In late August 2003, Mars came unusually close to the Earth. For about one month before and after, it appears to move `backwards' across the sky. We will track Mars and chart its motion over time.
Background Reading: Stars & Planets, p. 298 to 301 (The Solar System)
As seen from the Earth, the Sun, Moon, and planets all appear to move along the ecliptic. More precisely, the ecliptic is the Sun's apparent path among the stars over the course of a year. (Of course, it's actually the Earth that moves about the Sun, and not the other way around, but because of our orbital motion, the Sun seems to move across the backdrop of distant stars.) The planets don't remain exactly on the ecliptic, but they always stay fairly close to it.
Unlike the Sun, however, the planets don't always make steady progress along the ecliptic. They usually move in the same direction as the Sun, but from time to time they seem to slow down, stop, and reverse direction! This retrograde motion was a great puzzle to ancient astronomers. Copernicus gave the correct explanation: all planets, including the Earth, move around the Sun in the same direction; retrograde motion is an illusion created when we observe other planets from the moving planet Earth.
It's easiest to understand the retrograde motion of the inner planets, Mercury and Venus. These planets are closer to the Sun than we are, and they orbit the Sun faster than we do. From our point of view, the Sun trundles along the ecliptic (due, of course, to our orbital motion), while Mercury and Venus run rings around the Sun. So at some times we see these planets moving in the same direction as the Sun, while at other times we see them moving in the opposite direction.
For the outer planets, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto, the explanation is a bit more subtle. These planets are further from the Sun than we are, and they orbit the Sun more slowly than we do. From time to time we pass one of these planets, and when that happens, the planet seems to be moving backwards because we're moving faster than it is. At such times we naturally see the Sun and the planet in opposite parts of the sky; the planet is said to be in opposition to the Sun. Opposition is a good time to observe an outer planet; it's above the horizon all night, and relatively close to the Earth.
An outer planet's apparent motion is always retrograde for a month or more before and after opposition. The duration of retrograde motion depends on the planet; it's shortest for Mars, and generally longest for Pluto. The moment when a planet's apparent motion changes direction is called a stationary point, because at that instant the planet appears to be more or less stationary with respect to the stars. An outer planet always has one stationary point before opposition, and another stationary point after opposition.
Mars reached a stationary point on 07/29/03 and was in opposition on 08/28/03; it's now moving in a retrograde direction. Fig. 1 shows the first half of its retrograde ``loop'; notice that Mars is now moving backwards, parallel to the ecliptic and somewhat below it. By the end of the semester, Mars will have turned around again and gone back to normal motion. Our observations will begin where those in Fig. 1 end, and reveal the rest of Mars's path across this part of the sky.
|Fig. 1. Positions of Mars, plotted each Tuesday from 06/17/03 through 08/26/03. The slanting line is the ecliptic; the Sun moves west to east along this line. Mars was also moving to the east initially, but reached its first stationary point on 07/29/03 and then started moving to the west. Greek letters label stars in Aquarius.|
|Fig. 2. Orbits of Earth and Mars, as seen looking down on the Earth's orbit; Earth's northern hemisphere faces us. Both planets move in a counter-clockwise direction. Small circles show positions of Earth and Mars every 28 days; the filled circles are positions at the first night of class, 08/26/03, which is also the night when the two planets are closest.|
Fig. 2 shows the orbits of the Earth and Mars. On the first night of class (08/26/03), the positions of the Earth and Mars, shown by the small filled circles, are almost on a line with the Sun. This is quite reasonable, since opposition occurs just two days later. The Earth is moving faster than Mars - to see this for yourself, note the distances between the small circles along each orbit. As of early September, the Earth has just passed Mars on the inside, and is now pulling ahead of the red planet. From our point of view as we race around the Sun, Mars is falling behind; consequently, we see Mars moving in a retrograde direction from night to night across the sky.
Since the Earth always moves around the Sun faster than Mars, you might imagine that Mars's motion will always be retrograde. However, there's another factor involved, and that is the direction of each planet's motion. At the end of August, the Earth and Mars are both moving in the same direction through space. By October, however, the Earth will have pulled ahead in its orbit and will no longer moving in the same direction as Mars, and by December the Earth is so much further along that it will be moving more or less directly away from Mars! As the Earth ``peels away'' on its inside track, Mars will appear to slow down, stop, and finally reverse direction a second time, ending its period of retrograde motion.
