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Encke's comet goes round the Sun every 3.3 years…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Encke's comet goes round the Sun every years. Its nearest distance from the Sun is . Find
- the semi-major axis of its orbit;
- its farthest distance from the Sun;
- the ratio of its speeds at nearest and farthest.
Need a reminder? The key ideaShow
Kepler's laws. Orbits are ellipses with the Sun at a focus. The line to the Sun sweeps equal areas in equal times, so at the nearest and farthest points . And : for bodies around the Sun, with in years and in AU.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) .
Step 2. (b) .
Step 3. (c) .
Answer: (a) . (b) . (c) .
Check. Its farthest point lies between the orbits of Mars and Jupiter, as observed.
Watch out. The semi-major axis is half the longest width of the ellipse, the average of nearest and farthest.
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