Kepler: Kepler's calculation of the position of Mars
In mosaicCalc: R-Language Based Calculus Operations for Teaching

Kepler

R Documentation

Kepler's calculation of the position of Mars

Description

Astronomer Johannes Kepler (1571-1630) famously measured the position of the planet Mars. His interpretation of this data led substantially to Newton's theory of universal gravity. This data frame gives Kepler's measurements as a function of time, together with a modern reconstruction of the "actual" position of Mars at the time.

Usage

data(Kepler)

Format

A data frame with 28 rows and these variables:

time - Interval in Earth days from 8:15am Greenwich time on 9 March 1584.
kepler.radius - The radius of the orbit in AU (astronomical units. 1 AU is 93 million miles)
kepler.angle - The "true anomoly" measured in radians
actual.radius - Modern calculation of the above
actual.angle - Modern calculation of the above

Details

The raw measurements (not included here) that Kepler used in his calculation were made by Tycho Brahe (1546-1601). Those raw measurements were of the angle of Mars with respect to Earth. Kepler estimated the orbital period of Mars to be 687 Earth days. (The current accepted value is 686.980 days.) Knowing the period, Kepler could find pairs of Earth days separated by multiples of the period. In each pair, the Earth would be in a different position, but Mars would be in the same position. Thus the distance of Mars from Earth could be estimated by triangulation.

The angle was not directly measured for each occasion. Instead, knowing the radius versus time Kepler was able to discern when Mars was at its greatest and closest distance to the Sun. The angle tells where Mars is along its orbit. An angle of 0 is the position when Mars is closest to the Sun. An angle of 3.14 is when Mars is farthest from the Sun.