Transcript - Lincoln High School

CHAPTER 2:
Gravitation
and the
Waltz of the
Planets
WHAT DO YOU THINK?
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What makes a theory scientific?
What is the shape of the Earth’s orbit around the
Sun?
Do the planets orbit the Sun at constant speeds?
Do all the planets orbit the Sun at the same
speed?
How much force does it take to keep an object
moving in a straight line at a constant speed?
How does an object’s mass differ when
measured on the Earth and on the Moon?
The scientific method is used to develop new scientific
theories. Scientific theories are accepted when they
make testable predictions that can be verified using
new observations and experiments.
Early models of the universe attempted to explain the
motion of the five visible planets against the
background of “fixed” stars. The main problem was
that the planets do not move uniformly against the
background of stars, but instead appear to stop, move
backward, then move forward again. This backward
motion is referred to as retrograde motion.
Ptolemy explained this motion using a geocentric (Earthcentered) model of the solar system in which the planets
orbited the Earth indirectly, by moving on epicycles
which in turn orbited the Earth.
Nicolaus Copernicus developed the
first heliocentric (sun-centered) model
of the solar system. In this model, the
retrograde motion of Mars is seen
when the Earth passes Mars in its orbit
around the Sun.
We define special positions of the planets in their orbits depending
where they appear in our sky. For example, while at a conjunction, a
planet will appear in the same part of the sky as the Sun, while at
opposition, a planet will appear opposite the Sun in our sky.
However, the cycle of these positions (a synodic
period) is different from the actual orbital period of the
planet around the Sun (a sidereal period) because both
the Earth and the planet orbit around the Sun.
When a new “star” appeared in the sky during the 16th century, a Danish
astronomer named Tycho Brahe reasoned that the distance of the object
may be determined by measuring the amount of parallax.
The apparent
change in the
location of an
object due to the
difference in
location of the
observer is called
parallax.
Because the parallax of the “star” was too small to measure,
Tycho knew that it had to be among the other stars, thus
disproving the ancient belief that the “heavens” were fixed
and unchangeable.
After Tycho Brahe’s death,
Johannes Kepler (pictured
here with Tycho in the
background) used Tycho’s
observations to deduce the
three laws of planetary
motion.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #1. The orbit of a planet around the Sun is an ellipse
with the Sun at one focus.
The amount of elongation in a planet’s orbit is defined as
its orbital eccentricity. An orbital eccentricity of 0 is a
perfect circle while an eccentricity close to 1.0 is nearly a
straight line.
In an elliptical orbit, the distance from a planet to the
Sun varies. The point in a planet’s orbit closest to the
Sun is called perihelion (January 3rd, 147,098,291 km)
, and the point farthest from the Sun is called aphelion
(July 4th, 152,098,233 km).
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #2: A line joining the planet and the Sun sweeps out
equal areas in equal intervals of time.
Planet moves
slower in its orbit
when farther away
from the Sun.
Planet moves
faster in its orbit
when closer to the
Sun.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #3: The square of a planet’s sidereal period around the Sun
is directly proportional to the cube of its semi-major axis.
This law relates the amount of time for the planet to complete one orbit around the
Sun to the planet’s average distance from the Sun.
If we measure the orbital periods (P) in years and distances (a) in astronomical
units, then the law mathematically can be written as P2 = a3.
Radius(E
arth =1)
Mass
Dis. from Orbital
(Earth =1) Sun (AU) Period (yr)
# of
Moon
s
Orbital Eccentricity
Mercury
0.382
0.055
0.39
0.24
0
0.2056
Venus
0.949
0.815
0.72
0.62
0
0.0068
Earth
1
1
1
1
1
0.0167
Mars
0.532
0.107
1.52
1.88
2
0.0934
Jupiter
11.209
318
5.2
11.86
63
0.0483
Saturn
9.44
95
9.54
29.46
62
0.0560
Uranus
4.007
15
19.18
84.01
27
0.0461
Neptune
3.883
17
30.06
164.8
13
0.0097
Ceres
0.076
0.00016
2.76596
4.599
0
0.07976
Pluto
0.180
0.002
39.44
247.7
3
0.2482
Haumea
0.110
0.0007
43.335
285.4
2
0.18874
MakeMake
0.149
0.00067
45.791
309.88
0
0.159
Eris
0.235
0.0028
67.6681
557
1
0.44177
Galileo was the first to use a telescope to
examine celestial objects. His
discoveries supported a heliocentric
model of the solar system.
Galileo discovered that Venus, like the
Moon, undergoes a series of phases as
seen from Earth. In the Ptolemaic
(geocentric) model, Venus would be seen
in only new or crescent phases. However,
as Galileo observed, Venus is seen in all
phases, which agrees with the Copernican
model as shown.
Galileo also discovered
moons in orbit around the
planet Jupiter. This was
further evidence that the
Earth was not the center of
the universe.
Isaac Newton formulated three laws to
describe the fundamental properties of
physical reality.
NEWTON’S THREE LAWS OF MOTION
LAW #1: A body remains at rest or moves
in a straight line at constant speed unless
acted upon by a net outside force.
LAW #2: The acceleration of an object is
proportional to the force acting on it.
LAW #3: Whenever one body exerts a
force on a second body, the second body
exerts an equal and opposite force on the
first body.
Newton also discovered that gravity, the force that
causes objects to fall to the ground on Earth, is the
same force that keeps the Moon in its orbit around
the Earth.
NEWTON’S LAW OF UNIVERSAL GRAVITATION
Two objects attract each other with a force that is
directly proportional to the product of their masses
and inversely proportional to the square of the
distance between them.
With his laws, Newton
was able to derive
Kepler’s three laws, as
well as predict other
possible orbits.
Newton’s laws were applied to other objects in our
solar system.
Using Newton’s methods, Edmund Halley
worked out the details of a comet’s orbit
and predicted its return.
Deviations from
Newton’s Laws in the
orbit of the planet
Uranus led to the
discovery of the eighth
planet, Neptune.
F/m = a
Ag = G *
G = 6.67 x
-11
3
10 m /kg
2
M/r
2
s
Diameter
(Earth
=1)
Mass
(Earth
=1)
Dis. from
Sun (AU)
Gravitationa
l
acceleration
# of
Mass and radius
Moons of Earth
Mercury
0.382
0.055
0.39
0.24
0
5.97219 × 1024
kilograms
Venus
0.949
0.815
0.72
0.62
0
6,371,000 meters
Earth
1
1
1
1
1
Mars
0.532
0.107
1.52
1.88
2
Jupiter
11.209
318
5.2
11.86
63
Saturn
9.44
95
9.54
29.46
62
Uranus
4.007
15
19.18
84.01
27
Neptune
3.883
17
30.06
164.8
13
Ceres
0.076
0.00016
2.76596
4.599
0
Pluto
0.180
0.002
39.44
247.7
3
Haumea
0.110
0.0007
43.335
285.4
2
MakeMak
e
0.149
0.00067
45.791
309.88
0
G = 6.67x10-11 m3/kg s2
Ag = G * M/r2
WHAT DID YOU THINK?






