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Homework help on the Sidereal day

  1. Sep 12, 2007 #1
    I need help on this project. I can pay for "assistance".


    SYNOPSIS: The basic idea of this activity is to observe a star in the southern sky as it passes behind some object such as a chimney or church steeple. (In the graphic at the left, the stars move to the right over time. One bright star is just disappearing behind the chimney in view 3.) By noting the exact time of the disappearance of the star on the first night, and comparing it to the exact time of disappearance on the second night, you can calculate the number of hours between two the observations. This time difference is known as the "sidereal day." The sidereal day is slightly different from the standard, 24-hour solar day.
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    It is vitally important that you stand in the same position each night, and that you be at least 50 feet away from the chimney or whatever you are sighting against. (Do NOT sight against a tree or other irregular object.) If you have a stop watch that will run for a full day, you could start the stopwatch when the star disappears on the first night, and then stop it when it disappears on the second night. The time would be your "sidereal day." You need to write up your activity using the 5-point format, and include the questions at the bottom of this site. Then turn it in via email before the deadline.
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    As the Earth rotates about its axis, the sun appears to rise in the eastern sky, cross the southern sky during the day (the northern sky if you are in the Southern Hemisphere!), and set on the western horizon. The average period it takes to do this has been defined as exactly 24 hours. (Actually, the real sun isn't a very good clock. It is almost always running fast or slow by a few minutes. But the period of a day is, by definition, exactly 24 hours. Astronomers refer to a fictitious "mean sun" that travels with a uniform speed throughout the year. Thus the period between one rising of the mean sun and the next -- the "mean solar day" -- is defined as exactly 24 hours.)
    The sun is at the center of the Earth's orbit, and since we revolve around the sun once a year, the sun appears against a constantly changing backdrop of stars. The sun moves slightly each day relative to the stars. Of course, we can't see those stars because the sun is so bright, but when can see an ever changing parade of stars in the evening sky. Because of this motion (the Earth traveling around the sun), the period from one star-rise to the next is not exactly the same as one day relative to the sun. That is, one day relative to the stars (a sidereal day) is not exactly the same as 24 hour day relative to the sun (a mean solar day). They are close, but not quite the same.
    Your Purpose
    Your purpose in this activity is to determine the length of a sidereal day by observing the position of a single star from one night to the next. You also will compare this time period with a mean solar day, and determine how much the time difference amounts to in a month and year. Finally, your goal is to develop an understanding of how the sidereal day time period affects how the night sky looks in the different times of the year.
    The Procedure
    Be sure you have a good idea of what is required before you start. If you don't understand something, ask. Do not wait until it is too late.
    While it is difficult to observe the rising or setting of a star, it is not difficult to observe it when it is well up in the sky. What you need to do is to identify a particular star and observe it as it passes behind a tall pole, tower, church steeple or some other tall permanent object. Timing the exact moment it disappears on two consecutive nights will lead to you determination of the sidereal period.
    You must pick a bright star that is easily recognized from night to night. You do not need to know its name. You can use the star charts in the back of the book, the Sky Chart with North American Skies , or any other chart you have. In mid-winter, the brightest star will be Sirius; in the summer you will do well to use Antares; and in the fall you could use some of the stars in Sagittarius, or perhaps even Altair in Aquila. It doesn't really matter which star you use or even if you know which star it is. What does matter is that you can recognize the same star on at least two nights.
    Find a place to stand such that the star appears just to the left edge of whatever building or object you are using as a reference. Stand in a very specific position, which you can find again the next night to within an inch or so. Stand still (moving your head a lot can affect your outcome). As soon as the star disappears behind the building or object, mark down the time with as much accuracy as you can.
    The next night, repeat this procedure, go out about ten minutes earlier than the night before. Stand in exactly the same position, and make your timing. The difference between the two timings is your determination of the sidereal day.
    While I personally think you should figure this out on your own, if your browser can handle Javascript (most can), here is a calculator to help figure out the time difference from your two timings: TimeCalc.
