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Mars

Summary: Mars makes its closest pass to Earth in thousands of years on August 27, 2003. Mars and Earth make a fairly close pass to each other approximately every fifteen months, but this pass is one of the closest. As we pull away from the other planet, the apparent size will shirink noticably in the telescope over the course of this semester. Using the 10mm eyepiece, it should be possible to identify the south polar ice cap, dark surface markings, and possibly limb hazes and dust storms. Mars is an active plant; the last time it passed close to Earth, huge planet-wide dust storms obliterated most of the surface featuresnormally visible. What will happen this year? If we are lucky and dust storms don't wipe out anything we can see, you should be able to see the planet rotate before your eyes in the span of an hour or so.

Due Date: October 31.

Note: Clear skies are relatively rare in Nashville, so you should make the very best of your time at the telescope and use it to OBSERVE. Use it to make sketches, make notes and write down measurements and discuss the questions asked in the lab. Leave out all calculations, writing down your answers to the questions, etc., for later, and complete the lab in the comfort of a heated, well-lit room.

Background: For an excellent discussion of Mars from the point of view of an observer with a small telescope, see Mars at Its All-Time Finest on the Sky & Telescope website. Reading this article will help you succesfully complete this lab! Additionally, the June, July, and August 2003 issues of Sky & Telescope feature cover stories on Mars, both about our latest scientific understanding, and about what may be seen by an observer with a small telescope (like you!). The Stevenson Center Library has a subscrtiption to Sky & Telescope.

Procedure

1. Getting Started: As always, note the date and time. Make notes describing the atmospheric conditions tonight. Is the sky clear, partly cloudy, high cirrus clouds? Is the air moist? Is it windy? How does this night compare with other nights on which you have observed (better? worse? in which way?). Think about how the weather may affect your view of Mars.

2. First locate Mars and sketch the surrounding field. Using the 25 mm eyepiece, find Mars in the telescope and then center it in the field of view. Make a sketch of the field of view, showing the planet and surrounding stars. Try to make an accurate record of the positions of the objects in the field of view.  Indicate the scale of your drawing, based on your measurement of the field of view you made earlier.

   Indicate the orientation of your sketch (direction of North and East in the field of view). Remember, the sky rotates from East to West, so when you turn off the motor drive of the telescope, objects drift westward in the eyepiece. If you move the telescope in declination toward the South (lower declinations), objects will drift North in the field of view.

   Sketch Mars: Switch to the 10 mm eyepiece. Draw the disk of Mars using the template provided. Have a look at the examples kept in the storage shed. You will have to be patient, watch for a long time, and wait for clearer views of Mars through brief patches of still air. Take your time!  Details are small and of low contrast.  When you are done sketching, you should feel confident that you have recorded all there was to see, and only what you saw (the truth, the whole truth, and nothing but the truth). If Mars shows a phase (i.e. is not round, as should be the case later in the semestr), draw the phase as accurately as you can. You'll need this for #5 below. Indicate on your sketch the directions of North and East.

   If you see a distinct surface marking(s), you should plan to return to Mars about one hour later and sketch it again. This will reveal the planet's rotation.

   Try to match what you see with a map of Mars. For this, you will need to know what side of the planet was visible at the time of your observation. This is given by the longitude of the central meridian of Mars. The Sky & Telescope web site provides a tool (the "Mars Profiler") which will calculate the central meridian of Mars at any date and time, and will show you which figures are forward; before you come to lab, use this tool and write down the central meridian of Mars (and print out the map it provides) for each hour you think you might observe Mars in lab. (Yes, it rotates over the course of the lab, and thus the central meridian value changes over the course of a few hours.) The third page of the article "Mars at Its All-Time Finest" has a full map of the entire surface of Mars (cylindrical projection); click on the "Mars map" image to get it. Using this map and the value for the central meridian, you should be able to identify any feature you can see.

3. How far away is Mars? When the relative positions of the Sun, the Earth, and Mars are favorable, Mars shows a phase, as is the case during the later partof the Fall 2003 semester. We can use this phenomenon to determine the distance between Mars and the Sun and between the Earth and Mars. Once you have sketched Mars (with a precise rendering of the phase) and plotted its position on the 200% blow-up SC001 sky chart (Mars' orbital motion lab), you have all the observations in hand to do the calculation The following two figures show the geometry of the problem. A modest amount of high school trigonometry is required to understand the method.

   
   

   Figure 1

   
   

   Figure 2

   Our goal is to determine the size of the orbit of Mars (D) and the distance between the Earth and Mars (L). This can only be done by using a little bit of trigonometry and algebra. In Figure 1 above, the Sun-Earth distance is 1 Astronomical Unit (this defines this unite of distance: 1 A.U. = 1.496×10⁸ km, or about 93 million miles). If we apply the Law of Sines to the triangle in Figure 1, we have:

   

   The angle a is simply the Sun-Earth-Mars angle, and can be measured by plotting the position ofMars on the star chart (SC001 or the 200% blow-up) and reading off the difference in ecliptic longitude between the Sun and Mars. The angle b is what determines the phase of Mars, as can be seen in Figure 2 above. We are interested in the sine of angle b. We have:

   

   Applying the Pythagorean theorem, we find:

   

   Measure W and R (in mm) on your sketc of Mars, and compute Y, sin(b), and finally the angle b. The angle c is simply given by c=180^o-a-b. We now know all three angles of the triangle in Figure 1 and the length of one side. You can compute the other two sides, D and L, using the formulae above. Give your results in A.U. and km. It is quite remarkable that we can determine such vast distances with such simple measurements and calculations!

   Question: Does your value for the distances make sense? Explain.