This document summarizes models of the solar system from ancient to modern times. It describes the geocentric model where Earth is the center, then introduces the heliocentric model where the Sun is at the center accepted today. Kepler analyzed Brahe's planetary observation data to formulate his three laws of planetary motion: 1) Elliptical orbits with Sun at one focus, 2) Equal area swept in equal time, 3) Period squared is proportional to semi-major axis cubed. Newton later generalized gravity with his law of universal gravitation.

1. Astronomy Intro to

2. Solar System Models Geocentric – ancient people believed that the Earth was the center of the universe, and all planets and stars moved in orbits around Earth (remember, the sun appears to rise and set each day when it is really the Earth spinning that causes this) Heliocentric – this is the accepted model. It states that the sun is the center of the solar system, and all the planets move around the sun

3. GEO = EARTH HELIO = SUN CENTRIC = CENTER

4. All of the planets travel around the sun in the same direction , but not at the same speed Because of this, there may be times when Earth passes a planet in its orbit The planet will then appear to be moving in the opposite direction ( backward ) This is called retrograde motion The planet is not really moving backward (think about two cars traveling side by side…when one car speeds up, the other car may appear to move backward)

6. Copernicus proposed a heliocentric model, with the Sun as the center of the Solar System. His model was purely geometric and it was not based on astronomical observations. Brahe , a believer in the Ptolemaic system, made very accurate observations of the planetary motion, using only instruments with open sights (a telescope was not used for astronomy until about 1609). Kepler was at first an assistant of Brahe, but a firm believer in the Copernican model. Brahe mistrusted Kepler and kept some of his finest observations secret. After Brahe died, Kepler apparently stole the data documents. Based on Brahe’s data (especially on the trajectory of Mars), Kepler was able to empirically formulate the laws of planetary motion .

7. Nicolaus Copernicus 1473-1573 Tycho Brahe 1546 - 1601 Johannes Kepler 1571 - 1630

8. Kepler’s Laws of Planetary Motion

9. First Law – Elliptical Orbits All planets travel around the sun in an elliptical orbit (LAB) with the sun as one of the foci Because the orbits are not circular, the distance between the sun and the planet changes Eccentricity is how stretched out the planet’s orbit is (Ref. Tables, LAB)

10. eccentricity = dist. between foci length of major axis

14. When a planet is closest to the sun it is called perihelion , when it is farthest from the sun it is called aphelion Peri = Close Ap = Away Helion = SUN Earth’s perihelion is Dec. 21 st – first day of winter, and Earth’s aphelion is June 21 st – first day of summer

16. Second Law – Equal Area when the planets are closest to the sun they move faster , and when they are farthest from the sun they move slower Because of this, an imaginary line connecting the planet and sun would cover an equal amount of area during any part of its orbit

19. Third Law – Harmonic Law the farther a planet is from the sun, the longer its period of revolution (the longer it takes to go around the sun – common sense) Kepler stated this using the formula P² = D³ , where P is the period of revolution (in Earth years) and D is the distance from the sun (in AU’s)

20. Astronomical Unit - the average distance between the Earth and the Sun 1 AU = 93 million miles or 147 million km

23. Newton’s Universal Law of Gravitation the force of gravity between any two objects is directly related to the masses of the two objects, but inversely related to the square of the distance between the centers of the two objects Change in force = 1/distance²

24. Simplified: The larger the objects, the greater the force of gravity between them Also, the greater the distance between the two objects, the less the force of gravity pulls on them