Planetary Motion by Nick D

1
Planetary Motionby Nick DAnnaEarth Science
TeacherPlainedge Middle School
2
Planet Names

• Tuesday ? Martedì (Italian) ? Mars day
• Wednesday ? Mercoledì (Italian) ? Mercurys day
• Thursday ? Giovedì (Italian) ? Jupiters day
• Friday ? Venerdì (Italian) ? Venus day
• Saturday ? Saturns day
• Sunday ? Suns day (not a planet but still
  important)
• Monday ? Lunedì (Italian) ? Moons day (also not
  planet, but also important because it moves
  differently than the other things in the sky.

3
The Greeks believed that the planets traveled in
circular paths.
Since the acceleration (force of gravity) is
perpendicular to the velocity of the body, the
torque on the body is zero. Thus, the velocity
of the body remains constant.
4
However, the planets did not move with constant
speed.
Planet comes from the Greek word Planetes
WANDERER
5
The planets move differently than all the other
celestial objects.
6
Retrograde motion explained by Hipparchos
Ptolemy

• Ptolemy believed in a Geocentric (Earth Centered)
  model of the Solar System
• Ptolemy explained retrograde motion with
  DEFERENTS EPICYCLES.
• The math involved for Ptolemys model with
  epicycles became extraordinarily complicated.

7
Copernicus the Heliocentric model
(Sun-centered) Solar System
Copernicus was able to explain the retrograde
motion of the planets just as well as Ptolemy.
However, Copernicus model still had its
problems.
Copernicus used perfect circular motion, unlike
Ptolemy, who had the Earth offset as an equant
(not centered in circular orbits
8
Ockhams Razor

• Cited from http//sbast3.ess.sunysb.edu/fwalter/AS
  T101/occam.html The most useful statement of the
  principle for scientists is "when you have two
  competing theories which make exactly the same
  predictions, the one that is simpler is the
  better.
• The Copernican system was more elegant and
  more aesthetic than Ptolemys system. Hence, it
  had favor.

9
Johannes Kepler (1571 1630)

• Believed the Universe was driven by mathematical
  principals
• There must be a force, propelling planets to
  move. The force was something like magnetism
  between the Sun and the planets.
• Devised Three Laws of Planetary Motion

10
Keplers Laws

• Law of Ellipses (1609)
• Law of Equal Areas (1609)
• Harmonic Law (1618)

11
Keplers First Law
An ellipse is a geometric shape somewhere between
a circle and a parabola. ECCENTRICITY measures
how round or flattened an ellipse.
12
Ellipses
13
Eccentricity
E distance between the foci Length of major
axis
14
Effects of elliptical orbits

• Changes in gravitational pull between planet and
  Sun
• Changes in orbital velocity
• Changes in apparent angular diameter

15
Keplers 2nd Law
16
Keplers 2nd law can be equated to the
conservation of angular momentum.
If the net torque on a body is zero, then the
angular momentum will be conserved
17
A of ?AoB closely approximates the area swept out
in time (dt) by a line connecting the Sun and the
planet
d?
The base of ?AoB rd? and the height is r.
Area of triangle ½(base x height) Area
½(r)(rd?) ½r2d?
dA/dt ½(r2)(d?/dt)
d?/dt ?, where ? is the angular velocity
dA/dt ½r2? or r2?/2
18
The angular momentum (L) of a planet around the
sun is the product of the r and the component of
the momentum perpendicular to r.
L rp- (r)(mv-) (r)(m?r) mr2?
19

• Bringing it all together
• dA/dt (r2/2)(d?/dt) r2?/2
• L rp- (r)(mv-) mr2?

r2? L/m
dA/dt /2
r2?
dA/dt L/2m
If angular momentum is conserved, L is constant,
then dA/dt must also be constant.
20
Keplers 3rd Law Harmonic Motion
21
Galileo

• Lived at the same time as Kepler.
• Studied falling bodies and the way they
  accelerate toward Earth
• Introduced the Law of inertia
• Made crucial astronomical observations
• Moons orbiting Jupiter.
• The surface of the Moon looks like the surface of
  Earth. It has mountains and craters, etc It is
  not perfect.
• Dealt the final blow to the Ptolemic system of
  the Solar system. And also a major problem for
  the Roman Catholic Church

22
Isaac Newton (1643 1727)

• Unified Keplers and Galileos work.

23
Ode to Newton

• Once in a great while, a few times in history, a
  human mind produces an observation so acute and
  unexpected that people cant quite decide which
  is the more amazing the fact or the thinking of
  it. Principia was one of those moments
• Bill Bryson, A Short History of Nearly
  Everything.

24
Newtons 1st Law Inertia and Momentum
Inertia A moving body tends to keep moving, and
a stationary body tends to remain at rest.
Momentum The product of mass and velocity ? mv
25
Newtons 2nd Law Force

• ƒ ma

Newtons 3rd Law Reaction
For every applied force there is an equal and
opposite reaction force
26
Derivation of the Universal Law of Gravity from
Newtons Laws of motion and Keplers Laws.
For circular motion
a v2/r

• ƒ ma

v2/r
ƒ m
Centripetal Force on a planet
27
From F mv2/r, lets look at v

• Velocity is distance over time. For simplicity
  well use a circular path, so the distance is

2pr
(the circumference of a circle)
And the time for a planet to travel in its orbit
is called the Period
(P)
V
2pr/P
Therefore,
28
In the centripetal force equation, F mv2/r ,
the velocity is squared

• Recall v 2pr/P

Square it
4p2r2/P2
V2
29
Substituting everything into the centripetal
force equation, F mv2/r
m
v2
4p2r2/P2
r
F
30
Recall Keplers 3rd Law of Harmonic Motion P2
Ar3

• Apply this law to the centripetal force equation

F m4p2r2/
P2
r
Ar3
Simplify the equation to
F m4p2/Ar2
31
F m4p2/Ar2

• Remove the constant value from the above equation

F ? m/r2
The mass of the planet (m) is also constant,
therefore,
F ? 1/r2
Where, ? means proportional to
32
Were not done.According to Newtons 3rd law
(reaction), if the sun exerts a force on the
planet, the planet must exert a force on the Sun.
F ? m/r2 is the force on the planet by the sun,
then F ? M/r2 is the force on the Sun exerted by
the planet, where M is the mass of the Sun.
Which produces a net force of
F ? mM/r2
33
(No Transcript)
34
Satellite in Motion
35
Bibliography

• Zielik, Michael. Astronomy, The Evolving
  Universe 7th Edition. John Wiley Sons, Inc.,
  1994.
• Cutnell, John D and Kenneth W. Johnson. Physics,
  3rd Edition. John Wiley Sons, Inc., 1995.
• Abell, George O, David Morrison and Sidney C.
  Wolf. Exploration of the Universe, 6th Edition.
  Saunders College Publishing, 1991.
• Halliday, David, Robert Resnick and Jearl Walker.
  Fundamentals of Physics, Volume 1, 5th Edition.
  John Wiley Sons Inc., 1997.
• Epstein, Lewis C. Thinking Physics is Gedanken
  Physics. Insight Press, 1983.
• Byson, Bill. A Short History of Nearly
  Everything. New York Broadway Books, 2003.
• Seifert, Howard S and Mary Harris Seifert.
  Orbital Space Flight, The Physics of Satellite
  Motion. New York Holt, Rinehart and Winston,
  Inc., 1964.
• Goldstein, David L and Judith R. Goldstein.
  Feynmans Lost Lecture, The Motion of Planets
  Around the Sun. New York W.W. Norton Company,
  Ltd., 1996.