Blue Book

Kepler’s Laws Activity/Assignment

Part I: Kepler’s First and Second Laws

1)  Using two push pins, a piece of string, a sheet of paper, a piece of cardboard and a pencil, you will create an elliptical pattern. Stick the pins in 8-10 cm apart on the paper, using the cardboard as backing. Tie the string in a loop so that the loop circumference is 2-3 cm longer than twice the distance between the pins. Loop the string around the pins and use your pencil to pull the string tight (see diagram). Keeping the string tight, pull the pencil around the pins in a loop. The pattern you get will be an ellipse. [Note that in reality, planet’s paths are much closer to circular, but we are exaggerating the ellipse here for effect. A comet has an orbit similar to the one you have drawn.]

2)  Remove the pins and the string. The old pin locations are called the foci of the ellipse. Draw a star at one focus. This shows the pattern that planets take around their suns. What would happen to the ellipse if you moved the pins farther apart? How would you place the pins to obtain a perfectly circular pattern?

3)  Draw a planet on its path at the closest possible point to the Sun. Label this point perihelion (“helios” means Sun). Draw the planet on its path at the farthest point from the Sun. This point is called aphelion.

4)  Draw a force vector 1.0 cm long on the planet at aphelion to represent the force of the Sun’s gravity on the planet. In which direction should this arrow point? Now measure the distance (radius) between the planet and the Sun at both aphelion and perihelion and record these three values below. Do not do anything about Fperihelion until #5.

Faphelion= 1.0 cm . Fperihelion = ???

raphelion = ______rperihelion = ______

5)  Determine the number of centimeters needed to represent the gravitational force on the planet at perihelion. Remember that the gravitational field strength follows an inverse square law, so use your above numbers in the equation…

6)  Now draw in the force vector of this length at perihelion. (If it is too long to fit on your page, just draw a really long arrow and label how long it should be.)

7)  Repeat the above process for two other location on the planet’s orbit. Based on what you have drawn so far, where do you think the planet will be moving at its fastest speed? Why?

8)  In your notes, draw two similar, smaller ellipses side by side, and use them to make your own version Fig. 5-28 (p. 133, both parts) in your notes, including appropriate commentary.

## Part II: Kepler’s Third Law

9)  Derive Kepler’s Third Law yourself, without referring to notes or text. You may “study” first!

10)  Determine the mass of our Sun, using the period of Earth’s revolution and its distance from the Sun (1.5 ´ 1011 m). Use your answer to determine the value of r3/T2 (Kepler’s constant) for any planet in our Solar System. Check your answer in Table 5-1 (p. 133). Then, quickly calculate r3/T2 for several other planets in the table, to confirm their answers.

11)  Give two reasons why the values for Kepler’s constant are not exactly the same for every planet. (For inspiration, see p. 134-135.) You might be able to think of another if you were paying attention to Dr. Rob Thacker’s lecture.

12)  How were planets such as Neptune and Pluto discovered? Describe how this has also worked for planets revolving around other stars.

Problems: p. 142 P53, 56, 57, 61***