The Solar SystemIsaac Newton (1642)

• 1665-1666: new version of natural philosophy

Three Laws of Motion 1. the natural state of motion is a constant speed in a

straight line (based on Galileo)2. an object's motion changes as a result of forces,

larger force produces larger change, heavier masses are more resistant to change

3. objects' interactions are mutual (action/reaction) (based on Descartes)

• developed Calculus to apply the laws• allows prediction of motion, given forces• allows prediction of forces, given motion

• deduced inverse-square nature of gravitational attraction from Kepler’s laws (for circular orbits)

• Hooke (1674): asks Newton to consider motion under influence of inverse-square force • Newton finds orbits would be elliptical

• Edmond Halley (1684) asks Newton same question • urges Newton to publish his ideas on forces and motion

Philosophia Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy - 1687)• Law of Universal Gravitation: any two bodies will attract each other with a force that depends on the masses of the objects and the distance separating them. (inverse-square law)

• inverse-square law leads to elliptical orbits

Gravity is the underlying force that governs the motions in the solar system

• also reproduces Kepler’s Laws

Advances in InstrumentsRefracting Telescope

• use refraction (bending of path of light by glass) to concentrate light

• improved by increasing diameter and focal length of lens (increases length of telescope)

• two lenses gives greatly magnified image

17th century – Solar system observations

• Huygens: (1656) resolves rings around Saturn, moon of Saturn

• Cassini:  rotation of Jupiter (1663), rotation of Mars, moons of Saturn

Micrometer: adjustable scale and pointer attached to telescope (1638-1666)

• allows accurate measurement of position within telescope field of view

• pendulum regulates movement of clock mechanism

• allowed more precise timing of observations

• critical when examining motion

Pendulum clock: (1656 Huygens)

Size of Solar System• Cassini and Richer  (1670's) • based on observations of position of Mars

• observations made at same time from different places • once distance to Mars known, other distances follow

Earth-Sun distance = 150 million km = 1 Astronomical Unit (AU)

Sizes of Planets• determined from known distances and apparent size (from micrometer)

• eclipses of Jupiter's moons occur slightly later than expected when Earth moving away from Jupiter, slightly earlier when Earth moving towards Jupiter

• changes are a result of light having to travel further to reach Earth as Earth moves in orbit

• c = 3108 m/s = 300,000 km/s

Speed of Light (Roemer 1675)

• light is concentrated using reflection from curved mirror (1668, Newton)

• improved by making mirror larger, smoother

• became more popular towards end of 1600's due to lighter weight and high magnification

Equatorial mount: • one axis is parallel to Earth's axis • telescope only has to rotate around one axis to compensate for Earth's rotation • much more stable

Reflectors:

  0 3 6 12 24 48 96 (192) (384)

  4 7 10 16 28 52 100 196 388

Prediction 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8

Orbit Size(AU)

0.39 0.72 1.00 1.52   5.20 9.54 19.2 30.1

  Mercury Venus Earth Mars  ? Jupiter Saturn (Uranus) (Neptune)

The Discovery of New Members of the Solar System• William Herschel discovers Uranus, 1781

The Asteroids

• 1766 - Titius Law : radii of planets' orbits (up to Saturn) described by numerical sequence

Titius-Bode "Law"

• gap at 2.8 AU

• Uranus fit into sequence when discovered

• Von Zach (~1800) calculates orbital path for hypothetical object at 2.8 AU, initiates search 

• Piazzi (Jan 1, 1801) notes movement of 8th mag. object in Taurus

• observes until Feb. 11 - motion appears more planetary than cometary

• notifies Bode in Germany (March 20 1801), object no longer visible

• orbital calculations too primitive - object lost

• Gauss develops method for finding orbits on basis of 3 observations, applies to Piazzi's data and produces ephemeris

• Von Zach uses ephemeris to re-locate object (Dec 31 1801)

• Piazzi names object (planet) "Ceres"

• location at 2.77 AU reinforces Titius-Bode Law

• Herschel determines size of Ceres ~260 km  (modern value ~1000 km)

• "asteroid"  (star-like in appearance - much smaller than planet)

• Olbers discovers another object in similar orbit - 2.67 AU (Pallas)

• Juno (1804) and Vesta (1807) in similar orbits

• many smaller ones discovered through 19th and 20th cent.

• Asteroid belt: large pieces of rock (10 - 100 km diameter) orbiting between 2.2 and 3.3 AU

• left over material from formation of solar system

                Mars

Jan. 30 1995 Nov. 19 1995

a = 1.523664  a = 1.523741

e = 0.093418  e = 0.093354

i = 1.8498 i = 1.8497

= 49.522 = 49.529

= 336.020 =335.948

L =119.2770 L = 307.9440

• can predict motion of planets, comets, asteroids etc. using Newton's Laws of Motion and Law of Universal Gravitation

• position and velocity at initial time can be used to predict future

• need 6 pieces of data + knowledge of forces

• 3 observations of location in sky (R.A. and dec.)

• data transformed into 6 orbital elements

Celestial Mechanics

• orbital elements change over time due to gravitational influences of other planets and shapes of planets

• osculating orbit: the elements of the ellipse that best describes orbit at given time

• Kepler's Laws are approximations