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Homework #1: questions about Planetary Exploration (Astronomy) w/ key | ASTR 206
Typology: Assignments
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Due Date: start of class 1/27/
Turn in your own work. It is not acceptable to turn in work that is identical to that of another student. You may work together to understand the material, but the work you turn in must be in your own words.
There are 2 parts, plus an extra-credit part. Please put your answers to all questions in the space provided (you may use the back of the page if necessary).
PART 1 (32 pts total): Conceptual. Please provide a concise short answer (not more than a few sentences) for each of the following.
# 1. (8 pts) (Chapters 2) Suppose that you study the position of a particular planet (Saturn, for example) relative to the stars nearby it each night for over a year. Briefly describe what you will see.
The planet will move eastward most of the year, but will move westward during retrograde motion. It will also get bigger, smaller, brighter and dimmer, depending on how close it is to Earth. The closer it is, the bigger and brighter it is likely to be (except for the inner planets, but Saturn will be brighter when it is closer).
# 2. (8 pts) (Chapter 4 #21) Why does Venus have its largest angular diameter when it is new and its smallest angular diameter when it is full? In what way does this rule out the Earth-centered model of the solar system?
Venus is closer to us when it is in the new phase meaning that it is between us and the Sun (so that we cannot see the illuminated side) – at this point Venus is at its closest to Earth. When Venus is on the opposite side of the Sun, we see its fully illuminated side, hence it is full, and it is also at its farthest point from the Sun meaning that it is also the smallest. This rules out the Ptolemaic, Earth-centered model, because the full phase, where Venus is on the opposite side of the Sun, was not possible in this model.
# 3. (8 pts) (Chapter4: #29 of the textbook) Why was the discovery of Neptune an important confirmation of Newton’s law of universal gravitation?
Its existence and position in the sky was predicted using Newton’s law of gravitation using the forces from all of the known planets. It was then discovered rather easily, once the position had been determined. This confirmed the Newton’s theory.
# 4. (8 pts) (Chapter 4, #51) Which planet (excluding Pluto, which has been re-designated a “dwarf planet”) would you expect to exhibit the greatest variation in apparent brightness as seen from Earth? Which planet would you expect to exhibit the greatest variation in angular diameter? Explain your answers.
Mars exhibits the greatest variation in apparent brightness and angular diameter. This is due in part to its eccentric orbit and the variance in the Earth−Mars distance at oppositions. (The Earth-Mars distance varies between 2.66 AU and .38 AU; m = +1.8 at superior conjunction, m = −2.8 at inferior conjunction, where m is the apparent brightness as defined in the textbook) Venus also undergoes changes in angular size and brightness, however, as Venus gets closer to Earth, the crescent phase tends to diminish the apparent brightness. (The Earth-Venus distance varies between 1.73 AU and .27 AU; m = −3.9 at superior conjunction, m = −4.5 at inferior conjunction.)
PART 2 (18 pts total): Quantitative
# 1. (6 pts) (Chapter 4) Calculate the gravitational force exerted on the Moon by …
(a) The Sun
(b) The Earth
(c) compare these and comment on whether they make sense to you
Sure, the Sun exerts the strongest force on the Moon because the Sun is so massive. The force of gravity on the Moon by the Earth is also quite large, that is why it orbits the Earth. But, if the Earth were to suddenly disappear, the Moon would continue to orbit the Sun.
Some potentially useful information: mass of Earth = 6x10 24 kg, diameter of Earth = 1.2x10^7 m, mass of Moon = 7x10^22 kg, diameter of moon = 3x10 6 m, distance between Earth and Moon = 3.8x10^8 m, mass of Sun = 2x10 30 kg, diameter of Sun = 7x10 8 m, distance between Moon and Sun = 1.5x10^11 m.
Chapter 4 #
(a) a = 3 p^2 = 3 642 = 16 AU.
(b) The perihelion distance is the major axis minus the aphelion distance: Perihelion distance = 2× 16 AU – 31.5 AU = 0.5 AU.
Chapter 4 #
Since your weight is just the gravitational force you experience by the Earth, your weight on
Earth is 1 G 2 E E
mm F R
= , and your weight on the planet would be (^2 ) 4 G (4 )
E E
m m F R
= , then
you would weigh 1
2 F
times as much there, or
2
2
G 4 (4 )^4 G^16
E E E E
m m R mm R
=
or ¼ as much.
So, you would weigh less. Note that your instincts may have been that because this planet is so much bigger, you should weigh more … but don’t forget that the gravitational force involves two important factors, the mass of the objects and the distance between them. In this case the new planet is more massive, sure, but because it also has a larger radius, you are farther from its center, hence, the combination of effects leads to you having a smaller weight on it.