Transcript Kepler_Newton

Planetary motion: Let’s try this animation again! Venus, Mars
http://astro.unl.edu/naap/ssm/animations/configurationsSimulator.html
Copernicus’ heliocentric theory
of planets provided simple
explanation of the complicated
motion of the planets that we
observe:
a)Inner planets, Mercury and
Venus, never seen at large angles
from sun
b)Outer planets, Mars, Jupiter,
Saturn move slowly eastward
(over weeks and months) but
about once a year, reverse their
motion, go west for a distance,
then reverse again to move
eastward
So, what is a theory? A law?
The word "theory" means something very different in everyday
language than it does in science: to the average person, a theory is just
an idea…
A scientific theory is an explanation of something that has been
demonstrated through repeated experiments or testing. A scientific law
is often part of the theory, expressing a mathematical relationship
A scientific theory also makes predictions that can be tested.
What can we predict about the appearance of Venus when seen through
a telescope?
Galileo, in 1609, was the first to look at the planets through a telescope.
What he saw when he looked at Venus strongly supported the heliocentric
theory
Suppose early in the morning
you look at Venus, through a
telescope, and it appears like
this:
In the following weeks, its
angular distance from the sun gets
smaller, and finally it disappears
in the sun’s glow.
But Venus reappears, this time in the western evening sky. You watch it
for several more months as its angular distance from the sun increases
to about 45 degrees, then Venus starts to move closer to the sun again
Again, you look at it in a telescope.
What to you think it will look like
compared to the first time?
(hint: remember how the moon changes
depending on how we view it!)
Here is what you see:
Kepler: planets move in almost circular orbits
Kepler lived at the same time as Galileo, both born
shortly after Copernicus published his book. He
used the careful observations made by Tycho Brahe
to modify Copernicus’ idea of circular motion.
He realized, from the orbit of Mars, that the planets
move not on circular, but in elliptical orbits.
You will hopefully have a chance to explore these in a computer lab. The
web page looks like this:
On-line Simulator, Worksheet for Kepler’s Laws
http://astro.unl.edu/naap/pos/animations/kepler.swf
Plan B, should computer lab not be available: Lect-tutorial, p 21
Kepler’s Three laws, summarized:
1.
Planets orbit the sun in an ellipse
2.
Line connecting sun and planet sweeps out
equal areas in equal time: the result is that the
planets moves fastest when closest to the sun.
3.
The Period (“Year”) squared = separation cubed
Period X period =
separation
separation x separation x
Newton used these relations to formulate the
law of gravity…
Sir Isaac Newton, 16421727:
He was responsible for breakthroughs in
mechanics, optics, gravity, mathematics. (He
invented calculus to solve the problem of the
moon’s orbit)
Newton’s Law of Gravity: Force at a distance, or why does an apple fall?
What keeps the moon in orbit around the earth? And what holds you to the
surface of the earth?
The force of attraction between two bodies is directed along a line joining
them:
•The force increases with the mass of either body
•It decreases with the square of the distance between the two bodies
Let’s express as an equation
Examples:
1. Suppose mass Mb doubles. What happens to the force?
(What’s an example of M doubling?)
2. Suppose distance, r, doubles. What happens to the force?
Do the astronauts in space station feel
gravity? Let’s explore this.
What is the diameter of the
Earth?
How far above the Earth does
the space shuttle orbit?
How much farther from the
center of the earth are the
astronauts? (Suppose the
distance r increases by 5%
(0.05)Does the force change
very much?)
The space shuttle, and the astronauts inside, are falling around
the earth!
And the moon is
falling around the
earth
And the earth-moon
system is…
How far from a body (earth, sun, etc)
does gravity exist?
(does this force ever reach zero?)
Suppose an astronaut lands on the
moon, which has a mass 0.012 that
of the earth, and a radius 0.27 of
the earth. What happens to the
force between the astronaut and the
moon- what we call his weight?
A quick calculation (!)
shows that the astronaut’s
weight (the force pulling
him down) is only 0.17
what it was on earth.
The law of gravity in astronomy:
(Period (“Year”) 2)(Ma + Mb) = semi-major axis cubed
P2 (Ma + Mb) = R3
Combination of the law of gravity and Kepler’s third law allows us to calculate:
Masses of stars: binary star systems
Mass of our galaxy: how many stars in it
Mass of other galaxies