Answer, and give a reason. A planet twice as heavy as the Earth orbits the Sun at the Earth's…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Answer, and give a reason.
- A planet twice as heavy as the Earth orbits the Sun at the Earth's distance. Is its year different?
- In which month does the Earth move fastest round the Sun?
- Which conservation law is behind Kepler's law of equal areas?
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) No. In the planet's mass cancels, so its speed and year depend only on the Sun's mass and the distance.
Step 2. (b) In early January, when the Earth is nearest the Sun; equal areas in equal times means faster when nearer.
Step 3. (c) The conservation of angular momentum about the Sun: the Sun's pull points at the Sun and has no torque about it.
Answer: (a) No. (b) January. (c) Angular momentum.
Watch out. The seasons come from the tilt of the Earth's axis, not from its distance from the Sun.
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