Early Theories. Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle

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1 Planetary Motion

3 Early Theories Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle

4 Stars appear to move around Earth

7 Observations showed that some planets like Mars appeared to go backwards at some times in their orbits (retrograde motion) To fix this problem, Ptolemy proposed the planets revolved on circles attached to the crystal spheres

8 Retrograde motion of Mars

9 Retrograde motion of Venus over a 44 day period

10 Mars moving around Earth on an epicycle

11 Sun-Centered Theory Copernicus developed the sun-centered model to predict the motion of the planets without using epicycles Planets orbited the sun in perfect circles with the stars furthest away

12 Heliocentric model

13 Earth and Moon seen from Messenger probe in orbit around Mercury

14 Mercury crossing in front of the Sun Mercury

15 Tycho Brahe made very careful measurements of planetary motion which were used to reform the calendar (from Julius Caesar s to the modern one) discovered a comet that was shown to be very far away, and not in the atmosphere where Aristotle said it would be

16 Galileo Galileo discovered 4 moons of Jupiter, mountains on the moon and sun spots which could not be explained by Aristotle s model Galileo was a strong supporter of the Copernican system and was punished for it

17 Jupiter with 4 moons discovered by Galileo

19 He discovered Venus had phases like the Moon which meant Venus went around the sun

20 Galileo discovered that the Sun had sunspots and that the sunspots moved across the surface This meant the sun wasn t perfect and that it rotated like the Earth

21 Galileo was the first person to see the rings of Saturn

23 Johannes Kepler used Brahe s observations to mathematically describe the motion of the planets He determine that all orbiting objects obeyed 3 basic laws

24 Kepler s 1 st Law Planets travel in ellipses with the sun at a special point called the focus The other focus is empty

25 the orbits of many planets are almost circles, we will assume circular orbits

26 Jupiter s Moons

27 Earth s Orbit is NOT quite circular January July Sun appears larger in January because Earth is a little closer

28 The positions of the Sun at the 2010 solstice dates are at the upper (June 21) and lower (December 21) extremes of the analemma curve. On the equinox dates (March 20, September 23) the Sun was along the curve half way between the solstices. The tilt of planet Earth's axis and the variation in speed as it moves around its elliptical orbit combine to produce the curve

30 Halley s Comet

31 2 nd Law The planet will sweep out equal areas in equal times This means the planet will move faster when it is closer to the sun

33 3 rd Law The further away from the sun, the slower the planet moves the cube of the average distance from the sun to a planet is proportional to the square of the orbital period T r 2 3 constant

34 T is the period of the orbit r is the radius of the orbit (NOT the radius of the planet)

35 Example Determine Kepler s constant for the Sun using Earth and Jupiter data. Earth T = 3.16 x 10 7 s r = 1.49 x m Jupiter T = 3.75 x 10 8 s r = 7.75 x m

36 Solution T Earth x10 r x 10 m 7 s 2 3 K = 3.02 x s 2 /m 3 K = 3.02 x s 2 /m 3 sun for Earth orbiting the sun for Jupiter orbiting the

37 the constant will be the same for every object orbiting the same focus T 2 r 3 for one object T 2 r 3 for another object

38 for elliptical orbits, the average distance is the semi-major axis

41 Example Calculate the period of revolution for the planet Mercury (orbital radius = 5.79 x m) using the data for Earth (orbital radius of 1.49 x m).

42 Solution 2 T 2 T Earth Mercury r 3 r 3 Earth Mercury 1 year 2 T x m. x m T 2 = year 2 T = year (less than 3 months) 3

43 the average distance of Earth to the sun is called an astronomical unit (symbol is AU) any combination of units can be used for Kepler s Third Law if the units on the left are the same as the units on the right

44 Example The asteroid Ceres has a period of 4.60 years. Determine the orbital radius of Ceres in AU. 2 T Earth 3 r Earth 2 T Ceres 3 r Ceres

45 T 2 R 3 R 3 of Ceres Ceres Earth T 2 Earth years 1 AU R Ceres years R AU3 Ceres R Ceres AU 3 T R R 3 of Ceres Ceres T 2 Earth 3 R Ceres years years R AU3 Ceres R Ceres R Ceres AU AU

47 What s a Planet? According to the International Astronomical Union, which sets definitions for planetary science, a planet is a celestial body that: Orbits the sun. Has enough mass to assume a nearly round shape. (due to gravity) Has cleared the neighborhood around its orbit.

48 Dwarf Planets Ceres, Pluto, Eris

49 Recently discovered Makemake is one of the largest objects known in the Kuiper Belt orbits the Sun only slightly further out than Pluto

50 Discovery images of Orcus. Credit: Vrown, Rabinowitz, and Trujillo

51 Practice P 275: 1, 2, 3 See table on p 274

History of Astronomy. PHYS 1411 Introduction to Astronomy. Tycho Brahe and Exploding Stars. Tycho Brahe ( ) Chapter 4. Renaissance Period

History of Astronomy. PHYS 1411 Introduction to Astronomy. Tycho Brahe and Exploding Stars. Tycho Brahe ( ) Chapter 4. Renaissance Period PHYS 1411 Introduction to Astronomy History of Astronomy Chapter 4 Renaissance Period Copernicus new (and correct) explanation for retrograde motion of the planets Copernicus new (and correct) explanation