Download Chapter 4 Gravitation and the Waltz of the Planets

Chapter 4
Gravitation and
the Waltz of the
Planets
Guiding Questions
1. How did ancient astronomers explain the motions of the
planets?
2. Why did Copernicus think that the Earth and the other planets
revolved around the Sun?
3. What did Galileo see in his telescope that confirmed that
planets orbit the Sun?
4. How did Tycho Brahe attempt to test the ideas of Copernicus?
5. What paths do the planets follow as they move around the
Sun?
6. What fundamental laws of nature explain the motions of
objects on Earth as well as the motions of the planets?
7. Why don’t the planets fall into the Sun?
8. What keeps the same face of the Moon always pointed
toward the Earth?
Ancients knew that five “wandering stars” seemed to
slowly move among the constellations.
These wandering stars, commonly known as “planetes,” typically
move from west to east, except during brief periods where they move
backwards or retrograde. The early Greek model of a celestial sphere
did not adequately account for these retrograde loops.
Ancient astronomers invented geocentric
models to explain complex planetary motions
Claudius Ptolemy devised the longest used
geocentric model to explain retrograde loops by
putting planets on epicycles and deferents.
Nicolaus Copernicus devised the first
comprehensive heliocentric (Sun-centered) model
• Copernicus imagined a
universe where the Sun
was at the center instead of
Earth.
• He suggested that Earth’s
motion around the Sun
provided a more “natural”
explanation for retrograde
loops as Earth passed the
other planets.
Heliocentric planetary positions are
described relative to Earth
Opposition
Inferior conjunction
Superior conjunction
Greatest eastern
elongation (appears
east of the Sun in the sky)
Greatest western
elongation (appears
west of the Sun in the sky)
In this heliocentric model, the planets just “appear” to move
backwards as the faster moving Earth “laps” the more distant
planet once each year when it is at opposition.
Galileo’s discoveries of Jupiter’s moons with his
telescope showed that Earth was not the center of
all orbits strongly supported a heliocentric model
even though Copernicus’ model was no more accurate than Ptolemy’s.
Galileo’s discoveries of Venus’ phases with his
telescope showed that Venus must orbit the Su,.
strongly supporting a heliocentric model
even though Copernicus’ model was no more accurate than Ptolemy’s.
Venus is clearly smallest when it is at superior conjunction
and largest when it is close to inferior conjunction.
Venus can go through phases only
if it orbits the Sun.
Tycho Brahe measured positions precisely,
before telescopes were available.
Brahe constructed
enormous instruments to
meticulously record the
precise positions of the
planets in the sky to an
accuracy never
previously obtained.
Tycho Brahe’s astronomical observations
disproved ancient ideas about the heavens.
Using PARALLAX,
Brahe was able to
demonstrate that the
comet of 1577 was
beyond the Moon’s orbit
and that the supernova
of 1572 was in “the
distant realm of the
stars.”
Johannes Kepler proposed elliptical
paths for the planets about the Sun.
Kepler’s First Law of Planetary Motion
• The orbit of a planet about the Sun is an
ellipse with the Sun at one focus.
Kepler’s elliptical paths for planets’ orbits
Elliptical Eccentricity (e): a number ranging between
zero (for a flat line) and one (for a perfectly round circle).
Kepler’s Second Law of Planetary Motion
• A line joining a planet and the Sun sweeps
out equal areas in equal intervals of time.
Kepler’s Third Law of Planetary Motion
• The square of the sidereal period of a planet is
directly proportional to the cube of the semi-major
axis of the orbit.
p2 = a 3
Period p is in years (p=1 for Earth)
distance a from Sun is in AU (a=1 for Earth)
Kepler’s laws explain how the universe works, but they do not explain “why.”
Newton’s explanation shows why Kepler’s laws work.
Applying Kepler’s 3d law:
A satellite is placed in a circular orbit around the Sun, orbiting
the Sun once every 10 months. How far is the satellite from
the Sun?
2
 10 
a = p =    _______
 12 
3
2
a  ______
Sidereal and Synodic periods:
A satellite is placed in a circular orbit around the Sun, orbiting
the Sun once every 10 months. How often does the satellite
pass between the Earth and the Sun?
1
1
1


sidereal period Earth ' s sidereal year synodic period
1 1 1
 
P E S
1
1 1
 
10
1 S
12
1
 ________________
S
S  ________________
Isaac Newton formulated three laws that
describe fundamental properties of
physical reality.
1. A body remains at rest, or moves in a straight
line at a constant speed, unless acted upon by a
net outside force.
2. F = m a (the force on an object is directly
proportional to its mass and acceleration).
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’s description of gravity accounts
for Kepler’s laws and explains the
motions of the planets.
Newton’s Law of Universal Gravitation
Two bodies attract each other with a force that is
proportional to the mass of each body and inversely
proportional to the square of the distance between
them.
G m1 m 2
F=
2
r
Where G = 6.67 X 10-11 N m2/kg2 and r is the
distance between the objects with masses m1 and m2.
The law of universal
gravitation accounts for
planets not falling into the
Sun nor the Moon crashing
into the Earth:
Paths A, B, and C do not
have enough horizontal
velocity to “escape” Earth’s
surface whereas Paths D,
E, and F do.
Path E is where the
horizontal velocity is
exactly what is needed so
its orbit matches the
circular curve of the Earth.
Mathematically speaking, Newton discovered that
orbiting bodies may follow any one of a family of curves
called “conic sections.”
Newton’s laws also explain tidal forces which
can deform planets, reshape galaxies.
Newton’s laws
also explain tidal
forces which can
deform planets,
reshape galaxies.
Newton’s laws also explain tidal forces which
can deform planets, reshape galaxies.
Gravitational forces from the Sun in addition to
the Moon can create abnormally high tides,
called spring tides.
Gravitational forces
from the Sun can
also diminish each
other’s effects. When
the Sun and Moon
are at right angles,
they create
abnormally low
tides, called neap
tides.
We can use Newton’s gravity to
approximate the size of a black hole!
Gravitational energy  kinetic energy
GmM 1
2
 mv
r
2
Solve for r  ____________
Not even light can escape (v=c) if it is closer than r to a black
hole. This is the Schwarzschild radius:
R=_____________________
Guiding Questions
1. How did ancient astronomers explain the motions of the
planets?
2. Why did Copernicus think that the Earth and the other planets
of around the Sun?
3. What did Galileo see in his telescope that confirmed that
planets orbit the Sun?
4. How did Tycho Brahe attempt to test the ideas of Copernicus?
5. What paths do the planets follows as they move around the
Sun?
6. What fundamental laws of nature explain the motions of
objects on Earth as well as the motions of the planets?
7. Why don’t the planets fall into the Sun?
8. What keeps the same face of the Moon always pointed
toward the Earth?