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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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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