On the planet Kp orbiting the distant star Kk, lives the astronomer Su’Kin Repok

Question

On the planet Kp orbiting the distant star Kk, lives the astronomer Su’Kin Repok. Su’Kin and her
fellow Kpicans possess basic mathematics (geometry, trig, and basic algebra), but have not as yet
developed calculus or basic physics, and to date they have made only naked-eyestalk observations
of the universe. Their prevailing model of the universe is the Kpcentric Model in which Kp is the
center of the universe and circled every day by their star, Kk, and 4 naked eye planets.
Su’Kin, however, has proposed a radical Kkcentric Model in which Kp is in fact the 2th planet from
Kk and orbits along with the other 4 in the same direction on perfect circles. She has made these
observations of the other 4 planets:

where:
Emax = maximum elongation angle in degrees
TQ = time between opposition and quadrature in dak.

Kp has a circular orbit with a radius of 1 auk. Its day is 1 dak long, and its year is 1 yak=100 dak
in length. Conveniently, their angular units are the same as ours (360° per full circle).
Using the Kkcentric model, compute the sizes (in auk) and sidereal periods (in yak) of their solar
system. Make a table with your results, and draw the Kk system to scale looking down on its
orbital plane from above.

Note: The Kpicans are at a proto-Copernican stage of development, and Su’Kin has no hint of the
existence of either Kepler’s or Newton’s laws.

Bonus Points: As seen from Earth, on what actual star system do Su’Kin and her kind live?

Explanation / Answer

radius of Kp =1 auk

period of kp=100 dak

According to Kepler's law of harmonics T2/R3

=1*1/1*1*1

=1 yak

1 yak is the sidereal period of the solar system

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