Transcript Introduction - University of Toronto Scarborough

The Solar System
•
Isaac 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
• 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 (16381666)
• 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 • c = 3 108 m/s =

travel further to reach Earth as Earth
300,000 km/s
moves in orbit
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
• 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
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)
?
Titius-Bode "Law"
• 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
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
• 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
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
W = 49.522
W= 49.529
v = 336.020
v=335.948
L =119.2770
L = 307.9440