Measuring the Universe: Earth Eratosthenes (about 200 BC): Sun overhead at Syene on summer solstice Sun 7 º from zenith at Alexandria on same day SO: Alexandria is 7º in latitude from Syene In terms of fractions of a circle: Measuring the Universe: Distances to Planets
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Eratosthenes (about 200 BC):
SO: Alexandria is 7º in latitude from Syene
In terms of fractions of a circle:
Distances to planets and Sun helped settle whether Earth or Sun was at the center of everything…
Ancient people attempted measurements, but techniques weren’t accurate enough
ecliptic goes through zodiac constellations
LOOKING WEST AT SUNSET
LOOKING EAST AT SUNRISE
Mars in direct motion (compared to stars)
Mars in retrograde motion
At roughly what time would the planet at position 5 be highest above the horizon? (Remember that Earth rotates counterclockwise from this point of view.)
Where would planet A be seen in the sky from Earth at sunset?
(Claudius Ptolemy, around 140 AD)
All planets move on epicycles (circular paths) that circle Earth
Epicycles are needed to create retrograde motions of planets
happens when Earth catches and passes a superior planet
Where would you look to see a planet rise when it is in retrograde motion?
If you lived on the planet Mars and you monitored Earth’s position in the sky over the course of several years, what would see?
Nicolaus Copernicus (around 1530 AD)
maximum elongation (e): largest angle between planet and Sun
used to determine planet’s distance from Sun:
Discovered by trial and error…
Kepler’s First Law: (SHAPES OF ORBITS)
All planet orbits are ellipses with Sun at one focus
Solar eclipses can be either total or “annular”…
the Moon’s distance from Earth changes…
semi-major axis (a): half length of long side
average distance from Sun
aphelion: farthest point from Sun
perihelion: closest approach to Sun
SPECIAL CASE: CIRCLE
semi-major axis (a) equals radius
Orbits are flat (they can fit in a flat plane)
They are usually tilted relative to each other…
inclination (i): angle between Earth’s and object’s orbit planes
A line connecting Sun and planet sweeps out equal areas in equal times.
CLOSER TO SUN GREATER SPEED
P: orbital period of planet (sidereal period)
a: planet’s average distance from Sun (semi-major axis)
1 AU (Astronomical Unit) is Earth’s average distance from Sun
1 AU = 1.5 1011 m
applet - defunct
NASA wants to launch a spacecraft to go out to the planet Mars (without stopping there), and then come back. If the spacecraft follows the orbit below (dotted line),
If it takes Eris 557 years to orbit the Sun, what is its average distance from the Sun?
The asteroid Apophis has an orbit with the following characteristics:
If Earth’s orbit has a semi-major axis of 1 AU and Venus has a semi-major axis of 0.723 AU, does Apophis’ orbit cross the planet orbits?
Sidereal (orbit) periods (Porb):
time for a planet to make exactly one orbit around Sun
Synodic period (Psyn) :
time between “line-ups” of Earth, Sun, and planet
From Sun’s point of view:
Fast planet orbits in timePfast:
Slow planet orbits in timePslow:
It takes Earth, Venus, and Sun 584 days to go between line-ups. What is Venus’ orbit period?
(Hint: Which planet is the fast one, and which is the slow one?)
Two observers on Earth see planets in slightly different positions in sky (compared to stars)
… this is the same idea behind your two eyes
measured by speedometers, radar guns
measured by weather vanes
3 ways to accelerate a car:
any effort that can cause acceleration
a: acceleration (units: m / s2)
m: mass(units: kg)
F: force (units: Newton = kg · m / s2)
The pictures below show strobe-light pictures of trucks at different times.
Newton’s First Law says: If object is traveling on a curved path, there MUST BE an unbalanced force.
(friction between tires and road)
Newton’s Second Law says: object accelerates (turns) in direction of unbalanced force
force is NOT pushing planet forward
force IS pulling toward inside of orbit (toward Sun)
The picture below shows the velocity of a planet at different times in its orbit (larger arrow means larger speed).
Draw the direction of the force on the planet at the different positions shown
SUN’S FORCE TURNS AND SLOWS PLANET
SUN’S FORCE TURNS AND SPEEDS PLANET
SUN’S FORCE JUST TURNS PLANET
Newton’s Thought Experiment
Fire cannonballs from tall mountain at different speeds:
low speed: crash into surface
medium speed: circular orbit
high speed: ellipse orbit (cannonball gets farther from Earth)
A ball is attached to a string and swung in a circular path above my head. At the point shown below, I suddenly release the string. If this is viewed from directly above, which of the paths below would the ball most closely follow when released?
VIEW FROM ABOVE:
GAS FORCE ON ROCKET
ROCKET’S FORCE ON GAS
SKATER FORCES ON EACH OTHER
A compact car and a large truck collide head-on and stick together.
Two different masses dropped at same time hit ground at same time…
implies equal acceleration
At Earth’s surface, force is
which creates an acceleration:
that doesn’t depend on the mass of the object!
center of mass
Stars appear to be orbiting something dark…
and about 4 million times the Sun’s mass!
Newton’s Third Law: star moves slightly as planet orbits
If we can figure out roughly how massive the star is, we can figure out how big the planet’s orbit is…
PLANET’S FORCE ON STAR
STAR’S FORCE ON PLANET
A new planet is discovered orbiting a star that is 4 times as massive as the Sun. Astronomers find that it takes 0.5 yr to make one orbit. What does this say about the planet’s orbit?
Specific combinations of variables have the property of keeping the SAME TOTAL VALUE before and after collisions, etc.
MOMENTUM: mass velocity
Forces change momentum, but “equal and opposite forces” ensures total momentum remains constant
The larger the angular momentum, the harder it is to stop its spinning or revolving
CONSERVATION OF ANGULAR MOMENTUM: amount of angular momentum does not change unless a twisting force acts on the object
Your daring professor sits in the “CHAIR OF DEATH” and starts rotating with his arms outstretched. If he pulls his arms in toward his body, and then moves them back to their original position, what will happen?
If your daring professor sits in the “CHAIR OF DEATH” and starts rotating, what will happen if he moves his arms up and down parallel to his spin axis?
The ability to get masses to move…
higher temperature more thermal energy
EXAMPLE: GAS IN A BOX
How fast does a 1010 kg asteroid have to be traveling to have a kinetic energy equal to an H bomb (5 1015 J)?
The farther an object falls, the more “stored” energy is turned into kinetic energy:
POTENTIAL ENERGY DECREASES AND…
BECOMES KINETIC ENERGY
CONSERVATION OF ENERGY: energy can be transferred from object to object, or converted from one form to another, but never destroyed
A spacecraft is moving away from the Sun without firing its engines. Which of the following describes what will happen to…
miniature golf analogy: imagine the Sun at bottom of a well, and object rolling along the sides
Imagine objects rolling on a surface that is dented by the gravity of large masses:
… minimum speed needed to escape to infinite distance