The following table gives the length of year L (in earth years) of each planet in the solar system, along with the mean (average) distance D of the planet from the sun, in astronomical units (1 astronomical unit is the mean distance of the earth from the sun).

a. Plot the point (D, L) for each planet on a coordinate plane. Do these quantities appear to be linearly related?

b. For each planet, compute the ratio L²/D³. Interpret what you find by expressing L as a function of D.

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Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Mean Distance from Sun, D 0.388 0.722 1.000 1.523 5.203 9.545 19.189 30.079 Length of Year, L 0.241 0.615 1.000 1.881 11.862 29.457 84.013 164.783