MOTION IN THE SKY and MODELS OF THE UNIVERSE_WEEK 1.pptx

lecture

1. PHYSICAL SCIENCE PHYSICS – FOURTH QUARTER

2. LESSON 1: MOTIONS IN THE SKY

3. Celestial Sphere – an imaginary hollow sphere that encloses the Earth, where the stars, the sun and other heavenly bodies are embedded. The points where Earth’s rotational axis cuts this sphere is called NCP (North Celestial Pole) and SCP (South Celestial Pole). The Celestial Equator – projection of the Earth’s equator in the celestial sphere.

4. Diurnal Motion – It is t he apparent daily motion of stars and other celestial bodies across the sky caused by the Earth’s rotation about its axis. – Responsible for the daily rising and setting of the sun.

5. Annual Motion – the apparent motion of the sun caused by Earth’s revolution around it. It accounts for the visibility of the zodiac constellations at a specific time of the year. It is responsible for the seasons.

6. Ecliptic - the path that the sun appears to take around the celestial sphere. It is inclined 23.5 degrees with respect to the celestial equator.

7. Ecliptic - the path that the sun appears to take around the celestial sphere. It is inclined 23.5 degrees with respect to the celestial equator.

8. Ecliptic Precession – change in the orientation of the rotational axis of any rotating body. Earth requires 26 000 years to complete one cycle of precession. (50.2seconds/year) Hipparchus of Nicaea – was credited on the discovery of the precession of the equinoxes. Lunisolar Precession - Earth’s precession due to the gravitational pull of the moon and the sun.

9. Solstices – the two points on the ecliptic with the greatest distance from the celestial equator. Summer Solstice – point where the sun is at its northernmost position above the celestial equator. It happens every June 21. Winter Solstice - point where the sun is at its southernmost position at the celestial equator. It happens every December 21. Equinoxes – the two points where the ecliptic intersects the celestial equator. Earth’s rotational axis is perpendicular to the line joining the Earth and the sun. Day and night are equal. Autumnal Equinox – happens every September 22. Vernal Equinox – happens every March 21. Constellations- a series of star clusters where the ecliptic crosses. Zodiac – sequence of constellation

10. Proposal that Earth is Spherical It was Pythagoras and his pupils who were first to propose a spherical Earth. Anaxagoras further supported Pythagoras' proposal through his observations of the shadows that the Earth cast on the Moon during a lunar eclipse. He observed that during a lunar eclipse, the Earth's shadow was reflected on the Moon's surface. The shadow reflected was  circular .

11. Proposal that Earth is Spherical Aristotle listed several arguments for a spherical Earth which included the positions of the North star, the shape of the Moon and the Sun, and the disappearance of the ships when they sail over the horizon.

12. LESSON 2 : MODELS OF THE UNIVERSE

13. 3000 years ago - Egyptians Some 3000 years ago, the Egyptians established a 365-day calendar based on the tracks of the star SIRIUS. The pyramids of Giza in Egypt were constructed in such a way that each side faced north, south, east or west of a compass within a tenth of degree. The three pyramids represent the belt of stars of the Constellation Orion.

14. Early Universe At 600 BCE, Thales of Miletus proposed that Earth is a disk floating on water.

15. Early Universe At 520 BCE, Anaximander of Miletus, proposed that Earth is a cylinder and that its surface is curved.

16. Several Models were suggested which can be grouped into two: GEOCENTRIC and HELIOCENTRIC.

17. GEOCENTRIC MODELS A. THE PYTHAGOREAN MODEL Proposed by Pythagoras . First to assert that Earth is round and that the heavenly bodies move in circles. In this model, Earth is at rest at the center of the universe, and everything rotates around it.

18. GEOCENTRIC MODELS PLATO’S SAVING THE APPEARANCES Plato assumed that all motions in the universe are perfectly circular and that all heavenly bodies are ethereal or perfect.

19. GEOCENTRIC MODELS Retrograde Motion - the apparent motion of a planet in a direction opposite to that of other bodies within its system, as observed from a particular vantage point. Direct motion or prograde motion is motion in the same direction as other bodies

20. GEOCENTRIC MODELS B. EUDOXUS’ MODEL First use Plato’s Saving the Appearances using a 27 series of concentric spheres on which the sun, the moon and the planets moved in perfect circular motion. 1 sphere – fixed stars 3 spheres – moon 4 spheres – each for every five known planet (Jupiter, Mercury, Venus, Mars and Saturn)

21. GEOCENTRIC MODELS ARISTOTLE’S MODEL Also used 27 celestial spheres of Eudoxus . He added: 27 “buffering” spheres between celestial spheres and an outermost sphere that was the domain of what called the Prime Mover. The Prime Mover causes the other spheres to rotate. The prime mover was considered God, and the sphere of the firmament as heaven. There are two realms – terrestrial and celestial with the orbit of the moon as the boundary. Below the moon’s orbit is the terrestrial realm. The realm was composed of four primordial elements in the sequence: earth, water, air and fire. The celestial realm consists of the fifth element called ether. Earth is sphere.

