QUESTION IMAGE
Question
3 measure the period of a circular orbit and compare with the period of more elliptical orbits but with the same semi - major axis:
| type | period, t (years) | semi - major axis, a (au) |
| circular | ||
| midly elliptical | ||
| highly elliptical |
Step1: Recall Kepler's third - law
Kepler's third - law states that $T^{2}=k\times a^{3}$, where $T$ is the period of the orbit, $a$ is the semi - major axis, and $k$ is a constant for a given central body.
Step2: Analyze the situation
Since the semi - major axis $a$ is the same for the circular, mildly elliptical, and highly elliptical orbits, according to Kepler's third - law, the period $T$ will be the same for all of them.
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| Type | Period, T (years) | Semi - major axis, a (AU) |
|---|---|---|
| Mildly Elliptical | Equal to the others | Given value (same for all) |
| Highly Elliptical | Equal to the others | Given value (same for all) |