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Astro-7 Fall 1999


Review Problems, Midterm I


1.
Make a sketch showing the position of the Earth around the Sun in Winter, Summer, Fall and Spring. Draw an arrow to indicate the orientation of the North Pole with respect to the Sun.
(a)
Why are summers hot and winters cold?
(b)
If the axis of Earth were tilted 0 degrees instead of 23.5 degrees, what seasonal variations would you expect on Earth? How long would the Sun be up at the summer solstice (June 23) if you were standing on the equator? In Philadelphia? At the North Pole?

2.
Chiron is an asteroid-like object with strange orbital and compositional properties that have led some to suggest that Chiron was once a comet. Chiron follows an elliptical orbit about the Sun. Its perihelion distance is 12 AU and its aphelion distance is 20 AU.
(a)
What is the semi-major axis of Chiron's orbit?
(b)
How many years does it take Chiron to orbit the Sun?
(c)
A line joining the Sun and Chiron is found to sweep out $2 \times 10^{18}
{\rm km}^2$ of area during 1995. How much area is swept out in 1996? How much area is swept out over a period of ten years?

3.
The full Moon spans an angular size of 1/2 degree. The Moon is 400,000 km from the Earth. Io, one of Jupiter's largest moons, is about the same physical size as Earth's Moon. When Jupiter is $6.4
\times 10^8$ km from the Earth (remember, this distance changes as the two planets orbit the Sun), how many times smaller than the full Moon will the angular size of Io appear to us?

4.
At about what time does a full Moon rise and set? At about what time does a last-quarter Moon rise and set? You may find a sketch of the positions of Earth, Sun and Moon helpful.

5.
Imagine that the Moon was twice bigger in diameter than it really is, and its orbit was not changed. Explain how solar eclipses would be different from the way they are in the real world.

6.
Explain, with words and a drawing, why, at midnight, Mercury cannot be seen from Philadelphia. Do you think Mercury exhibits phases similar to those of Venus? Why?

7.
Suppose you were a Jovian and you wished to measure the size of Jupiter. One day, your fellow Jovian who lived 10000 km away across the Great Red Spot emailed you to report that the Sun was shining directly overhead. You looked out instantly and found the Sun to be 5 degrees from the zenith at your location. What is the circumference of Jupiter? What is its radius?

8.
Suppose a tenth planet of the Solar System is discovered. The planet is found to orbit the Sun once every 1000 years. Pluto orbits the Sun every 250 years.
(a)
Is the distance from the planet to the Sun comparable to, larger, or smaller than the distance of Pluto to the Sun?
(b)
By what factor?

9.
You observe an asteroid in orbit around the Sun. You discover that its speed is not constant, but varies between 20 km/s at maximum and 10 km/s at minimum.
(a)
Make a drawing of the orbit as accurate as you can indicating where in the orbit the asteroid reaches its maximum and minimum speed.
(b)
If you measure the distance from the Sun when it reaches maximum speed and again when it reaches minimum speed, what will be the ratio? What principle or law do you use?

10.
The speed of light is $3\times 10^5 \, {\rm km/s}$, and $1 {\rm AU} =
1.5\times 10^8$ km.

(a)
How many AUs is the Earth from the Sun? How long does it take light to reach the Earth from the Sun?
(b)
Pluto, the farthest planet in the Solar System (on average), is about 40 AU from the Sun. How many hours does it take light to reach Pluto from the Sun?
(c)
The Milky Way, the galaxy we live in, is shaped like a flattened disk with a diameter of approximately 80000 light years. Suppose you were to make a scale model in which the Milky Way is the size of a delicious 10-inch pizza. What would the size of the Solar System be in this scale model? Is this closer to the size of a black olive in the pizza, or to the size of a bacteria in the pizza that might make you sick, or to the size of a single molecule making up a black olive?



 
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Jordi Miralda-Escude
1999-10-01