Transcript A105 Stars and Galaxies - Department of Astronomy

A100
Solar System
Review Chapter 1, Kepler’s Laws
Read Chapter 2: Gravity & Motion
2nd Homework due Friday
Kirkwood Obs. open tonight, 8:30-10:30
IN-CLASS QUIZ TODAY!!
Today’s APOD
The Sun Today
Extra Announcements
Caty can’t do office hours this week…
(send email with questions)
Nathalie will lecture on Friday
Postpone due date for HW2 until
Monday, Sept. 29 (web problems, use
alternate URL)
 astro.unl.edu/naap/pos/animations/kepler.html
Kepler’s 3 Laws
of Planetary
Motion
 Planets move in elliptical orbits
with the Sun at one focus of the
ellipse
 A planet’s orbital speed varies in
such a way that a line joining the
Sun and the planet will sweep
out an equal area each month
 P2 = a3 (the square of the period
of a planet orbiting the sun is
equal to the cube of the semimajor axis of the planet’s orbit)
But WHY
????????
The Problem of
Astronomical Motion
Astronomers of
antiquity did not
connect gravity and
astronomical motion
Galileo investigated this connection with
experiments using projectiles and balls rolling
down planks
He put science on a course to determine laws of
motion and to develop the scientific method
inertia!
Galileo
experimented
with inclined
planes
Demonstrated the ideas of inertia and forces
Without friction…
a body at rest tends to remain at rest
a body in motion tends to remain in motion
Isaac Newton, the Laws
of Motion, and the
Universal Law of
Gravitation
Newton
Born same year Galileo died
Attempts to understand motion of the
Moon
Leads him to deduce the law of gravity (as we
still use it today!)
Requires him to invent new mathematics
Leads him to deduce the general laws of motion
Galileo’s ideas of inertia became
Newton’s First Law of Motion:
A body continues in
a state of rest or
uniform motion in a
straight line unless
made to change
that state by
forces acting on it
Newton’s First Law
 Important ideas
What is a force?
A push or a pull
The sum of all the
forces on an object is
the net force
If the forces all
balance, the net
force is zero, and the
object’s motion will
not change
If the speed or
direction of motion of
an object changes,
then a nonzero net
force must be present
Astronomical
Motion
Planets move along
curved (elliptical)
paths, or orbits
Speed and direction
are changing
Must there
be a net
force on
the planets?
Yes!
Gravity
is that
force
Gravity gives the Universe its structure
a universal force that causes all objects to
pull on all other objects everywhere
holds the Earth in orbit around the Sun, the
Sun in orbit around the Milky Way, and the
Milky Way in its path within the Local Group
Newton’s Law of Gravity
Everything attracts everything else!!
Orbital Motion
and Gravity
Newton
Explained the Moon’s
motion with force that
pulls the Moon from a
straight, inertial
trajectory
Showed that the force
must decrease with
distance
defined the properties
of gravity
wrote the equations of
motion with gravity
 The Moon moves “parallel” to
the Earth’s surface at such a
speed that its gravitational
deflection toward the surface
is offset by the surface’s
curvature away from the
projectile
Orbital Motion Using Newton’s First Law
At a sufficiently
high speed, the
cannonball travels
so far that the
ground curves out
from under it.
The cannonball
literally misses the
ground!
Newton’s 2nd Law: Acceleration
 Acceleration
 An object increasing or decreasing in speed along a straight
line is accelerating
 An object changing direction, even with constant speed, is
accelerating
 Acceleration is produced by a force
 Acceleration and force are proportional (double the force,
double the acceleration
Newton’s Second Law: Mass
 Mass is the amount of matter
an object contains
 Technically, mass is a
measure of an object’s inertia
 Mass is generally measured in
kilograms
 Mass should not be confused
with weight, which is a force
related to gravity – weight
may change from place to
place, but mass does not
Newton’s Second Law of Motion
F = ma
The amount of acceleration (a) that an
object undergoes is proportional to the
force applied (F) and inversely
proportional to the mass (m) of the
object
This equation applies for any force,
gravitational or otherwise
F = ma
Newton’s Third Law of Motion
When two objects
interact, they
create equal and
opposite forces on
each other
This is true for any
two objects,
including the Sun
and the Earth!
Newton solved the premier scientific problem of his
time --- to explain the motion of the planets.
To explain the motion of the planets, Newton
developed three ideas:
F = ma
1. The laws of motion
Gm1m2
2. The theory of universal gravitation
F=
3. Calculus, a new branch of mathematics
r2
“If I have been able to see farther than others
it is because I stood on the shoulders of
giants.”
--- Newton’s letter to Robert Hooke,
probably referring to Galileo and Kepler
ASSIGNMENTS
this week
Review Chapter 1, Kepler’s Laws
Read Chapter 2: Gravity & Motion
2nd Homework due Friday
Kirkwood Obs. open tonight, 8:30-10:30