Mars

Goals of the Lab

• To identify and observe the features of Mars.

Required Equipment: a calculator, a watch, and several printouts of the Observation Template.

Background: Mars is the fourth planet from the sun in the Solar System. It is named after the Roman god of war due its color. Its reddish color is a result of iron oxide (rust) on its surface. It is much smaller than the earth: its radius is about half of the Earth's, and its mass is about 10% of the Earth. Mars has a very thin atmosphere, about 1% of Earth's. As a result of its distance from the sun and its thin atmosphere, the surface temperature of Mars is rather cold. Surface temperatures measured by the Viking Landers in the mid 1970s ranged from 150 K (-190 degree Fahrenheit) to over 300 K (80 degrees Fahrenheit).

Mars rotates on its axis once every 24.5 Earth hours; its day/night cycle is similar to what we experience. Its revolution around the sun takes about 1.9 Earth years. Its axis of rotation is tilted at a 25 degree angle perpendicular to the plane of its orbit, which is almost the same as Earth's 23.5 degree tilt. Since Earth's tilt causes the seasons, we can deduce that Mars also experiences four seasons. The polar ice caps changes with the seasons.

Using the 10mm eyepiece, it is be possible (with good seeing conditions) 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 features normally visible. Hopefully, tonight you will observe the planet's rotation in the span of an hour or so.

In the Fall of 2005, Mars was closer to Earth than it will be for the next several centuries. Although not quite as close as it was then, it will give us an excellent chance to get a good view of Mars. For a discussion of Mars from the point of view of an observer with a small telescope, see this article on the Sky & Telescope website. Reading this article may help you with this lab. Look also at recent issues of the Sky & Telescope magazine, available in the science library.

Part I: Observing Mars

Note:All observations need to include directions N/S and E/W, the time, the date, and weather conditions.

1. Using the 25mm eyepiece, locate and center Mars in the field of view. Sketch the field of view, including any stars in the field of view. Indicate the scale of your drawing, based on your measurement of the field of view you made earlier.

2. Switch to the 10mm eyepiece. Draw Mars using 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. NOTE WRITE DOWN WHAT YOU SEE

3. Sketch Mars again between an hour and a hour and a half later. You should be able to see the planet's rotation, manifested as a motion of any dark markings you saw across the surface of the planet.

Part II: Estimating the distance to Mars

1. When the relative positions of the Sun, Earth, and Mars are favorable, Mars shows a phase. 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 of Mars 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 sketch of Mars, and compute Y, sin(b), and finally the angle b. The angle c is simply given by c=180°-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.