Orbit of Mars Lab

To plot the orbit of Mars.

You should have the following materials at your lab table.

1. Kepler's Laws photograph packet with transparencies

2. ruler

3. protractor

1. The photograph letter and transparency letter MUST match.

2. The transparency letter and numbers MUST be oriented so they read properly.

3. Place the transparency on top of the photograph.

4. Orient the transparency so each small circle on the transparency has a star (bright spot) in it. The transparency can rotate at any angle.

5. The brightest spot found inside the "goal post" and NOT inside a small circle is MARS.

DO NOT WRITE OR DRAW ON THE TRANSPARENCY.

6. Project a line through the brightest spot and parallel to the sides of the goal post to the bottom of the "goal post".

DO NOT WRITE OR DRAW ON THE TRANSPARENCY.

7. The projected line and the bottom of the "goal post" intersect at an angle reading. Record the angle reading to the nearest degree (no decimals).

8. Record the date of the photograph.

9. Complete your data table for letters A through P.

You will now triangulate the position of Mars.

1. On your lab sheet, plot the first of each month on Earth's orbit. Let's simplify the calendar:

• 1 year = 360 days
• 1 month = 30 days

Now let's begin triangulating the position of Mars.

Triangulation is the process of determining the location of an object by forming a triangle to the object from two known points. The two known points will make one side of the triangle. The two known points are paired readings from your data table: A-B, C-D, E-F, G-H, I-J, K-L, M-N and O-P.

3.Locate the date of each paired readings on Earth's orbit. For example, pair I-J

• I is November 22nd - 21 degrees from November 1st.
• J is October 11th - 10 degrees from October 1st.

4. Place a protractor on each letter's date and project the line of sight at the recorded angle. Where the lines of sight intersect is the position of Mars.

THE PROTRACTOR MUST ALWAYS HAVE ZERO DEGREES POINTING TO THE RIGHT.

REMEMBER - THE PROTRACTOR MUST ALWAYS HAVE ZERO DEGREES POINTING TO THE RIGHT.

5. Repeat this process for each pair of dates.

6. Triangulate the two extra pairs of dates, Q-R and S-T below.

7. After all the dates have been triangulated, sketch the orbit of Mars and complete the Analysis Section on your lab sheet

All planets move in elliptical orbits with the sun at one focus.

The foci of the ellipse lie on the major axis of the ellipse and are equidistant from the origin. An ellipse represents the locus of all points, the sum of whose distance from the two fixed points are a constant value. These two fixed points are the foci of the ellipse.

• a is the semi-major axis
• b is the semi-minor axis
• f are the foci (focus is singular; foci is plural)
• c is the distance from the origin to the foci

1. Using a ruler draw the major and minor axis of Mars' elliptical orbit. NOTE - The major and minor axes with be tilted (no horizontal and vertical).

2. The intersection of the major and minor axis is the origin.

3. Measure the length of the semi-major axis (a) and semi-minor axis (b) and calculate "c". Recall "c" is the distance from the origin to the foci.

4. Measure and mark the location of both foci along the major axis.

5. Draw the Sun at one of the focal points.

A line joining any planet to the sun sweeps out equal areas in equal times.

1. From the sun to Mars' orbit, draw two "wedges" of equal area centered about the major axis.

2. Color in both areas.

The square of the period of any planet is proportional to the cube of the semimajor axis of orbit.

1. Using a ruler measure the radius of the Earth's orbit.

2. Using a ruler measure the semi-major axis of Mars' orbit.

3. Using the period of the Earth's orbit is 365 days, calculate the period of Mars' orbit in days and years.