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The astronomer Johannes Kepler determined that the time D, in days, for a planet to revolve around the Sun is related to the planet's average distance from the Sun k, in millions of kilometres. This relation is defined by the equation log D = 1.5log k- 0.7. Verify that Kepler's equation gives a good approximation of the time it takes for the Earth to revolve around the Sun, if Earth is about 150 000 000 km from the sun.

The astronomer Johannes Kepler determined that the time D, in days, for a planet to revolve around the Sun is related to the planet's average distance from the Sun k, in millions of kilometres. This relation is defined by the equation log D = 1.5log k- 0.7. Verify that Kepler's equation gives a good approximation of the time it takes for the Earth to revolve around the Sun, if Earth is about 150 000 000 km from the sun.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
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The astronomer Johannes Kepler determined that the time D, in days, for a planet to revolve around the Sun is related to the planet's average distance from the Sun k, in millions of kilometres. This relation is defined by the equation log D = 1.5log k - 0.7. Verify that Kepler's equation gives a good approximation of the time it takes for the Earth to revolve around the Sun, if Earth is about 150 000 000 km from the sun.
Transcribed Image Text:The astronomer Johannes Kepler determined that the time D, in days, for a planet to revolve around the Sun is related to the planet's average distance from the Sun k, in millions of kilometres. This relation is defined by the equation log D = 1.5log k - 0.7. Verify that Kepler's equation gives a good approximation of the time it takes for the Earth to revolve around the Sun, if Earth is about 150 000 000 km from the sun.
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