Question

while researching a topic, a student has taken the following notes:

• keplers first law of planetary motion states that the orbit of a planet around the sun is an ellipse.
• the law also states that, in an elliptical orbit, the object being orbited is one of the ellipses foci.
• keplers laws of planetary motion also apply to natural satellites (e.g., moons).
• umbriel is a moon of uranus that orbits the planet in 4.14 earth days on average.
• umbriels orbit is elliptical.

the student wants to provide an explanation and example of keplers first law of planetary motion. which choice most effectively uses relevant information from the notes to accomplish this goal?
a) umbriels orbit of uranus is elliptical, demonstrating keplers first law of planetary motion, which describes the elliptical orbits of planets, but applies to moons as well.
b) keplers first law of planetary motion states that the orbit of a planet around the sun is an ellipse; for example, planetary satellites orbit their planets in an elliptical fashion.
c) keplers first law of planetary motion, which describes the orbits of uranus and other planets in the solar system, states that the object being orbited is one of the ellipses foci.
d) uranuss moon umbriel completes an orbit in 4.14 earth days on average, a clear example of keplers first law of planetary motion, which describes the elliptical orbit of planets.

Explanation:

• Option A:
• It correctly states that Umbriel's elliptical orbit (as a moon, which is a natural satellite) demonstrates Kepler's first law.
• It also mentions that the law applies to moons (natural satellites) as well as planets, which is in line with the note "Kepler's laws of planetary motion also apply to natural satellites (e.g., moons)".
• Option B:
• The example "planetary satellites orbit their planets in an elliptical fashion" is too vague. It doesn't name a specific satellite like the notes mention Umbriel.
• Option C:
• It doesn't mention the elliptical orbit aspect which is key in Kepler's first law (the first note is about the orbit being an ellipse). Also, it focuses on Uranus (a planet) but the law's application to moons (as in the notes) is not well - represented.
• Option D:
• The fact that Umbriel completes an orbit in 4.14 Earth days is not relevant to Kepler's first law (which is about the shape of the orbit, not the time of orbit).

Answer:

A. Umbriel's orbit of Uranus is elliptical, demonstrating Kepler's first law of planetary motion, which describes the elliptical orbits of planets, but applies to moons as well.