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