7. what did ptolemy publish as a result of his calculations, and what did his mistake cause as a result?

Geocentric Universe Model

His fundamental contribution was his model of the universe: he believed that the Earth was motionless and occupied the center of the universe, and that the Sun, the Moon, the planets and the stars revolved around him.

Explanation:

The first thing that Ptolemy does is justify a universe based on the geocentric system described by Aristotle. It is a vision of the world based on the fact that the Earth is fixed and around it the sphere of the fixed stars rotates every day, taking with it the spheres of the sun, the moon and the planets, using combinations of circular movements called epicycles. Once this model is established, Ptolemy goes on to describe the mathematics he needs in the rest of the work. In particular, it presents trigonometric methods based on the Crd (string) function (which is related to the sine function by sin a = (Crd 2a / 120)).

In examining the theory of the sun, Ptolemy compares his own observations of the equinoxes with those of Hipparchus and with the ancient observations of Meton in 432 B.C. He confirmed the duration of the tropic year as 365 days and 1/4 minus 1/300 of the day, the exact value obtained by Hipparchus. As Ptolemy knew, the accuracy of the rest of his data depended heavily on this value and the fact that the true one is 365 days and 1/4 minus 1/128 of the day, produced errors in the rest of his work