PH112Man19 Lab06

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CUNY Queensborough Community College *

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Course

112

Subject

Astronomy

Date

May 22, 2024

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pdf

Pages

6

Uploaded by ChiefCobra78

PH-112 SPACE, ASTRONOMY and OUR UNIVERSE LABORATORY LAB # 6 Testing Kepler's First Law: The Orbit of Mercury OVERVIEW About four centuries ago, the mathematician, Johannes Kepler, discovered three laws that describe the motions of the planets accurately. Using the observations of a Danish astronomer, Tycho Brahe, Kepler found that the true path of every planet was an ellipse. He stated this in his first law: Law #1: Planets travel in elliptical orbits with the Sun at one focus. Most astronomers before Kepler thought that the paths were circular or were a composite of several motions all based on the circle. Kepler's discovery brought about a genuine revolution in astronomical thinking. After examining the features of the ellipse, we will use some of Tycho Brahe's observations of Mercury to verify Kepler's first law. Part 1: The Ellipse The figure of an ellipse is made as follows: « Take a length of string and tie the ends together to make a loop. » Place the loop around two fixed points on a surface. Each of these points is called a focus. « Hold a pencil against the string inside the loop and pull it to form a triangle. While keeping the pencil point on the surface, slide the pencil along the string. The figure you draw is an ellipse. focus ““‘ ‘.Illlll.llll.ll.lll.lllllglll.l.lllla ellipse (unfinished) Rewinder: All astronomy students are required to attend one evening telescope observing session. Have you attended a session?
Lab #6: Testing Kepler's First Law (continued) Page 2 of 6 The important features of an ellipse are shown in the diagram below. The shape of an ellipse is given by the ratio c¢:a, which is called the eccentricity (e). Note that the eccentricity of a circle is zero. Tear off the paper millimeter ruler on page five of this lab and use it to find ¢ and a. Compute e. 2 e=_28 mm : 34 4 a=___ mm Jocus e=c/a= 82 semi-major axis () Place the bottom of this page on a cork board and insert a pin at each of the two foci. Place a loop of string around the two pins and draw the ellipse in the manner shown on page one. Measure ¢ and a with the millimeter ruler and compute e. c=_ 26 mm a=__ 2’ mm e=c/a= 26/57=.45
Lab #6: Testing Kepler's First Law (continued) Page 3 of 6 Part 2: The Orbit of Mercury Because its orbit lies entirely within the Earth's orbit, Mercury is never seen far from the Sun. In the illustration below, the Sun is setting in the western sky as seen from New York and Mercury is at its Greatest Eastern Elongation, which occurs when the angle Sun-observer-Mercury reaches its greatest extent. When Mercury is at its Greatest Western Elongation it can be seen in the morning sky. Tycho Brahe and other astronomers measured the greatest elongations of Mercury in order to better define the planet’s orbit. A list of some of these observations are printed on the next page. The first thing to note is that the angles are not the same. Why this is so will become clear once you have plotted Mercury’s orbit. Mercury On the next page a circle has been drawn with the months of the year along its outer edge. It is an approximate representation of the Earth's orbit around the Sun. If we know the date of an observation of a greatest elongation as well as the elongation in degrees, the actual orbit of Mercury can be plotted. « Tear off the protractor at the bottom of the page. Fold over the edges as indicated. « Use the protractor to plot the greatest elongations in the table. To do this, place the point representing the Earth on the protractor on the date of an elongation. (The first date has been plotted.) Adjust the protractor so that the zero degree line points toward the Sun. Make a mark at the elongation listed in the table and draw a line from the Earth through the mark almost to the other side of the Earth's orbit. Do this for all the dates in the table.
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