Download law

6
The Science of Astronomy
Astronomy is a physical science that is based on
the Scientific Method.
Do not confuse it with astrology!
Scientific Method
Using the scientific method, our understanding of the
universe happens more or less as follows:
 Observation
 Hypothesis
 Testing, testing…
 Theory (or Model)
 Testing, testing…
 Natural Law
7
Geocentric Cosmology
ALL celestial motions appear centered on .
 Plato: uniform circular motion
 Aristotle: imperfect  at center of universe
With the geocentric model, it is easy to explain
 Daily motion, annual motion of the sun, moon’s
motion, prograde motion of planets
But how do you explain retrograde motion of planets?
Ptolemy (A.D. 140): Last of the great Greek astronomers
who explained retrograde motion using the epicycle.
Ptolemaic model flourished for almost 15 centuries!
8
Problems began to crop up with the Ptolemaic model:
 Very complicated
 Failed to accurately predict positions of planets
 Became arbitrary—death of a theory or “law”!
Heliocentric Cosmology
First proposed by Aristarchus ~280 B.C.
Nicolaus Copernicus (1473-1543): re-introduced the
idea of a Sun-centered universe.
By having the sun at the center of the planets’ orbits, and
putting  in motion:
 Retrograde motion was very simply described
 Actual order of planets was determined
 Relative scale of the solar system was found
9
However, the Copernican model was not taken seriously
by most scientists for many decades.
Tycho Brahe (1546-1601): Showed heavens were not
“perfect” (1572)
 Collected very precise observations of planetary
motion and positions for 20 years
 Wanted to prove his own model of the universe, so he
hired a mathematician to help—Kepler.
Johannes Kepler (1571-1630): Using Brahe’s excellent
data, he realized the key to heliocentrism was the ellipse.
Three laws of planetary motion:
Kepler’s 1st law: planetary orbits are ellipses with the sun
at one focus.
Kepler’s 2nd law: “Law of equal areas”
10
Kepler’s 3rd law: “Harmonic law”
 p2 = a3
 p = sidereal period (in years)
 a = semimajor axis (in AUs)
These laws solidify the Heliocentric Model, but they are
descriptive only, they do not explain the motions!
Galileo Galilei (1564-1642): In 1609, he became the first
astronomer to use a telescope to observe objects in the
sky. He discovered:
 Milky Way is made of countless individual stars
 Mountains and craters on moon
 “Appendages” on Saturn
 Spots on the sun
 Phases of Venus—correlated with angular diameter
 4 largest moons of Jupiter clearly orbit the planet
Galileo’s discoveries—and his public support of the
Copernican model of the universe—caused him trouble!
11
Sir Isaac Newton (1643-1727): Through observation and
experimentation, he formulated three “laws of motion”.
Newton’s 1st law: an object in uniform motion remains
in that state of motion, unless acted upon by an outside
force. “Law of Inertia”
Newton’s 2nd law: F = ma
 F = force
 m = mass of an object
 a = acceleration
Therefore, a force applied to an object causes an
acceleration that depends on the mass of the object.
Mass  weight!
Newton’s 3rd law: for every action there is an equal and
opposite reaction.
12
Newton’s Universal Law of Gravitation: F = GMm
r2
F = force of gravity
G = universal gravitation constant
M,m = masses of any two bodies
r = distance between the two bodies
This law describes the attractive force between any two
bodies in the universe.
We can use Newton’s 2nd law of motion and law of
gravity to determine the rate of acceleration of an object
of mass m falling near Earth’s surface.
In this case, the force causing the object to accelerate is
gravity:
2nd law: F = ma
= mg (“a” is called “g” for the acceleration
due to gravity)
Law of Gravity: F = GMm
r2
13
Set laws equal to each other and solve for g:
mg = GMm
r2
cancel terms: g = GM  only the mass of  matters
r2
Therefore, the acceleration due to gravity is independent
of the small object’s mass.
Plug the values:
G = 6.67 x 10-8 cm3/gms2
M = 5.97 x 1027 gm
r = 6.378 x 108 cm
into:
g = GM = 979 cm/s2 = 9.8 m/s2
r2
14
All of Kepler’s laws can be derived using Newton’s laws
of motion and gravity:
Kepler’s 3rd law:
p2 = a3 (if p is in years and a is in AUs)
p2  a3 (for any units)
From the Universal Law of Gravitation (Newton):
p2 = 42  a3
GM
We can use this equation with any object that orbits the
sun to determine the mass of the sun.
The tides on Earth can also be explained using Newton’s
law of gravity:
Tides
 2 high and 2 low tides per day on Earth due to
moon’s differential gravitational pull