The Solar System Isaac Newton (1642) 1665-1666: new version of natural philosophy Three Laws of Motion the natural state of motion is a constant speed in a straight line (based on Galileo) an object's motion changes as a result of forces, larger force produces larger change, heavier masses are more resistant to change 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 also reproduces Kepler’s Laws Gravity is the underlying force that governs the motions in the solar system

Advances in Instruments Refracting Telescope use refraction (bending of path of light by glass) to concentrate light two lenses gives greatly magnified image improved by increasing diameter and focal length of lens (increases length of telescope)

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 clock: (1656 Huygens) pendulum regulates movement of clock mechanism allowed more precise timing of observations critical when examining motion 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) Speed of Light (Roemer 1675) 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 = 3108 m/s = 300,000 km/s

Reflectors: 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

The Discovery of New Members of the Solar System Titius-Bode "Law" 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 gap at 2.8 AU Uranus fit into sequence when discovered   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) Titius-Bode "Law"

Von Zach (~1800) calculates orbital path for hypothetical object at 2 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

position and velocity at initial time can be used to predict future Celestial Mechanics 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                 Mars 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 Jan. 30 1995 Nov. 19 1995 a = 1.523664  a = 1.523741 e = 0.093418  e = 0.093354 i = 1.8498 i = 1.8497 W = 49.522 W= 49.529 v = 336.020 v=335.948 L =119.2770 L = 307.9440