What makes a theory scientific?
If it makes predictions that can be objectively
tested and potentially disproved.
What is the shape of the Earth’s orbit around the
Sun?
Elliptical
Do the planets orbit the Sun at constant speeds?
The closer a planet is to the Sun in its orbit, the
faster it is moving. It moves fastest at perihelion
and slowest at aphelion.
WHAT DID YOU THINK?






Do all the planets orbit the Sun at the same
speed?
No. A planet’s speed depends on its average
distance from the Sun.
How much force does it take to keep an object
moving in a straight line at a constant speed?
Unless an object is subject to an outside force, it
takes no force at all to keep it moving in a
straight line at a constant speed.
How does an object’s mass differ when
measured on the Earth and on the Moon?
Its mass remains constant.
Key Terms
acceleration
angular momentum
aphelion
astronomical unit
configuration (of a planet)
conjunction
conservation of angular
momentum
cosmology
ellipse
elongation
focus (of an ellipse)
force
Galilean moons
(satellites)
gravity
heliocentric cosmology
hyperbola
inferior conjunction
Kepler’s laws
kinetic energy
law of equal areas
law of inertia
light-year
mass
model
momentum
Newton’s laws of
motion
Occam’s razor
opposition
parabola
parallax
parsec
perihelion
physics
potential energy
retrograde motion
scientific method
scientific theory
semimajor axis (of an
ellipse)
sidereal period
superior conjunction
synodic period
universal constant of
gravitation
universal law of
gravitation
velocity
weight
work