G RAVITATION · Part 2

gravitational constant . Acceleration due to gravity of the earth . Acceleration due to gravity below and above the surface of earth . Gravitational potential energy . Escape speed . Earth satellites . Energy of an orbiting satellite Summary Points to ponder Exercises B A C P S S ' b a proposed a definitive model in which the planets moved in circles around a fixed central sun. His theory was discredited by the church, but notable amongst its supporters was Galileo who had to face prosecution from the state for his beliefs. It was around the same time as Galileo, a nobleman called Tycho Brahe ( - ) hailing from Denmark, spent his entire lifetime recording observations of the planets with the naked eye. His compiled data were analysed later by his assistant Johannes Kepler ( - ). He could extract from the data three elegant laws that now go by the name of Kepler’s laws. These laws were known to Newton and enabled him to make a great scientific leap in proposing his universal law of gravitation. . KEPLER’S LAWS The three laws of Kepler can be stated as follows: . Law of orbits : All planets move in elliptical orbits with the Sun situated at one of the foci Fig. . (a) An ellipse traced out by a planet around the sun. The closest point is P and the farthest point is A, P is called the perihelion and A the aphelion. The semimajor axis is half the distance AP. Fig. . (b) Drawing an ellipse. A string has its ends fixed at F and F . The tip of a pencil holds the string taut and is moved around. of the ellipse (Fig. .1a). This law was a deviation from the Copernican model which allowed only circular orbits. The ellipse, of which the circle is a special case, is a closed curve which can be drawn very simply as follows. Select two points F and F . Take a length of a string and fix its ends at F and F by