Solar System ModelsSolar System Models

• Geocentric – ancient people believed that the – ancient people believed that the Earth was the center of the universe, and all Earth was the center of the universe, and all planets and stars moved in orbits around Earth planets and stars moved in orbits around Earth (remember, the sun appears to rise and set (remember, the sun appears to rise and set each day when it is really the Earth spinning each day when it is really the Earth spinning that causes this)that causes this)

• Heliocentric – this is the accepted model. It – this is the accepted model. It states that the sun is the center of the solar states that the sun is the center of the solar system, and all the planets move around the system, and all the planets move around the sunsun

GEO = EARTH

HELIO = SUN

CENTRIC = CENTER

• All of the planets travel around the sun in the All of the planets travel around the sun in the same directionsame direction, but , but notnot at the same speed at the same speed

• Because of this, there may be times when Earth Because of this, there may be times when Earth passes a planet in its orbit passes a planet in its orbit

• The planet will then appear to be moving in the The planet will then appear to be moving in the opposite direction (opposite direction (backwardbackward) )

• This is called This is called retrograde motionretrograde motion – The planet is not really moving backward (think The planet is not really moving backward (think

about two cars traveling side by side…when about two cars traveling side by side…when one car speeds up, the other car may appear to one car speeds up, the other car may appear to move backward)move backward)

• CopernicusCopernicus proposed a proposed a heliocentricheliocentric model, with the Sun model, with the Sun as the center of the Solar System. His model was purely as the center of the Solar System. His model was purely geometric and it was geometric and it was notnot based on astronomical based on astronomical observations.observations.

• BraheBrahe, a believer in the Ptolemaic system, made very , a believer in the Ptolemaic system, made very accurate observations of the planetary motion, using accurate observations of the planetary motion, using only instruments with open sights (a telescope was not only instruments with open sights (a telescope was not used for astronomy until about 1609). used for astronomy until about 1609).

• KeplerKepler was at first an assistant of Brahe, but a firm was at first an assistant of Brahe, but a firm believer in the Copernican model. Brahe mistrusted believer in the Copernican model. Brahe mistrusted Kepler and kept some of his finest observations secret. Kepler and kept some of his finest observations secret. After Brahe died, Kepler apparently stole the data After Brahe died, Kepler apparently stole the data documents. Based on Brahe’s data (especially on the documents. Based on Brahe’s data (especially on the trajectory of Mars), Kepler was able to empirically trajectory of Mars), Kepler was able to empirically formulate the formulate the laws of planetary motionlaws of planetary motion. .

Nicolaus Copernicus1473-1573

Tycho Brahe1546 - 1601

Johannes Kepler1571 - 1630

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion

First Law – Elliptical OrbitsFirst Law – Elliptical Orbits

• All planets travel around the sun in an All planets travel around the sun in an elliptical orbit (LAB) with the (LAB) with the sun as one of the foci

• Because the orbits are not circular, the Because the orbits are not circular, the distance between the sun and the planet distance between the sun and the planet changeschanges

• Eccentricity is how stretched out the the planet’s orbit is (Ref. Tables, LAB) planet’s orbit is (Ref. Tables, LAB)

eccentricity = eccentricity = dist. between focidist. between foci length of major length of major

axisaxis

• When a planet is closest to the sun it is When a planet is closest to the sun it is called called perihelion, when it is farthest from the , when it is farthest from the sun it is called sun it is called aphelion

Peri = Close

Ap = Away

Helion = SUN• Earth’s perihelion is Dec. 21Earth’s perihelion is Dec. 21stst – first day of – first day of

winter, and Earth’s aphelion is June 21winter, and Earth’s aphelion is June 21stst – – first day of summerfirst day of summer

Second LawSecond Law – – Equal AreaEqual Area

• when the planets are when the planets are closest to the sun they move faster, and when they are , and when they are farthest from the sun they move slower

• Because of this, an imaginary line Because of this, an imaginary line connecting the planet and sun would connecting the planet and sun would cover an equal amount of area during cover an equal amount of area during any part of its orbit any part of its orbit

Third LawThird Law – – Harmonic LawHarmonic Law

• the the farther a planet is from the sun, the longer its period of revolution (the (the longer it takes to go around the sun – longer it takes to go around the sun – common sense)common sense)

• Kepler stated this using the formula Kepler stated this using the formula P² = D³, where P is the period of revolution , where P is the period of revolution (in Earth years) and D is the distance (in Earth years) and D is the distance from the sun (in AU’s)from the sun (in AU’s)

Astronomical Unit - the average distance Astronomical Unit - the average distance between the Earth and the Sun between the Earth and the Sun

1 AU = 93 million miles or 147 million km1 AU = 93 million miles or 147 million km

Newton’s Universal Law of Newton’s Universal Law of GravitationGravitation

• the force of gravity between any two objects the force of gravity between any two objects is directly related to the masses of the two is directly related to the masses of the two objects, but inversely related to the square objects, but inversely related to the square of the distance between the centers of the of the distance between the centers of the two objectstwo objects

Change in force = 1/distance²Change in force = 1/distance²

Simplified:Simplified:

• The The larger the objects, the greater the force of gravity between thembetween them

• Also, the Also, the greater the distance between the two objects, the less the force of gravity pulls on them pulls on them