Download lecture 32 orbits

LECTURE 32
ORBITS
Instructor: Kazumi Tolich
Lecture 32
2
! 
Reading chapter 12-3
!  Kepler’s
laws
Stars, planets, the sun and the moon
3
! 
! 
! 
The stars seem to move in circles
around Earth with their axis of
rotation fixed in the direction of the
North Star.
There are five objects, visible to the
naked eye, that appear starlike but
do move across the fixed stars;
these are the planets (wanderers in
Greek).
The sun and moon also move across
the stars.
Theory of Earth centered universe
4
! 
! 
! 
! 
The ancient Greeks postulated
that Earth is located at the center
of the universe.
The stars were fixed to the
outermost shell.
There are 7 concentric spherical
shells, each containing one object:
Sun, Moon, or a planet (5 planets
were known then).
The shells rotate uniformly around
Earth.
Contradicting observation
5
! 
! 
! 
The planets do not move at a constant rate, and sometimes
even move backwards with respect to the surrounding stars
(retrograde motion).
During a planet’s retrograde motion, it appeared brighter than
at other times.
This suggested to the Greeks that the planet was closer to
Earth during its retrograde motion.
Cartoon example of what you might see
Modified theory of epicycles
6
! 
The Greeks attempted
to accommodate this
complex motion using
epicycles – smaller
spheres around the
planets.
Venus: “the morning/evening star”
7
Venus always appears near
the sun in the sky.
!  Ptolemy reasoned that the
center of Venus’s epicycle
lies between Earth and the
sun.
! 
More observations and more complications
8
To agree with the
observations, each planet
needed a lot of epicycles,
as many as 80!
!  Each of the centers of the
shells was shifted from the
location of Earth.
!  This theory was getting
more and more complex.
! 
New theory of sun centered universe
9
Copernicus looked for a
much simpler solution, and
came up with the suncentered model.
!  The sun is at the center of the
universe and the planets,
including Earth, are in
circular orbits around the sun.
! 
Simplicity of the new theory
10
! 
Copernicus’ theory leads to a simple explanation of
retrograde motion, as Earth overtakes Mars in its
orbit.
Observations supporting the new theory
11
! 
Once Galileo had invented the telescope, he was
able to observe the phases of Venus, including the
“full-Venus.”
Earth-centered theory disproved
12
! 
We would never see “full-Venus” according to the
Earth-centered universe model.
Contradicting observations again
13
In the late 16th century, Tycho
Brahe made detailed
observations of the motions of
the planets.
!  He found that the actual motions
of the planets did not agree
precisely with the predictions of
the Copernican theory.
! 
Kepler’s laws & Newton’s law of gravity
14
In the early 1600s, Kepler proposed three laws of
planetary motion based on Brathe’s observations.
!  Almost a century later, Newton deduced Kepler's
laws from Newton's own laws of motion and his law
of universal gravitation.
! 
Kepler’s
st
1
law
15
All planets move in elliptical orbits with the sun at one
focus.
Demo: 1
16
! 
Ellipse Drawing Board
Confirming observations
17
! 
Planets discovered (Uranus, Neptune, and Pluto)
after Kepler’s theory was developed also move in
elliptical orbits.
!  Note:
Pluto is no
longer called a
planet. It is
called a “dwarf
planet.”
Kepler’s
nd
2
law
18
A line joining any planet to the sun sweeps out equal
areas in equal times.
! 
! 
As the planet moves close to the
sun, it moves faster.
This is a consequence of
conservation of angular
momentum.
Kepler’s
rd
3
law
19
The period of any planet is proportional to its mean distance
from the sun raised to the 3/2 power.
T = ( constant ) r 3 2
⎛ 2π ⎞ 3 2
T =⎜
⎟r
⎝ GM s ⎠
Example: 1
20
! 
A comet has a very elliptical orbit with a period of
127.4 y. What is the ratio of its mean distance from
the sun to the mean distance between the earth and
the sun?
Geosynchronous satellites
21
Geosynchronous satellite orbit above the equator
with a period of one day.
!  They appear stationary in the sky.
!  They are useful for communications and weather
forecasting.
! 
Example: 2
22
! 
A satellite hovers over a certain spot on the equator
of (rotating) Earth. What is the altitude of its orbit
(called geosynchronous orbit)?
Global Positioning System
23
The GPS satellites have
an average altitude of
12,550 miles, and orbit
Earth every 12 hours.
!  They can provide a
precise determination of
an observer’s position
on Earth.
! 
Orbital maneuvers to a lower orbit
24
! 
Moving to a lower orbit
using rocket:
!  Decelerating
rockets at
A and B.
!  The satellite speeds up
as it falls inward
between firings.
Orbital maneuvers to a higher orbit
25
! 
Moving to a higher
orbit using rocket:
!  Accelerating
rockets at
A and B.
!  The satellite slows
down as it moves
farther away from
Earth between firings.
Current understanding of the universe
26
! 
! 
! 
! 
The planetary orbits are observed to
be not exactly elliptical due to the
gravitational attraction from other
planets.
Our sun is a star like other stars, and
our galaxy, Milky Way, is like a
hundred billion other galaxies.
There is no “center of the universe.”
Big mystery: 23% dark matter and
73% dark energy fill the universe?
Observations continue….
27
Our interest in the stars and the universe continues
to grow, as the sophistication of our instruments
increases.
!  Hubble telescope was launched in 1990.
! 
Hubble telescope
Images from Hubble
28
Super-Kamiokande
29
Super-Kamiokande is for detecting neutrinos from
the sun.
!  Super-K is filled with water, and surrounded by
thousands of light sensors.
! 
Super-Kamiokande neutrino detector
The sun viewed with neutrinos
Radio telescopes
30
! 
Instead of visible light, radio telescopes detect
radio waves coming from galaxies, etc.
Images from radio telescope arrays
31
! 
Processing the data from multiple radio telescopes
produces dramatic high resolution images of the
universe as viewed with radio waves.
“Superluminal” Quasar
t=0
Saturn
The Sun
Mars
t = 6 years