Transcript a 3 (in astronomical units)

Goals
• Explain how accurate observations led to Heliocentric model
• Explain retrograde motion
• Describe contributions of Copernicus, Tycho, Galileo, and Kepler
• Explain how we know the size of our Solar system
• Explain Newton’s laws of motion and gravity
Ancient astronomers noticed some of the stars
would “wander” against the background of fixed
stars. These “planets” were given extreme
significance as people tried to find meanings from
the heavens.
The planets as well as the Sun and Moon were
each given a day of the week in their honor.
Saturn-Saturday, Sun-Sunday, Moon-Monday, etc.
Planetary Motion
Early astronomers were obsessed with perfection
and thought the motions of the heavenly bodies
should be circles.
They also thought the Earth was stationary
because they could not fell the Earth move
beneath them.
This led to the Earth centered or Geocentric
model of which Ptolemy was the main supporter.
While observations were crude the model seemed
to work, but as observations improved it became
clear that something was wrong.
One main concern was how to account for retrograde motion
where the normal eastward motion of the planets is briefly
interrupted with the looping motion. In order to modify his
theory, Ptolemy had to add circles to circles (deferent and
Epicycle) to explain retrograde motion.
Retrograde motion is
defined as the brief
westward motion
that a planet appears
to take when a
slower outer planet
is passed by a faster
inner planet.
While the geocentric model required a complicated set of circles on
circles to explain retrograde motion, the Sun centered (Heliocentric)
model easily explained the observations. Copernicus became the
main supporter for the Heliocentric model.
While the Copernican theory did explain
the observations better with a simpler
model, civilization at the time resisted the
model partly because the church of the
time had declared the geocentric model
was described in the Bible as correct with
out regard for scientific observations.
What finally convinced everyone was the
observations of Galileo Galilei.
Using his telescope, Galileo discovered:
• the Moon had craters and mountains like the Earth and was not
perfect.
• the Sun was imperfect (sunspots) and rotated on its own axis.
• Jupiter had four moons in orbit around it which showed things
could orbit other things besides the Earth.
• Venus showed complete set of phases only explainable if it
was in orbit around the Sun not the Earth.
Because of his insistence of the Heliocentric model based on his
observations, Galileo was arrested by the church and was not
forgiven of his “crimes” until 1992.
The only way to
explain the phases
of Venus was if it
orbited the Sun
and not the Earth.
Kepler
Now that we have the correct heliocentric model
we need to explain why it is the way it is.
• What causes the planets to orbit the Sun ?
• Why do the different planets have different
speeds?
• How can we predict their positions in the future?
With new higher accuracy
observations of Tycho Brahe,
Kepler was able to form three
laws of planetary motion.
Kepler’s Laws of Motion
First Law: The orbits of the planets are in the shape of an
ellipse with the sun at one focus.
Second Law: a vector from the sun to the planet sweeps out
equal areas in equal times (conservation of angular momentum).
Third Law: the period of a planet and its semimajor axis
are related by.
P2 (in Earth years) = a3 (in astronomical units)
Mtotal (in solar units)
Newton’s Laws
While Kepler discovered certain relationships
and facts concerning how the planets moved
about the Sun he could not explain why.
Newton invented calculus to derive Kepler’s
Laws and made three of his own.
First Law: objects remain in motion or at rest
unless acted upon by a force.
Second Law: F = Ma: where F = force, M= mass, a = acceleration
Third Law: F12 = - F21
Gravity: Fg = GMm/d2 Where Fg is the force due to gravity, G is a
constant, and M and m are the mass of the two objects, and d is the
distance of their separation.
Thus gravity provides the force which causes objects to orbit
other objects. Newton invented calculus to help him solve
his problems and also laid the groundwork for the theory of
earth orbiting satellites.
Kepler’s third law allows us to
detect planets around other
stars and determine their mass.
With Kepler’s laws we
can now relate the
relative sizes of the
orbits of the planets.
This allows modern
astronomers to measure
the distance between
planets and thus
determine the size of the
solar system.