Describe how Newton used each of the following phenomena to support the law of universal gravitation
a) the orbit of the moon
b) kepler's third law
http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html
a) The orbit of the moon:
Newton used the orbit of the moon as evidence to support his law of universal gravitation. He observed that the moon orbits around the Earth in a nearly circular path, always staying a fixed distance away. Newton observed that the moon's motion could be explained by the force of gravity between the Earth and the moon.
To understand how Newton used this phenomenon to support his law, we need to know about Kepler's laws of planetary motion. Kepler's first law states that the planets move around the sun in elliptical orbits, with the sun at one of the foci of the ellipse. Kepler's second law states that a line segment connecting a planet to the sun sweeps out equal areas in equal intervals of time. Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of its average distance from the sun.
Newton used these laws to explain the motion of celestial bodies, including the moon. He realized that the force of gravity between the Earth and the moon acts as a centripetal force, constantly pulling the moon towards the Earth. This force is responsible for keeping the moon in its orbit.
By combining Kepler's laws with his law of universal gravitation, Newton was able to show that the moon's orbit is the result of the gravitational attraction between the Earth and the moon. This provided strong evidence in support of his law of universal gravitation.
b) Kepler's third law:
Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of its average distance from the sun. Newton used this law to support his own law of universal gravitation.
To understand how Newton used Kepler's third law, we need to know that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This relationship is given by Newton's law of universal gravitation.
By combining Kepler's third law with his own law of universal gravitation, Newton was able to derive a mathematical relationship between the mass and distance of celestial bodies. He found that the gravitational force between two objects affects not only their motion but also their orbits.
Newton used Kepler's third law to explain why different planets have different orbital periods and distances from the sun. He showed that the force of gravity determines the shape and size of planetary orbits. By applying his law of universal gravitation to Kepler's third law, Newton was able to provide a comprehensive explanation for the motion of celestial bodies and further support his own theory.