    Note: how long you observe the star is not important. If you start observing at 10:30 pm and see the star disappear at 10:35 pm, that 5 minutes is not the difference you are looking for here. What is important is that it disappeared at 10:35 pm. (You could find the correct answer this way if you went out at exactly the same time each night, but this is not the way we are doing it.) Then find out the time it disappears on the second night, say 10:29 pm and determine the time difference between the two times.
    It is essential that you use as accurate a clock or watch as you can, preferably one with a second hand. Be sure to use the same clock or watch each night. Also, select a reference building or object that is at least 50 to 100 feet away from you (or more). You can stand next to the building if you are using an edge of the building that is at least 50 feet away.
    Again, the procedure again is to pick out a bright star and write down the exact time it passes behind an object at least 50 feet away from you. Standing in exactly the same position, repeat this procedure the next night and take the difference between the two timings to yield your determination of the sidereal day.
    EXAMPLE (not real times): If the star disappears at 10:07 p.m. on the first night and 10:00 p.m. on the second night, the difference would be 7 minutes. Thus, the time it takes the Earth to turn 360 degrees relative to the stars would be 24 hours minus 7 minutes, or 23 hours, 53 minutes. If the sighting on the second night had been later than the first by 7 minutes, we would add it to 24 hours, yielding an observed sidereal day of 24 hours, 7 minutes.
    Questions
    Be sure to answer the following questions, after your statement of conclusions. There are NOT your statement of conclusions, but should be included in addition to the conclusions. List each question separately, followed immediately by your answer. Do not lump them all into a single paragraphi. If you do, you will lose points.
    • Is the sidereal day longer or shorter than a solar day?
    • By how much?
    • How much would this difference amount to in a month? A year?
    • What can you conclude from this?
    Recap
    Find a reasonably bright star in the southern sky. Observe the same star on two (preferably consecutive) nights, noting its position on each by reference to some object such as a pole or building. By determining the time the star passes the object, you can determine how long it takes the Earth to turn relative to the star. This is known as the sidereal day. Write up your activity with all five points of the 5-point format, and include the questions above as directed.
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    NOTE #1: Because this activity requires clear skies and outdoor observing, it is important to do it when the opportunity arises. Do not wait until the last minute or you may not have the proper conditions.
    NOTE #2: While you can use a star anywhere in the sky, timing can be difficult if you look anywhere other than in the southern sky. Stars east and west move at too much of an angle to the horizon, and stars in the north can move up, down or sideways. the bottom line is that stars in the southern sky appear to move more in horizontal lines across the sky and are just easier to use for this activity. If you don't know the directions, you need to find out. There are general directions here: Directions. (FYI, if you lived in the Southern Hemisphere, you would need to reverse these instructions and use a star in the northern sky!)
    NOTE #3: It is vitally important that you stand in the same position each night, and that you be at least 50 feet away from the chimney or whatever you are sighting against. (Do NOT sight against a tree or other irregular object.) If you have a stop watch that will run for a full day, you could start the stopwatch when the star disappears on the first night, and then stop it when it disappears on the second night. The time would be your "sidereal day." You need to write up your activity using the 5-point format, and include the questions at the bottom of this site. Then turn it in via email before the deadline.
    NOTE #4: You can use two non-consecutive nights, but you must remember to divide your timing difference by the appropriate number. For instance, if your two readings are not one, but two days apart, divide the answer you get by two. If they are three days apart, divide by three and so on.
    NOTE #5: Sometimes there may be a bright planet in the southern sky that is easier to see and identify than any star in the vicinity. Since planets move against the backdrop of the stars, they cannot be considered as "fixed" to the celestial sphere. Thus, using a planet to determine the sidereal day is incorrect. However, Jupiter and especially Saturn have very slow motions of their own, and their positions relative to the stars changes little from night to night. You may use either of these planets, but be sure to note this in your activity.
     
  2. jcsd
  3. Sep 12, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    Why would you want to pay for "assistance"? Why don't you just do it and then ask for help interpreting the results if you even need it. In spite of the long-windedness of the description, it's not that hard.
     
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