Applied Astronomy Lab

Big Points.

Directions.

Neatly Number and Label all your work. Good Drawings complete sentences. You may work together but each of you is responsible for your own understanding, explanations and the original report you hand in. List your partners after your name. Do not quote them but indicate their contributions. If you need help with the charts or the pictures come see me.


On December 4th, 2005 an astronomer observed that two of the three planets circling Snoopy in the Dogstar galaxy aligned behind their sun in his line of sight. Determined to capture this image but unprepared at the time, he began observing the planets’ movements through the course of month until he was able to determine the speed of each planet. Armed with this information he calculated that the first planet, Brutus, makes one complete orbit about its sun every two years. The second planet, Hooch, takes three years to complete its orbit, while the last planet, Sadie, takes ten years, to complete its cycle. Since all the planets’ orbit were relatively circular he decided it would be best to convert this data in to a rotational speed (that is a speed given in degrees about the sun per year) to make finding the next time of alignment more easily.

1. If we break each planets orbit into 360 degrees, find the rotational speed of each planet in the units degrees of travel per year (about Snoopy) and also degrees of travel per month (you will need one or both to answer the following questions).

On December 4th, 2005, he observed that it was only the innermost and outer most planets that were aligned while Hooch was 1/6 of her orbit out in front of them.

2. Based on this information, what was the angular distance between Hooch and the other two planets on that day. Draw a picture to represent this, presenting and labeling the the planets in their proper order circling the star and entitle it "The Dogstar galaxy" December 3rd, 2005

If we use the aligned angular position of Brutus and Sadie on the day of their alignment as the reference point (the place from which we will do all measuring) it should be clear that since they are both at the reference their positions are both zero.

3. What would Hooch’s angular position be?

4. Since you have the speed of each planet you should be able to develop a chart indicating each planets’ angular distance from the reference position each month over the next year. Keep in mind that Hooch begins out in front and do so now.

5. Having done that develop another chart indicating the position each planet over the next five years skipping by a half year intervals.

6a and 6b. Use each chart to develop a linear equation for each planet that gives the planet’s location (L) as function of the time that has passed since Dec 4th, 2005. For time in your monthly equation use m (for months. For time in your yearly equation use y (for years).

7. Now you should have two equations representing each planets’ movement. Evaluate each equation to find the location of each planet, once for m= 18 and again for y =1.5. Compare your results and explain what you observe. (if you use m = 12y something cool happens too!)

8. Use your equation to find how many degrees of separation will keep Sadie from Hooch on my 30th birthday. February 4th 2007Inorder for two planets to align they must be at the same angular location L at exactly the same time. As such a system of equations can be used to solve for when and where this special occurrence of alignment will happen.

9. Use your monthly equations to create a system that can be solved to find when Hooch and Brutus will next align.Going back to the charts, we should keeping in mind that 360 degree is an equivalent position to 720 or 1080 or even 0, and 45 is the same as 405. In so doing we find that we can reduce any values for location greater than 360 by subtracting that number repeatedly until the results are within the range of 0 to 360 (0 and 360 being the same). When you make this adjustment in all your charts you will find a number of places where two of the planets are in alignment.

10. Make this adjustment then find and circle the places where at least two of the planets are in alignment.Your chart should now indicate that 2.5 years from now Brutus will again aligned with Sadie. While this is of no help to the astronomer (as the planets are perpendicular to his line of sight) it can show us something valuable when solving systems of equations like this.

11. If you test y=2.5 in both Brutus’s and Sadie’s equations you get different results that are actually the same. What are the results and Why are they actually the same?

What question 11 reveals to us is that when dealing with a cyclic system like this we can add or subtract 360 to the constant row for free to get a new, but no less valid equation and which will give a new, but no less valid result. Try these last three problems with this idea in mind.

12. Take your original equations for Brutus and Sadies location and set them up as a system to solve. Solve them. What is the result and why would it be of no help to the astronomer?

13. Take your original equations for Brutus and Sadie again and change one of the zeros in one of the equations to any multiple of 360 and try again (that is to say: since 0 = 360 in terms of angular location, add 360 to one of your equations at no cost). What are your new results and what do they mean.

14. Repeat question 13 with a different multiple of 360 (if you should get a negative be reminded that means months or years ago rather than months or years in the future but it is still okay). List your new results and explain what they mean to the astronomer?Hopefully at this point you are prepared to answer the seemingly trivial question which follows.

15. How long must the astronomer wait until the two planets he originally observed will be aligned in his line of sight (that is at either 180 or 0 with the reference) so that he can take his picture with both planets and Snoopy too.

Bonus:Having done all this work above what follows is for a five point bonus on your final exam:

Find, Explain, Show the work or the tables you used and prove to me by testing in your original equations your answer is correct for the following question.

How long must the astronomer wait to get a picture of all three doggie planets and their sun in alignment in his line of sight?


Hope you’ve had fun learning. Have a nice break. Mr. Rosever