Question

kepler’s laws activity sheet: third law
course:
context (student grade level, ages, required prior knowledge, special needs, etc.): can be used in any middle to higher educational level. some basic geometric notions would be good to facilitate the discussion.
phet sim (name and link): kepler’s laws: https://phet.colorado.edu/en/simulations/keplers - laws
learning goals
explore the relationship between the semi - major axis and the period of an orbit, and their corresponding powers described by the kepler’s third law
pre - lab activity
distances in the orbit
unlike the circle, drawing an arbitrary diameter is not enough to measure an ellipse. instead, we use two important lines called the axes, which are the smallest and biggest possible diameters (minor and major axis respectively).
the most important measurement of an ellipse is certainly the semi - major axis represented with the symbol a which is the distance measured from the center to the border, along the major axis. the name also indicates that its length is exactly half of the major axis.

1. in the above image, use a ruler to verify that the longest distance from the center is indeed a.
2. think of different shaped orbits. is the orbital period related to any other property? list the orbital elements you think influence the period.

Explanation:

Step1: For question 1

Use a ruler to measure the longest distance from the center of the ellipse - like shape in the image. Compare it to the length labeled as 'a' to verify if they are the same.

Step2: For question 2

The orbital period \(T\) is related to the semi - major axis \(a\) according to Kepler's Third Law \(T^{2}=k\times a^{3}\) (where \(k\) is a constant). Other factors that can influence the period include the mass of the central body \(M\) (since \(k = \frac{4\pi^{2}}{GM}\), \(G\) is the gravitational constant). Also, the presence of other massive bodies nearby can cause perturbations and affect the period.

Answer:

1. Measure the distance with a ruler and compare to 'a'.
2. The semi - major axis (related by Kepler's Third Law \(T^{2}\propto a^{3}\)), mass of the central body, and presence of other massive bodies nearby.