Part a) The table below shows the mean (average) distances d of the planets from

Question

Part a) The table below shows the mean (average) distances d of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods T (time of revolution in years) Using a calculator, fit a power model to the data. Keplers Third Law of Planetary Motion states that The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun. Does your model corroborate the Third Law of Kepler? Mercury0.3870.241 Venus Earth Mars Jupiter5.20311.861 Saturn Uranus 19.190 84.008 0.723 0.615 1.000 1.523 1.000 1.881 9.541 29.457 Neptune 30.086 164.784

Explanation / Answer

solution:-

a) B. Kepler’s Third Law of Planetary Motion says that “The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun.”  

Answer: Yes. Kepler says that T 2 = kd3 for some constant k. In other words, T = kd1.5 . This is very close to our answer, with e 0.000431 playing the role of k.

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