's motion around the sun is not. The Earth's orbital motion is in accordance with Kepler's Laws. When the Earth is closest to the sun it is moving its fastest in its orbit.
This means the Earth will have to turn more each solar day to bring the Sun into the noon position. This is the case in January when the Earth is closest to the Sun so solar days are longest then. In July, when the Earth is further from the Sun and the Earth is travelling slower in its orbit so the Earth does not have to turn as far to bring the sun into the noontime position and solar days are shortest this time of year. The 24 hour solar day is defined as the average amount of time it takes for the Sun to go from noon to noon over an entire year.
Chapter 6, page 191, Questions for review
5. What is the Oort cloud? Where is it located and what kinds of objects come from it?
The Oort cloud is a region of the solar system taken to be beyond Neptune's orbit and extending out to the aphelion of the long period comets' orbits. This is anywhere from 40,000 to 100,000 AU from the sun. Since long period comets come from all directions uniformly, we assume that the Oort cloud is roughly spherical around the Sun.
As we've implied, the Oort cloud is home to swarms of comets and other material left over from the formation of the solar system.
8. What is the solar nebula? What is its shape and why?
The solar system formed from a large cloud of material in which gravitational collapse was started by some outside triggering event. As the cloud collapsed a region became more dense than other regions and its gravity became the focus of the cloud's collapse. As material approached this focus it began to rotate around the focus just as hurricanes and water going down a drain rotate. The physics of this rotation is called conservation of angular momentum.
As more and more material nears the focus the rotation causes the formation of a rotating disk of material which sonn has a bulge of gas at the center heated by the compression of the gas by the force of gravity. This object is called the solar nebula.
9. Why are there two types of planets?
In the solar nebula the temperature increased as you got closer to the core (which became the Sun). Material became selected by whether or not it would melt as it spiralled in towards the hotter central region of the nebula. If the material melted, its gas would be blown by the proto-sun's wind out to regions where the temperature was coll enough for it to solidify. Once solid the proto-solar wind could not push it away. This caused an accumulation of materials with high melting points near the proto-sun and a corresponding accumulation of materials with low melting points further away from the proto-sun. We feel that this is the reason why the planets near the present sun have iron/nickel/silicon composition and why the planets in the outer solar system have hydrogen/heluim and hydrogen/heluim/methane/ice compositions.
Chapter 6, page 192, Numerical Problems
1. Calculate the densities of Venus and Jupiter given the following data: The mass and radius of Venus are 4.87 x 1027 grams and 6,051 kilometers. The mass and radius of Jupiter are about 1.9 x 1030 grams and 71,492 kilometers. How do these numbers compare with the density of rock (silicon) about 3 grams per cc, and water at 1 gram per cc.
Venus with a density of 5.25 gm/cc is denser than rock and this supports the idea that a lot of Venus is some material more dense than rock such as iron and nickel. Jupiter may have some riock and iron somewhere but it can't have much with a density nearly as low as water.
2. Look up the mass and radius of Mercury and Jupiter and calculate their escape velocity using the expression in chapter 2. Does this help explain why the one body has an atmosphere but the other doesn't?
The escape velocity is given by:
For Mercury we have:
For Jupiter we have:
Jupiter's escape velocity is (60/4.3) 14 times higher than Mercury's. This means that a gas molecule would have to be moving 14 times faster to escape Jupiter than it would to escape Mercury. The escape velocity of the planets is one factor in whether or not they have an atmosphere.
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