Respond to the following based on your reading (write your answers using 1–2 paragraphs). 1. Describe the universal gravitational law. 2. Evaluate the techniques and models used by Ptolemy and Copernicus to explain the setup of the universe. 3. A child picks up a tennis ball tied to the end of a rope. He swings the rope around, over his head, in a circle. Once the ball is spinning, he lets go of the string and the ball goes flying. Explain which of the following images correctly shows which way the ball will fly and why. Two images of figures throwing a ball and their potential trajectory 1. Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. 2. Ptolemy believed in the theory that the earth was the center of the universe (geocentric) and it is not moving in the center while Copernicus later proposed otherwise, in his heliocentric theory he believed that the sun was the center of the universe but it was not moving. Both theories were influenced by their observation of how the light shade from the sun changes during the day, and also through observation of other celestial bodies whose light intensity changes which made them arrived to the conclusion that they are not equidistant nor stationary with respect to earth. 3. Plan A Explanation: Acceleration in a circle is toward the center of the circle, while velocity is always a straight line that's tangent to the circle. When the boy let's go of the rope the Acceleration toward the center of the circle disappears. The v ball then follows the straight path, tangent to the circle.

Explanation:

1. Discovered by Sir Isaac Newton, this law states that every object in the universe that has mass attracts every other object in the universe that has mass. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. When applying this to a situation with two objects, the object with the smaller mass will do most of the moving because the other object has too much inertia to move any noticeable amount.

2. Without advanced technology like we have today, Ptolemy and Copernicus tried to best explain the model of the universe through observation. Ptolemy’s model came first and placed a stationary earth at the center of the model. Everything else moved in respect to earth. This was widely accepted since it seemed like earth wasn’t moving. Ptolemy stated that the planetary bodies moved around earth in circular paths. However, this wasn’t always witnessed through observation. He adjusted his model to state that some planets must be moving in secondary orbits.

Copernicus put a rotating earth in a sun-centered model. The rotation of earth was able to account for the rising and setting of stars. The orbital motion of the earth and moon also accounted for the motion of the sun and moon with respect to the stars. This was easier to understand but encountered scrutiny due to its differences from religious teachings.

One big difference between the approaches in the two is that Copernicus didn’t try to adjust his model to match what was going on; he used observations to develop the model. In addition, one common trend in science is that the simplest explanation is usually most accurate or closer to accurate. Copernicus’ model was more straightforward; Ptolemy’s was more complex.

3. Acceleration in a circle is toward the center of the circle, while velocity is always a straight line that's tangent to the circle. Thus, when the boy lets go of the rope, the centripetal force (acceleration) toward the center of the circle disappears. The ball then follows the straight path, tangent to the circle, and follows Path A.