Basic Newton

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Basic Newton

G mEarth m2 F
gravity on Earth ------------
r2
What about the Moon? mEarth 5.97e24
kg Earth-Moon has FEarth 4.05e13, Sun-Moon has
FSun 8.84e13
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Dynamics Kepler I
Kepler I planetary orbits are ellipses with the
Sun at a focus

a (1 - e2)
rSun --------------
1 e cos
f e, eccentricity (1 - b2minor/a2major)1/2 f,
true anomaly angle between perihelion and
current position Newton I both bodies move
along elliptical paths, with one focus of each
ellipse located at the center of mass

m1r1 m2r2
rcm ----------------

M M m1 m2 Application discovery of
extrasolar planets
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Dynamics Kepler II
Kepler II a line between a planet and the Sun
sweeps out equal areas in equal times
dA/dt
constant
Newton II a line connecting
two bodies (or connecting one body to the center
of mass position) sweeps out equal areas in equal
times
dL/dt
0
(conservation of angular momentum) Application
spectroscopic binary orbits prediction of planet
locations
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Dynamics Kepler III
Kepler III planetary orbital periods and
distances from the Sun are directly (and simply)
related as long as you assume SS units
P2 (yr)
a3 (AU)
Newton III it also works
outside of the Solar System
4p2a3

a3 P2 (yr) ----------------
or Mtotal -------
G (m1 m2)
P2

solar masses, AU, yrs Application stellar and
planetary masses need fractional mass, f, for
individual masses double dirty little secret
of exoplanet masses
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Orbital Elements
a semimajor axis size e eccentricity shape
i inclination tilt P orbital
period time T epoch of periastron a
date O longitude of ascending node flip
angle ? longitude of
periastron t?ist angle
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Flip Longitude of Ascending Node
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T?ist Longitude of Periastron
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Orbital Elements
a semimajor axis size e eccentricity shape
i inclination tilt P orbital
period time T epoch of periastron a
date O longitude of ascending node flip
angle ? longitude of
periastron twist angle equinox equinox of
date sets direction of equinox f fractional
mass a number Two observations will not yield
an orbit. Why? Each point has (position X,
position Y, time). There are 7 classical
unknowns, so you need a third point to give you 9
pieces of data to solve equations.
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GJ 1245 AC
Pushing Towards Exoplanets
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New Orbits in Solar System
located 45 AU Psun 300
yrs HST WFPC2 images Porb 570 days sep
4000-40000 km mtot 0.02 Pluto
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Reality Check 3-body Systems
theory about 71 ratio in semimajor axis is
critical point two well-defined sets of
triples SETI sample projected separations our
Solar System is different
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Counter-Intuitive Dynamics
Lagrangian Points where objects feel no net
force in rotating frame gravitational force of
two masses cancels centrifugal force because of
rotation 5 per two body system Trojan asteroids
at Jupiter (3000), Mars (4), Neptune (6) small
moons at Sat/Tethys (TelestoCalypso) and
Sat/Dione(HelenePolydeuces) Earth orbiting
spacecraft
WMAP
SOHO
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Counter-Intuitive Dynamics
Tadpole orbits librating positions around L4 and
L5 (note corotating frame!) Trojan asteroids at
Jupiter, Mars, and Neptune
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Counter-Intuitive Dynamics
Horseshoe orbits orbit swapping due to particles
passing in orbits, or in resonance with larger
bodies (note corotating frame!) Janus and
Epimetheus (Saturn) swap orbits every 4
years Cruithne and Asteroid 2002 AA29 around
Earth
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Counter-Intuitive Dynamics
Horseshoe orbits Cruithne --- each loop takes 1
yr
http//www.astro.uwo.ca/7Ewiegert/3753/3753.html
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Counter-Intuitive Dynamics
Horseshoe orbits Asteroid 2002 AA29 --- each
vertical loop takes 1 yr
http//www.astro.uwo.ca/7Ewiegert/AA29/AA29.html
at least three others http//www.astro.uwo.ca/7
Ewiegert/3753/3753.htm
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Counter-Intuitive Dynamics
Chaotic motion trajectories that begin
arbitrarily close together will diverge
exponentially with time (note that 4.6 Gyr is
often not sufficient time) Mars axis
tilt Hyperion rotation in Saturn-Titan
tug-of-war Resonances orbital periods with
ratios A B (both integers) Io Europa
Ganymede (1 2.008 4.044) oblate?
tides? Neptune Plutinos (32) Asteroids
Jupiter (lots) --- pumped up e leads to Kirkwood
gaps Saturn ring particles Saturn moons
(Mimas, Atlas, )
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Saturns Rings
300,000 km wide X 10 m (!) thick
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Saturns Rings
300,000 km wide X 10 m (!)
thick particles forced into
plane by orbits albedo 0.8
shiny snowballs of H2O
total mass only that of small moon
young likely formed by Roche limit crossing
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Saturns Ring Structure
6 major regions 2 divisions 1000s of
ringlets ABC rings seen from ground major DEF
rings seen from Voyager/Cassini
minor Cassini Division Mimas 21 resonance A
ring Atlas on edge (in 32 with Mimas) Encke
Gap Pan within A ring F ring (braided) shepherds
Prometheus Pandora E ring Enceladus
volcanism (outside Roche) spokes collisions in
rings
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Saturns Rings Details
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Jupiters Rings
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Jupiters Rings Details
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Jupiters Rings Details
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