Please help! I do not know where to measure the angel from on the assignment below. Name: Score: /100

Lab 3: Orbit of Mars

Introduction Have you noticed that NASA launches planetary probes to Mars every two years? This is because about every two years the Earth and Mars get relatively close to each other and it requires less fuel to send the probes to Mars. In this activity you are going to determine the orbit of Mars using the method developed by Kepler.

Objectives determine the eccentricity of Mar's orbit

Materials protractor compass ruler graph paper

Procedure Mars' orbital period (687 days) is close to twice that of the Earth (365 days 2 = 730 days). Thus, every time Mars comes back to the same point in its orbit, the Earth has not completed two orbits yet. So if you are on the Earth and make an observation of Mars every time Mars is at the same point on its orbit, you will see the planet in a different direction with respect to the background stars. The two lines of sight intersect at a point on the orbital path of Mars as shown in the figure below.

The observational data you will use (found in the table on the next page) shows Mars' position on various dates between 1991 and 1998. Each pair of observations (e.g., A and A') are made when Mars is exactly at the same point in its orbit. The angle to Mars is measured from the vernal equinox as seen from the Earth. The Earth's position is the angle measured from the vernal equinox to the Earth as seen from the Sun.

All angles are measured from the direction of the vernal equinox in the counterclockwise direction.

Pairs Date Earth's position Angle to Mars Pairs Date Earth's position Angle to Mars A Mar 21, 91 180 83 G Feb 27, 92 160 309 A' Nov 9, 96 45 153 G' Oct 19, 97 24 254 B May 17, 91 234 117 H Apr 24, 92 213 353 B' Jan 5, 97 107 182 H' Dec 15, 97 83 300 C Jul 13, 91 292 150 I Jun 20, 92 270 35 C' Mar 4, 97 165 183 I' Feb 10, 98 144 345 D Sep 8, 91 347 185 J Aug 17, 92 327 73 D' Apr 30, 97 218 169 J' Apr 8, 98 198 26 E Nov 4, 91 40 221 K Oct 13, 92 19 104 E' Jun 26, 97 276 183 K' Jun 5, 98 253 67 F Jan 1, 92 101 265 L Dec 9, 92 77 119 F' Aug 22, 97 332 217 L' Aug 1, 98 312 109

1. Draw a 10-cm radius circle on a large sheet of graph paper to represent the Earth's orbit and assume that the Sun is located at the center of the circle. 2. Draw a line from the Sun to the right and parallel to the grid lines on the graph paper (see the reference figure). This line represents 0 and points toward the vernal equinox. This direction will serve as the reference for measuring angles on the Earth's orbit. The Earth crosses the 0 line on the autumnal equinox (around September 23) and the 180 line on the vernal equinox (around March 21). 3. Locate the Earth's position on your plot of the Earth's orbit for the date of each observation. Label each position. 4. To determine the angle to Mars on any given date, draw a line from the Earth's position parallel to the 0 line. This line should be parallel to the grid lines on the graph paper. Use a protractor to measure the angle to Mars in the counterclockwise direction from the 0 line. Two lines for each pair of observations will intersect at a point on Mars' orbit. 5. When you have finished plotting all ten points, use a compass, and by trial and error, draw the best circle that fits the plotted points.