22. GEOCENTRIC MODELS PTOLEMY’S MODEL Epicycle – a circle on which a planet moves. The center of this small circle in turns moves around the Earth along a bigger circular path called deferent. Hipparchus refined this model by considering that the Earth was off center or eccentric in the deferent where the sun moved. In 140 AD, he defined a point on the other side of the deferent’s center and called it the equant. The circumference of the Earth is 25000 miles. Eratosthenes measured it in 253 BCE using trigonometry and the knowledge of elevation of the sun at noon in Alexandria and Syene

23. HELIOCENTRIC MODELS COPERNICUS’S MODEL Nicolaus Copernicus asserted that Earth spins on its axis every day and revolves around the sun just like the other planets; only the moon orbits the Earth. Uniformed circular motion and Ptolemy’s Epicycles FLAWS: 1. Absence of Stellar Parallax 2. Lack of perceived motion of Earth Stellar Parallax – the apparent displacement of a star because of a change in the observer’s point of view. It is contained in Copernicus’s Book: Revolutionibus Orbium Coelestium (On the Revolution of Celestial Orbs

24. Tycho Brahe He measured and recorded the positions of the sun, moon and the planets for 20 years. His data did not fit models of Ptolemy and Copernicus. He proposed that the sun orbited the Earth, but the other planets revolved around the Sun.

25. GALILEO’S ASTRONOMICAL DISCOVERIES: Four major moons of Jupiter The phases of Venus The changes in apparent sizes of Venus and Mars The mountains of the moon. Sunspots The small apparent sizes of the stars

26. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW OF ELLIPSES Planets move around the Sun in ellipses, with the Sun at one focus LAW OF EQUAL AREAS The line connecting the Sun to a planet sweeps equal areas in equal times. LAW OF HARMONIES The square of the orbital period of a planet is proportional to the cube of the mean distance from the Sun.

27. LAW OF EQUAL AREAS The line connecting the Sun to a planet sweeps equal areas in equal times.

28. LAW OF HARMONIES The square of the orbital period of a planet is proportional to the cube of the mean distance from the Sun.

29. Problem 1: The average distance of Mercury to Sun is 0.387AU. If the eccentricity is 0.206, what is its semi-minor axis?

30. Problem 2: The average distance of Mercury to Sun is 0.387AU. If the eccentricity is 0.206. What is its perihelion and aphelion distances?

31. TO DO: DRAW THE ELLIPTICAL ORBITS OF THE MERCURY AND VENUS Use the data table shown earlier. Compute the eccentricities and aphelion and perihelion distances of the two planets using the equations given. Plot the position of the Sun in your sketches. DATA: 1 AU = 10cm MERCURY = 0.38700 AU (Semi-Major), 0.37870 AU (Semi-Minor) VENUS = 0. 723 AU (Semi-Major), 0.72298 AU (Semi-Minor)

32. TO DO: PROVE KEPLER’S LAW OF HARMONIES GRAPH THE CUBES OF THE SEMI MAJOR AXES OF PLANETS (AU) IN THE Y-AXIS VS THE SQUARES OF THEIR ORBITAL PERIODS (YEARS) IN THE X-AXIS.

33. Problem 1: The orbital period of Mars is 1.881 years. Its average distance to the Sun is 1.524 AU. If Saturn’s average distance to the Sun is 9.58 AU, (a) how long does it take for Saturn to orbit the Sun (in years); (b) What are the perihelion and aphelion distances of Saturn and Mars; (c) What is the eccentricity of Saturn and Mars if their semi-minor axes are 9.567and 1.5174 AU respectively?

34. Problem 2: The aphelion radius of Venus is 0.728 AU, and its perihelion radius is 0.718 AU. Considering it is on a leap year, it takes 225 days for Venus to complete its revolution around the Sun. If the average distance of Jupiter to Sun is 5.203 AU, how long does it take for Jupiter to orbit the Sun (in years)?