What did johannes kepler contribute to the study of planets?

a - he formulated the universal law of gravitation.

b - he identified the first moon of jupiter

c - he collected detailed data that led to the proposal of the heliocentric model

d - he provided mathematical support for the heliocentric model

Kepler provided mathematical support for the heliocentric model of the solar system. (choice-D)

He showed that IF the orbit of each planet is an ellipse with the sun at one focus, and IF the line from the sun to the planet sweeps out equal areas in equal amounts of time, and IF (the orbital time-period) ² divided by (the length of the orbit's major axis) ³ is the same number for every object that orbits the sun, THEN we would see the planets doing exactly what we actually do see them doing in the sky when we watch them for a long period of time.

And as if that weren't beautiful enough, the situation became even more awesome about 100 years later, when Newton wrote his formula for universal gravity. He was able to show that IF his formula for gravity AND his three laws of motion are all correct, then objects in orbits MUST do exactly what Kepler described, and what we see them actually do.

(I used to be able to take Newton's laws of gravity and motion, and massage them and manipulate them to derive Kepler's laws of planetary motion. But that was a long time ago, and when you work as an Electrical Engineer, your employers don't ask you to do that too often.)