1 Tycho Brahe ( ) best observer of his day Made most accurate measurements of his time

2 Tycho’s Observatory at Uraniborg He developed new instruments and new techniques for conducting observations. Kepler used his observations to derive his laws of planetary orbits. It was the precision of Brahe's observations that enabled Kepler to determine that the orbits of the planet’s are ellipses with the Sun at one focus.

3 Johannes Kepler ( ) Developed three laws of planetary motion. Was able to describe how the planets moved.

4 First law: The orbits of the planets are ellipses.

5 Eccentricity (e) is a number between 0 and 1 that tells you how elliptical an orbit is. Some sample eccentricities: Earth’s orbit: e = (only slightly off-circular) Pluto’s orbit: e = (more elliptical) Halley’s comet: (very elliptical)

6 Kepler’s second law: Planets sweep out equal areas in equal times -means planets orbit at varying speeds, faster closer to sun, slower further from sun (Kepler didn’t know why)

7 Kepler’s Third Law: Kepler found a simple relationship between a planet’s orbital period (P) and its average distance from the Sun (A) P 2 Planet = A 3 Planet P = period of planet’s revolution in years A = average distance of planet from sun in A.U.

8 Example: Mars orbits at 1.5 A.U. (1.5) 3 = = P 2 So P = square root of (3.375) = 1.8 years Exercise: Object orbits sun at 4 A.U. How long does it take to go around?

9 note: Uranus, Neptune & Pluto were discovered much later (during s) with advent of more powerful telescopes presence predicted Solar System

10 Isaac Newton (1642 – 1727) developed laws for physical matter

11 Newton’s First Law: INERTIA A body remains at rest, or moves in a straight line at a constant speed, unless it is acted upon by a net outside force “Outside” force means a force that acts to push or pull from outside the object Person at rest Forces balanced when a car starts moving, you are pushed back in seat when car turns RIGHT, your body leans LEFT when a car stops suddenly, you are thrown forward in your seat (stopped by seatbelt) chair gravity

12 Law of INERTIA person moving at a constant speed car stops but person keeps moving

13 Newton’s Second Law: When forces act on a body, they change the (speed & direction) motion of the body: acceleration, deceleration Velocity – rate of motion (speed: 35 mph; 5 m/s) with direction Acceleration – rate of change of motion (could be speed or direction!) F = m * a Gravity causes an acceleration!

14 Newton’s Third Law For every action (force) there is an equal and opposite reaction (force)

15 Newton’s Laws explain that something must be acting on the planets to keep them in orbit According to the law of inertia planets should fly off in a straight line

16 What determines how strong the force of gravity is ? Mass of object (being acted on) Mass of object (acting on) Distance between them!

17 Newton’s Law of Universal Gravitation Two bodies attract each other with a force that is proportional to the mass of each body and inversely proportional to the square of the distance between them. Where the gravitational constant G = 6.67 · N m 2 /kg 2 and r is the distance between the objects with masses m 1 and m 2.

18 Newton’s law of gravitation for the Solar System M r m M is the mass of the Sun m is the mass of a planet (i.e., Earth) r is the distance between them Example: What if you discovered a planet TWICE as far from the Sun as the Earth – how would its gravitational pull compare to Earth’s?

19 What does it mean for an object to be in orbit?

20 Is there gravity beyond the Earth’s surface? “weightless” : not beyond influence of gravity treat astronaut as any other orbiting body Earth’s pull is what keeps astronaut in orbit feels ‘weightless’ because she and spacecraft are experiencing gravity together