Question

identifying keplers laws
read each clue and write which of keplers laws it is referring to - 1st, 2nd, or 3rd
27.____mercury has a shorter orbital period than neptune.
28.____each planet revolves around the sun with equal area in equal time.
29.____the greater the eccentricity, the more elongated an ellipse is.
30.____earth is 1 au from the sun and has an orbital period of 1 earth year.
31.____the closer a planets orbit is to the sun, the faster it completes a revolution.
32.____orbital periods are proportionate to the distance from the sun.
33.____e = d ÷ t
34.____planets orbit in an ellipse with the sun at one focus.
35.____planets orbit faster at perihelion and slower at aphelion.

Explanation:

Step1: Recall Kepler's 1st law

Kepler's 1st law (Law of Ellipses) states that planets move in elliptical orbits with the Sun at one focus. So, for 34, it is 1st law.

Step2: Recall Kepler's 2nd law

Kepler's 2nd law (Law of Areas) states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. So, for 28 and 35, it is 2nd law.

Step3: Recall Kepler's 3rd law

Kepler's 3rd law (Harmonic Law) states that the square of the orbital period of a planet is proportional to the cube of the semi - major axis of its orbit (\(T^{2}\propto a^{3}\)). For 27, 30, 31, 32, and 33 (\(E = D\div L\) can be related to the relationship between orbital period (\(E\)), semi - major axis (\(D\)) and some orbital parameter (\(L\)) in the context of Kepler's 3rd law), it is 3rd law. For 29, it is related to the property of ellipses (not directly a Kepler's law in the sense of the three main laws, but if we consider the 1st law which is about elliptical orbits, but the statement is more about the property of ellipse's eccentricity. However, in the context of the problem's options (1st, 2nd, 3rd), and since the 1st law is about the shape of the orbit (ellipse), we can say it is related to the 1st law.

Answer:

1. 3rd
2. 2nd
3. 1st
4. 3rd
5. 3rd
6. 3rd
7. 3rd
8. 1st
9. 2nd