The big picture in Fig. 2 helps explain several things in addition to Mars's retrograde motion. First, the distance from the Earth to Mars will increase throughout the semester - by mid November, for example, Mars will be twice as far as it was in late August. As the distance increases, Mars will appear fainter when seen with the naked eye and smaller when seen through a telescope. These changes will be pretty obvious, and we will use a simple procedure, outlined below, to measure the change in Mars's brightness. Second, the angle of the sunlight falling on Mars will change - in late August the Sun was behind us and Mars's globe was fully illuminated, but by the end of the semester the sunlight will be falling from one side, and Mars will appear distinctly less than full when viewed through a telescope.
The chart handed out in class should be used to plot the position of Mars each week. It shows more stars than you can see with your naked eyes, but most of these stars will be visible with binoculars. The chart has a scale of 1 cm per degree; thus, two stars separated by 1° in the sky are plotted 1 cm apart on these charts. At the top of the chart is an arrow pointing toward the North celestial pole. Finally, the small crosses show the positions of Mars on a few dates before the beginning of this assignment.
Your assignment is to plot Mars on this chart every time we observe. This should be pretty routine after a few weeks, and a reasonably complete set of plotted positions will nicely show the track of the planet as it ends its period of retrograde motion and resumes its normal (west to east) progress along the ecliptic. Here's how to plot Mars's position:
The point of this exercise is to track Mars over the entire semester as it switches back from retrograde to normal motion. Don't worry if we miss a few observations due to bad weather; we can just pick up again when the weather improves. If you want, you can make additional observations whenever you have the chance. For example, if we miss an observation due to bad weather on Tuesday, you can go out the next clear night and fill in the gap (of course, always write the current date next to your mark).
Mars will fade dramatically during this semester. In September, Mars outshines every star in the sky; by December, the brightest stars will outshine Mars. This change is largely due to the increasing distance between Earth and Mars.
To measure the change in Mars's brightness, we will use the inverse-square law. This law states that the brightness of a light source is proportional to the inverse of the square of its distance. For example, a 100 watt bulb looks fairly bright from a distance of 10 feet. If you move to 20 feet, which is twice that distance, the bulb will appear only 25% as bright - in other words, it takes four bulbs at a distance of 20 feet to equal one bulb at a distance of 10 feet. (This law is further discussed in The Inverse-Square Law.)
Now, how can we use the inverse-square law to measure Mars's brightness? The procedure is fairly simple. We will set up an ``artificial Mars'' - a point source of light which you can compare directly with Mars itself. If you stand very close to the light, it will be brighter than Mars, while if you stand much further away, it will be fainter than Mars. Your task is to find a place where Mars and the light source both have equal brightness. Once you've done that, you can measure your distance to the light source with a tape measure, and record that distance as an indication of Mars's brightness.
We will repeat this measurement several times over the course of the semester. Early on you will find that you need to stand fairly close to the light source to match Mars's brightness, while later in the semester you will need to stand much further away. By graphing the distance you measure at different times, you can show how Mars fades out as it recedes from the Earth. This graph will be part of the report you'll turn in for this lab.
As the Earth races ahead of Mars, the angle of the sunlight falling on Mars will change. Right now, Mars is very close to opposition, and we view it with the Sun right behind us; thus the side of Mars facing towards us is in full sunlight. By the end of the semester, however, the Sun will no longer be right behind us when we look at Mars, but rather somewhat off to one side, and Mars will no longer appear ``full'' when viewed through a telescope. (A similar effect is responsible for the Phases of the Moon.)
As we view Mars through our telescopes throughout the semester, you will begin to notice that Mars is no longer so full - not a round disk, but rather a bit lopsided. This change will be quite subtle at first, but more and more obvious as the semester goes on. As part of this lab, you should make a series of simple sketches showing how much of Mars's disk is illuminated. These sketches will become part of your lab report.
This chart shows a 25.4° by 19.0° region of the sky. When printed at a resolution of 100 dpi, the GIF image has a scale of 1 cm per degree. The Postscript file should automatically print at this scale. The faintest stars shown are about 8th magnitude, which is roughly the limit for our binoculars from Kapiolani park.
Animation showing Mars as seen from the Earth each night from 08/26/03 to 12/30/03 at 21:00 (08/27/03, 07:00 UT to 12/31/03, 07:00 UT). Note that Mars goes from full to waning gibbous phase as it recedes. Generated using NASA's Solar System Simulator.
A cautionary tale, recounted by Johannes Kepler in the Dedication of his New Astronomy, describes what happens to those who contemplate the motions of Mars too long.
Make the observations described in the sections on TRACKING MARS, BRIGHTNESS MEASUREMENTS, and PHASE OBSERVATIONS, and write a report on your results. This report will be due in late November; the due date will be announced in class and posted on the Handouts and Assignments web page. Your report should include, in order,
In more detail, here are several things you should be sure to do in your lab report:
Last modified: September 2, 2003