Question

allow 5 min to play with the phet sim keplers laws - third law. describe three main things you have discovered. share your discoveries with the rest of the group. collect and interpret data measuring periods now we will analyze how the period of a planetary orbit is defined, and different ways to measure it within the simulation. 1. based on the behavior of the period tool, how would you define the period of an orbit? 2. take multiple period measurements of the same orbit. does the starting point alter the measurement? explain 3. measure the period of a circular orbit, and compare with the period of more elliptical orbits but with the same semi - major axis: table with columns type, period, t (years), semi - major axis, a (au) 4. compare the results with a partner. whats your conclusion? does eccentricity impact the period of an orbit?

Explanation:

Step1: Define orbital period

The period of an orbit is the time it takes for an object to complete one full - revolution around the body it is orbiting. In the context of the simulation, it can be measured using the Period Tool as the time interval between two consecutive identical positions of the orbiting body in its path.

Step2: Multiple period measurements

Taking multiple period measurements of the same orbit should yield the same result if the orbit is stable. The starting point does not affect the measurement of the period as long as the time interval is measured for one complete orbit. Mathematically, if we start at point A and measure the time to return to point A, it will be the same as starting at point B and measuring the time to return to point B.

Step3: Compare orbital periods

According to Kepler's third law, $T^{2}=k\times a^{3}$, where $T$ is the period, $a$ is the semi - major axis, and $k$ is a constant. For orbits with the same semi - major axis, the period is the same regardless of the eccentricity. So, the period of a circular orbit, a mildly elliptical orbit, and a highly elliptical orbit with the same semi - major axis will be equal.

Step4: Conclusion

When comparing results with a partner, the conclusion is that the eccentricity of an orbit does not impact the period as long as the semi - major axis remains the same. This is in accordance with Kepler's third law which relates the period of an orbit to the size (semi - major axis) of the orbit.

Answer:

1. The period of an orbit is the time taken for an object to complete one full revolution around the body it is orbiting.
2. Multiple measurements of the same orbit should give the same period, and the starting point does not affect the measurement as long as one full - orbit is measured.
3. The periods of circular, mildly elliptical, and highly elliptical orbits with the same semi - major axis are equal.
4. Eccentricity does not impact the period of an orbit when the semi - major axis is the same.