Advanced Physics LC1 Project Done By:- Supervised by:- Abdulrahman Hussain Mrs. Lina Marouf Rashed Hamdan Zayed Aqeel 12.05

Nicolaus Copernicus a Polish astronomer, noticed that the best available observations of the movements of planets and stars did not fully agree with the Earth-centered model. The results of his many years of work were published in 1543, when Copernicus was on his deathbed. His book showed that the motion of planets is much more easily understood by assuming that Earth and other planets revolve around the Sun.

Tycho Brahe Tycho Brahe was born in Denmark in 1546 to a noble family. He built an observatory on his island that was called Hven the island. For over 20 years, Brahe used the island as his base from which to make astronomical observations. He did not use telescopes. Instead, he used huge instruments that he designed and built in his own shop on the Danish island of Hven. He spent the next 20 years carefully recording the exact positions of the planets and stars. Brahe concluded that the Sun and the Moon orbit Earth and that all other planets orbit the Sun. Tyco Brahe hired Johannes Kepler as his assistant. In later years, Kepler would use Brahe's work as the basis for the laws of planetary movement which he developed.

Johannes Kepler Johannes Kepler was a German mathematician and astronomer who discovered that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. inherited 30 years’ worth of Brahe’s observations. He studied Brahe’s data and was convinced that geometry and mathematics could be used to explain the number, distance, and motion of the planets.

Johannes Kepler johannes Kepler, a 29-year-old German, became one of Brahe’s assistants when he moved to Prague. Brahe trained his assistants to use instruments, Upon his death in 1601, Kepler inherited 30 years’ worth of Brahe’s observations. He studied Brahe’s data and was convinced that geometry and mathematics could be used to explain the number, distance, and motion of the planets. Kepler believed that the Sun exerted a force on the planets and placed the Sun at the center of the system. After several years of careful analysis of Brahe’s data on Mars, Kepler discovered the laws that describe the motion of every planet and satellite.

Keplers 1 st law of Gravitaion Kepler’s first law of Gravitaion stated that the paths of planets are ellipses, with the sun at one "focus" of the ellipse

Keplers 2 nd law of Gravitation The radius vector from the Sun to the planet sweeps out equal areas, in equal periods of time.

Kepler's second law of Gravitation The planet moves faster near the Sun, so the same area is swept out in a given time as at larger distances, where the planet moves more slowly.

Keplers 3 rd law of Gravitational Motion The square of the orbital period is proportional to the cube of the semi-major axis.

3 rd example problem

Newton’s law of gravitation states that every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Universal Gravitation and Kepler’s Third Law Newton’s second law of motion, Fnet=ma, can be written as F net = ma c, where F Is the gravitational force, m p is the mass of the planet, and a c is the centripetal acceleration of the planet. For simplicity, assume ac=4(3.14)2r/T2. This means that F net = m p a c may now be written as F net =m p 4(3.14_2r/T2. In this equation, T is the time required for the planet to make one complete revolution about the Sun. If you set the right side of this equation equal to the right side of the law of universal gravitation

References WikipediaGoogle Physics book Glencoe