Describe two major discoveries or contributions that Galileo made to science and the study of mechanics.

Galileo made several important discoveries and contributions to science and the study of mechanics during the Renaissance period. Two significant achievements of Galileo were his work with the telescope and his studies on the motion of objects.

Galileo is known for his significant contributions to the field of Astronomy. One of the most famous discoveries he made was by using the telescope, which he improved upon to have a stronger magnification than the ones available at that time. His observations led to several key findings: a. Moons of Jupiter: Galileo discovered four of Jupiter's moons, which are now called the Galilean moons. This observation further supported the heliocentric model of the solar system, in which planets revolve around the sun. b. Surface of the Moon: He observed that the Moon's surface was not smooth and contained mountain ranges and craters, challenging the idea of a perfect celestial sphere. c. Phases of Venus: His observations of the phases of Venus provided further evidence for the heliocentric model of the solar system.

Galileo's work on the motion of objects made significant contributions to the field of mechanics: a. Uniformly Accelerated Motion: Galileo conducted experiments with objects rolling down an inclined plane and concluded that the distance covered by an object under uniformly accelerated motion is proportional to the square of the time it takes, or s ∝ t^2. b. Free Fall: He also formulated that all objects, regardless of mass, fall at the same rate in the absence of air resistance. This statement was later proven by dropping two objects with different masses from the Leaning Tower of Pisa and observing that they hit the ground at the same time. c. Inertia: Galileo also developed the concept of inertia, which states that an object at rest tends to remain at rest, and an object in motion tends to remain in motion at a constant velocity unless acted upon by an external force. This idea laid the foundation for Newton's first law of motion. These two major contributions by Galileo had a profound impact on the field of science and the study of mechanics, helping to lay the groundwork for future discoveries and advancements in these subjects.