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8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.

8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.
Transcribed Image Text:8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.
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