Question

use the following table to find the eccentricity (e = c÷a)
planet distance from center of ellipse to focus in aus c semi - major axis in aus a eccentricity e
mercury 0.080 0.387
venus 0.005 0.723
earth 0.017 1.000
mars 0.142 1.524
jupiter 0.250 5.203
saturn 0.534 9.540
uranus 0.901 19.180
neptune 0.271 30.060
pluto 9.821 39.440

1. what doesmost eccentric orbit mean?
2. what planet has the most elliptical orbit?
3. what planet has an orbit closest to a circle?
4. which two planets have the closest eccentricity? &
5. what other planet has an orbital eccentricity most similar to earths?
6. explain keplers first law in your own words.

Explanation:

Step1: Calculate eccentricity for each planet

Use the formula $e=\frac{c}{a}$. For Mercury: $e_{Mercury}=\frac{0.080}{0.387}\approx 0.207$. For Venus: $e_{Venus}=\frac{0.005}{0.723}\approx 0.007$. For Earth: $e_{Earth}=\frac{0.017}{1.000} = 0.017$. For Mars: $e_{Mars}=\frac{0.142}{1.524}\approx 0.093$. For Jupiter: $e_{Jupiter}=\frac{0.250}{5.203}\approx 0.048$. For Saturn: $e_{Saturn}=\frac{0.534}{9.540}\approx 0.056$. For Uranus: $e_{Uranus}=\frac{0.901}{19.180}\approx 0.047$. For Neptune: $e_{Neptune}=\frac{0.271}{30.060}\approx 0.009$. For Pluto: $e_{Pluto}=\frac{9.821}{39.440}\approx 0.249$.

Step2: Answer question 4

A most - eccentric orbit means an orbit with the highest value of eccentricity. The more eccentric an orbit is, the more elongated (less circular) it is.

Step3: Answer question 5

Pluto has the highest eccentricity value ($\approx 0.249$) among the given celestial bodies, so Pluto has the most elliptical orbit.

Step4: Answer question 6

Venus has the lowest eccentricity value ($\approx 0.007$), so Venus has an orbit closest to a circle.

Step5: Answer question 7

Uranus ($e\approx 0.047$) and Jupiter ($e\approx 0.048$) have the closest eccentricity values.

Step6: Answer question 8

Mars has an eccentricity of approximately $0.093$, which is relatively close to Earth's eccentricity of $0.017$ compared to other planets.

Step7: Answer question 9

Kepler's First Law states that the orbit of a planet around the Sun is an ellipse, with the Sun at one of the two foci of the ellipse.

Answer:

1. An orbit with the highest eccentricity value, more elongated.
2. Pluto
3. Venus
4. Jupiter & Uranus
5. Mars
6. Planets orbit the Sun in an elliptical path with the Sun at one focus.