Introduction - University of Toronto Scarborough

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```					                    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
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

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
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       0.39     0.72    1.00    1.52          5.20     9.54       19.2       30.1
Size(AU)
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
Mars
• orbital elements change over time due to
Jan. 30 1995     Nov. 19 1995
gravitational influences of other planets and
a = 1.523664     a = 1.523741
shapes of planets
e = 0.093418     e = 0.093354
• osculating orbit: the elements of the           i = 1.8498       i = 1.8497
ellipse that best describes orbit at given time   W = 49.522       W= 49.529

v = 336.020      v=335.948
• Kepler's Laws are approximations
L =119.2770      L = 307.9440

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