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use the following table to find the eccentricity (e = c / a) | planet |…

Question

use the following table to find the eccentricity (e = c / a)

planetdistance from center of ellipse to focus in aus csemi - major axis in aus aeccentricity e
venus0.0050.723
earth0.0171.000
mars0.1421.524
jupiter0.2505.203
saturn0.5349.540
uranus0.90119.180
neptune0.27130.060
pluto9.82139.440

Explanation:

Step1: Recall the eccentricity formula

The formula for eccentricity is $e = \frac{c}{a}$, where $c$ is the distance from the center of the ellipse to the focus and $a$ is the semi - major axis.

Step2: Calculate eccentricity for each planet

For Mercury: $e=\frac{0.080}{0.387}\approx 0.207$.
For Venus: $e = \frac{0.005}{0.723}\approx0.007$.
For Earth: $e=\frac{0.017}{1.000}= 0.017$.
For Mars: $e=\frac{0.142}{1.524}\approx0.093$.
For Jupiter: $e=\frac{0.250}{5.203}\approx0.048$.
For Saturn: $e=\frac{0.534}{9.540}\approx0.056$.
For Uranus: $e=\frac{0.901}{19.180}\approx0.047$.
For Neptune: $e=\frac{0.271}{30.060}\approx0.009$.
For Pluto: $e=\frac{9.821}{39.440}\approx0.249$.

Answer:

Mercury: $e\approx 0.207$, Venus: $e\approx0.007$, Earth: $e = 0.017$, Mars: $e\approx0.093$, Jupiter: $e\approx0.048$, Saturn: $e\approx0.056$, Uranus: $e\approx0.047$, Neptune: $e\approx0.009$, Pluto: $e\approx0.249$