Transcript Models of the solar system

Models of the solar system
(Ch.29.1)
•1st model of
the solar
system
•Aristotle (300’s BC) said solar
system was geocentric
•1st model of
the solar
system
•Aristotle (300’s BC) said solar
system was geocentric,
meaning that the earth is
center.
•1st model of
the solar
system
•Aristotle (300’s BC) said solar
system was geocentric,
meaning that the earth is
center.
This model did not make sense
because some planets seem to
sometimes move backward
(retrograde motion)
•New model of •Copernicus (Poland
the solar
•1500’s): Established
system
heliocentric model
What does this mean?
•Galileo (Italian)
got in trouble with
the Roman Catholic
Church for
popularizing
Copernican model
•Kepler’s
3Laws of
Planetary
Motion
•Kepler (Denmark):
Reinforced Copernicus
with laws of physics
Law 1: Law of
Ellipses
•Planets orbit in an ellipse
•an ellipse is an oval shape
determined by two center points
called foci (focus is singular)
•One of our foci is the sun
Law 1: Law of
Ellipses
• perihelion: the closest point of
Earth to the sun in an orbit
•aphelion: the farthest point from
the sun in an orbit
•When is Earth at perihelion?
•Does that make sense?
Law 2: Law of
Equal Areas
•See diagram below
Distance unit in •The average distance between the
our solar system Earth and Sun is 1 AU (or
astronomical unit)
Illustration of Kepler's second law. The planet
moves faster near the Sun, so the same area is
swept out in a given time as at larger
distances, where the planet moves more
slowly. The green arrow represents the
planet's velocity, and the purple arrows
represents the force on the planet.
Law 3: Law of
Periods
•Describes the relationship
between the average distance of a
planet from the sun and the orbit
period of the planet.
•for Earth, r³ = p² (where r = avg
radius and p = orbit period).
•Unlike Kepler's first and second laws that
describe the motion characteristics of a
single planet, the third law makes a
comparison between the motion
characteristics of different planets. The
comparison being made is that the ratio
of the squares of the periods to the cubes
of their average distances from the sun is
the same for every one of the planets.
Amazingly, every planet has the same T2/R3 ratio.
•Amazingly, every planet has the
same p2/r3 ratio.
Planet
Orbit Period
Avg.
(yr)
Distance (AU)
p2/r3
(yr2/AU3)
Mercury
0.241
0.39
0.98
Venus
.615
0.72
1.01
Earth
1.00
1.00
1.00
Mars
1.88
1.52
1.01
Jupiter
11.8
5.20
0.99
Saturn
29.5
9.54
1.00
Uranus
84.0
19.18
1.00
Neptune
165
30.06
1.00
Pluto
248
39.44
1.00
Kepler and
Newton
Newton’s laws of motion reinforce
Kepler’s Laws of Planetary Motion.
•For example: and object in motion
wants to stay in motion unless
acted upon by an outside force.
•What is the force that keeps
planets from going off in a straight
line?
Newton's
Laws
reinforce
Kepler's
Laws
mathemati
cally
•Since the planets move on ellipses (Kepler's 1st
Law), they are continually accelerating, as we
have noted above. This implies a force acting
continuously on the planets.
•Because the planet-Sun line sweeps out equal
areas in equal times (Kepler's 2nd Law), it is
possible to show that the force must be directed
toward the Sun from the planet.
•From Kepler's 1st Law the orbit is an ellipse with
the Sun at one focus; from Newton's laws it can
be shown that this means that the magnitude of
the force must vary as one over the square of the
distance between the planet and the Sun.
•Kepler's 3rd Law and Newton's 3rd Law imply
that the force must be proportional to the
product of the masses for the planet and the Sun.