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Galileo worked on an incline to use a component of gravity. In
this way his timing could be more accurate. For an incline, the
component of gravity acting down the incline was equal to "g
sine (theta)" where theta was the angle of incline. He found the
distance covered was always proportionate to the square of
time.

The Three Laws of Kepler focused attention on the ability to
use mathematics to establish scientific theory. Newton
used these laws to step forward with his own theory of
gravitation.

LAW I--THE ORBIT OF EACH PLANET ABOUT THE SUN IS AN ELLIPSE WITH THE SUN AT THE FOCUS OF THE ELLIPSE LAW I--THE ORBIT OF EACH PLANET ABOUT THE SUN IS AN ELLIPSE WITH THE SUN AT THE FOCUS OF THE ELLIPSE. (A CIRCLE IS A SPECIAL CASE ELLIPSE)

LAW 2- THE LINE JOINING THE SUN AND THE PLANET (THE RADIUS VECTOR) SWEEPS OVER EQUAL AREAS IN EQUAL TIMES AS THE PLANET TRAVELS AROUND THE ORBIT.

LAW 3-- THE SQUARE OF THE PERIOD OF REVOLUTION (TIME FOR ONE COMPLETE ORBIT) IS PROPORTIONAL TO THE CUBE OF THE AVERAGE DISTANCE OF THE PLANET FROM THE SUN.

NEWTON'S UNIVERSAL LAW OF GRAVITATION
ESTABLISHED THE NEED FOR VECTOR
MATHEMATICS. VECTORS REQUIRE BOTH
DIRECTION AND MAGNITUDE AND FORCE IS
SUCH A QUANTITY. NEWTON WAS AWARE OF
THE NEED FOR VECTORS AND INTRODUCED
THEM INTO HIS WORK. HE ENVISIONED EACH
MASS AS CREATING A VECTOR FIELD OF
GRAVITATIONAL FORCE. THIS FIELD POINTED
TOWARD THE MASS AND THE LENGTH OF EACH
VECTOR WAS RELATED TO DISTANCE BY AN
INVERSE SQUARE FACTOR.

FORCES OCCUR IN PAIRS AS STATED BY NEWTON IN
HIS THIRD LAW--"FOR EVERY ACTION FORCE THERE IS
AN EQUAL BUT OPPOSITE REACTION FORCE". THE
EARTH PULLS ON THE MOON BUT THE MOON ALSO
PULLS ON THE EARTH WITH AN EQUAL FORCE.