Astronomy 110 PRINT Name   __________________________ Fall 2005   Section 006 Homework 2 : Where is? (Due Thursday, Sep 8, 2005)

Some of the questions in this homework require you to indicate various answers on the diagram below, as well as giving reasons for your answer. You should therefore answer all the questions on a separate sheet of paper and you must attach the signed question sheet. Try to explain your answers as fully as possible. You must include an explanation to get a grade for the question.

The skymap on the left shows an image of the sky over Honolulu on some day. The dots represent bright stars (if you could see them while the sun is up) and the names of constellations are given. Also shown are the positions of the Sun and planets if they happen to be in the particular direction shown; a key to these symbols is given below. The horizon is toward the bottom of the picture (though it may be out of the field of view of the picture). North is at the top and east is to the left (as with all skymaps).
KEY :
--- Sun    --- Mercury
--- Venus

One of the straight lines on the skymap represents the celestial equator and the other represents the ecliptic. You'll notice that one is marked off in hours of time and the other in degrees of arc; note that one hour of time is the same as 15 degrees of arc.Indicate on the picture which line is the equator and which is the ecliptic, and explain why. 3 pts.

This skymap shows the location of various objects in the sky much like a regular map. The celestial equator divides north and south in the sky just like the equator on Earth divides the Northern and Southern Hemispheres, and like on a map of the world the equator is a horizontal line running through the center of the map. The ecliptic is the path that the Sun and other objects in the Solar System appear to follow in the sky, that is tilted from the equator at 23.5 degrees. This is because the axis that Earth is spinning on, is tilted at that angle compared to the plane of the Solar System. So the tilted line on the map is the ecliptic.

Can you say what the date is, roughly, and explain why? 6 pts.

The map shows the Sun crossing the equator. This happens twice a year at the Equinoxes in March and September, which defines the start of Spring and Fall (in the Northern Hemisphere). So we know the date for this map is either around March 21 or September 21. In order to know which date it is we need to look at what else is depicted on the map. The planets Mercury and Venus don't help us much because they have complicated motions in our sky, due to our own orbits. So that leaves the stars. The constellation Aquarius appears in the diagram, so you might think that the figuring out when we can see Aquarius will give us our answer. Aquarius is visible in the night sky, now in September, so does that mean that the map is showing the September equinox? Actually it means that it can't be September, because Aquarius is in the night sky, meaning that it is not near the Sun. For Aquarius to be up during the day (and therefore near the Sun) we have to go to six months from September, to March. So the map represents the sky sometime around March 21.

How many hours of sunlight will there be on this day? Explain why, and include a diagram.3 pts.

There will be exactly 12 hours of sunlight on this date, because it is an equinox (which means equal night). Due to the 23.5 degree tilt of our axis, the length of the day changes throughout the year. In the Northern Hemisphere the day grows longer from December 21 until June 21, and then gets shorter again. This is because the North Pole (the northern part of the axis) is pointed as far away from the Sun as it can get on December 21, and is pointed towards it on June 21 (see diagrams 2.16 and 2.18 in the textbook). Halfway in between on March 21, the tilt is neither towards or away from the sun, so on that day, everywhere on Earth gets the same amount of daylight, exactly half of the day: 12 hours.

Label roughly where you expect the Sun to be one week later, and explain why.3 pts.

The start of spring is defined by the Sun moving into your hemisphere. Spring begins (in the north) on March 21 as the Sun appears to move from above the Southern Hemisphere to above the Northern Hemisphere. So since on this map North is up, we know that the Sun will be North of where it is shown, after a week. Clearly, since the ecliptic is defined as the apparent path of the Sun, the Sun will still be on this line. So a correct answer would have the Sun somewhere along the ecliptic and north of the equator.

Suppose the tilt of the Earth's exis were to change from 23.5 degrees to 10 degrees. Draw on the skymap how the ecliptic would look in that case. What would be the latitudes of the arctic and antarctic circles? Explain. Would Honolulu still be in the tropics? 5 pts.

If the Earth's tilt were at 10 degrees instead of 23.5 degrees, then the Sun path through the year would stay closer to the equator. On the map the angle between the ecliptic and the equator would simply be reduced to 10 degrees. This change would also affect the lines that define the tropics and the Arctic and Antarctic circles. These lines are at 23.5 degrees latitude and (90-23.5=) 66.5 degrees latitude, respectively. So the new tropics would be between 10 degrees north and 10 degrees south, and the Arctic and Antarctic circles would be at 80 degrees north and 80 degrees south. Honolulu, at about 20 degrees north latitude, is in the tropics with a latitude less than 23.5 degrees, however if the tropics were at 10 degrees, Honolulu would then be outside the tropics.