Newton, Einstein and Gravity 1642 - 1727 Figure 05.1A

Kepler, Newton, Galileo Kepler discovered three laws of planetary motion. Newton refined Kepler's model using his Law of Gravity. Galileo systematically studied falling objects. Galileo helped establish the Law of Inertia.

Newton's First Law Isaac Newton began with Galileo's ideas about inertia and developed Laws of Motion. The first law is directly from Galileo's work and is Newton's Law of Inertia. If an object is moving, it will continue to do so. If an object is at rest, it will remain so. Figure 05.5A

F=ma Newton's Second Law In order to change what an object is doing, a force must be applied. The more mass an object has the bigger the force needed to change its condition. A small force will accelerate it slowly while a large force will accelerate it quickly. This is Newton's Second Law of Motion. F=ma Figure 05.5B

Newton's Third Law All forces occur in pairs. If you push on something, it will push back with an equal and opposite force. As you sit on a chair, you do not accelerate (crash) to the floor because the chair is pushing back on you. This is Newton's Third Law. Figure 05.5C

F = GMm/r2 Inverse Square Law Newton continued work on gravity. He discovered that gravity behaves according to the inverse square law. Newton used the orbiting moon to determine if his idea was valid. F = GMm/r2

Newton’s laws of gravity F = m1a F = (Gm1 m2)/d2 m1a = (Gm1 m2)/d2 a = (G m2)/d2 Where a = g so g = (G m2)/d2

Newton's Laws Newton's laws could be used to determine orbits. There is a critical velocity in order for an object to fall around a planet. An orbit is actually a fall in which the object misses the planet. V=the square root of GM/r

Escape Velocity To escape the influence of a planet's gravity, you must go faster. This is called the escape velocity. Ve = the square root of 2GM/r Newton's ideas about orbits helped explain how planets obey Kepler's Laws of Planetary Motion.

Escape velocity KE = PE 1/2muv2esc = Gmume/r Vescape = √(2Gme /r)

Escaping the Earth me = 6 x 1024 kg re=6.4 x 106m Vescape = Vescape = √(2Gme /r) Vescape = √[2(6.67x10-11)( 6 x1024) / 6.4 x 106] = 11 183 m/s = 11.2 km/s

Escaping the sun Ms = 2 x 1030 kg rs=7 x 108m Vescape = √[2(6.67x10-11)( 2 x 1030) / 7 x 108m] = 6.2 x 105 m/s = 2 200 000 km/h

Conservation of Angular Momentum A skater's speed increases as she pulls in her arms. This is due to a conservation of angular momentum. A planet orbiting the sun also conserves its angular momentum. This explains Kepler's second Law of Planetary Motion.

Elliptical Orbits Kepler's First Law is explained by Newton's Law of Gravity. Newton showed that an object in orbit, under an inverse square law, will orbit as an ellipse. Newton's laws fixes the amount of energy an object has due to its position and speed around the sun. This helps explain Kepler's Third Law.

Gravitational Astronomy Newton's ideas of motion and gravity established gravitational astronomy. The underlying reason for planetary motion was understood. Newton's work was published in his Mathematical Principles of Natural Philosophy known as the Principia.

That’s all folks