Transcript Newton`s Law and Gravity

Astronomy 1020
Stellar Astronomy
Spring_2016
Day-7
Course Announcements
•
SW-2 … hop to it.
1st set of Dark Sky observing nights:
•
•
•
•
Mon. Feb. 8 – 7:30pm at the observatory.
Tues. Feb. 9 is the weather backup if both are cancelled.
Del Square Psi meeting – 5:30pm Wed. 2/3
Colored Card Question

In what direction is
the observer facing?
Celestial Sphere Rotation
Star B
2
Star A
1




A) toward the South
B) toward the North
C) toward the East
D) toward the West
2
Celestial Sphere
Celestial Sphere
3
1
4
3
4
Celestial Sphere
Rotation
Figure 2
Horizon
Colored Card Question

Imagine that from your current location you
observe a star rising directly in the east. When
this star reaches its highest position above the
horizon, where will it be?
A. high in the northern sky
B. high in the southern sky
C. high in the western sky
D. directly overhead
Colored Card Question

Where would the
observer look to see
the star indicated by
the arrow?
Star B
2
Star A
1
2
Celestial Sphere
Celestial Sphere
3
1
4
A. High in the Northeast
3
B. High in the Southeast
C. High in the Northwest
4
D. High in the Southwest
Celestial Sphere
Rotation
Horizon
I Realize this is Like Trying to Drink
from a Fire Hose
Earth’s rotation causes the Sun, Planets,
Moon and stars to appear to move when
viewed from Earth
Photo: Dr. Spencer Buckner
Rotation
Celestial Sphere Rotation
Celestial Sphere Rotation
Star B
Star B
2
2
Star A
Star
A2
1
North Star
1
Celestial Sphere
2
3
3
1
1
4
4
3
3
Earth’s Equator
4
4
Celestial Sphere
Rotation
Celestial Sphere
Rotation
Figure 1
Figure 2
Horizon
Rotation
Celestial Sphere Rotation
Celestial Sphere Rotation
Star B
Star B
2
2
Star A
Star
A2
1
North Star
1
Celestial Sphere
2
3
3
1
1
4
4
3
3
Earth’s Equator
4
4
Celestial Sphere
Rotation
Celestial Sphere
Rotation
Figure 1
Figure 2
Horizon
Tutorial: Motion – pg.3
 Work with a partner
 Read the instructions and questions carefully
 Talk to each other and discuss your answers with each
another
 Come to a consensus answer you both agree on
 If you get stuck or are not sure of your answer ask
another group
 If you get really stuck or don’t understand what the
Lecture Tutorial is asking as one of us for help
How long did it
take to get this
picture?
Why does the sky change with
your location?
As you move away from the pole your horizon moves with you but the
locations of the celestial poles and celestial equator remains the same
Why does the sky change over
the course of a year?
As we orbit the sun the direction opposite the sun changes and we only see
the stars when the sun is not up
Kepler’s First Law: The orbit of a planet about
the Sun is an ellipse with the Sun at one focus.
Kepler’s Second Law: A line joining a planet and
the Sun sweeps out equal areas in equal
intervals of time.
According to Kepler’s second law, a
planet with an orbit like Earth’s would:
A. move faster when further from the Sun.
B. move slower when closer to the Sun.
C. experience a dramatic change in orbital speed
from month to month.
D. experience very little change in orbital speed
over the course of the year.
E. none of the above.
Kepler’s THIRD LAW
 The size of the orbit determines the
orbital period
 planets that orbit near the Sun orbit with shorter
periods than planets that are far from the Sun
3
a
=
AU
2
P
years
Kepler’s THIRD LAW
 The size of the orbit determines the orbital period
 planets that orbit near the Sun orbit with shorter periods than
planets that are far from the Sun
p = ~ 12 years
p = 1 year
Kepler’s THIRD LAW
The size of the orbit determines the orbital period
planets that orbit near the Sun orbit with shorter periods
than planets that are far from the Sun
MASS DOES NOT MATTER
Both have p = 1 year
Which of the following best describes what would
happen to a planet’s orbital speed if it’s mass were
doubled but it stayed at the same orbital distance?

A. It would orbit half as fast.

B. It would orbit less that half as fast.

C. It would orbit twice as fast.

D. It would orbit more than twice as fast.

E. It would orbit with the same speed.
Newton’s First
Law of Motion
• A body remains at rest or moves in a straight line at
a constant speed unless acted upon by an outside
(net) force.
• A rockets will coast in space along a straight line at
constant speed.
• A hockey puck glides across the ice at constant
speed until it hits something
Newton’s Second
Law of Motion
• (net)Force = mass x acceleration or
Fnet = m x a
• Acceleration is the rate of change in velocity – or
how quickly your motion is changing.
• Three accelerators in your car!!
Newton’s Third
Law of Motion
• Whenever one body exerts a force on a second
body, the second body exerts an equal and opposite
force on the first body.
• Don’t need a rocket launch pad!
• The Bug and the Windshield – who is having the
worse day?
Newton’s Laws of Motion &
Gravitation
• All my favorite Projectiles behave like this!!!

Velocity
Force
Acceleration
 The gravitational
force results in an
acceleration.
 All objects on Earth
fall with the same
acceleration known
as g.
 g = 9.8 m/s2
F
g
w
eight m
 Orbits describe one body
falling around another.
 The less massive object
is a satellite of the more
massive object.
 The two bodies orbit a
common center of mass.
 For a much smaller
satellite, the center of
mass is inside the more
massive body.
 An astronaut inside an
orbiting space shuttle
will experience free fall
because he is falling
around Earth at the
same rate as the shuttle.
 He is not weightless.
 Gravity provides the
centripetal force that
holds a satellite in its
orbit.
 Uniform circular
motion: moving on a
circular path
at constant speed.
 Still experiencing an
acceleration since the
direction is constantly
changing.
 Circles and ellipses are bound orbits.
 Objects with higher orbital speeds can
escape bound orbits to be in unbound orbits.
 Parabolas and hyperbolas are examples.
Newton’s Law of Gravitation
• Newton’s law of gravitation states: Two bodies
attract each other with a force that is directly
proportional the product of their masses and is
inversely proportional to the square of the distance
between them.

Gm
m
1
2
F

grav
2
d
What the ….? I thought I understood gravity?
Newton’s Law of Gravitation
• To figure out the gravitational force just multiply the
mass of the two things together then divide by the
distance they are apart (squared).

Gm
m
1 2
F

grav
2
d
m1
d
m2
Tutorial: Newton’s Law and
Gravity – pg.29
 Work with a partner
 Read the instructions and questions carefully
 Talk to each other and discuss your answers with each
another
 Come to a consensus answer you both agree on
 If you get stuck or are not sure of your answer ask
another group
 If you get really stuck or don’t understand what the
Lecture Tutorial is asking as one of us for help
Lab This Week
•
Hydrogen Energy Levels
•
What you need to know:
You get to explore the possible energy
transitions for Hydrogen.
Reading ahead in Chapter 5 will help.
•
•
Tutorial: Newton’s Law and
Gravity – pg.29
 Work with a partner
 Read the instructions and questions carefully
 Talk to each other and discuss your answers with each
another
 Come to a consensus answer you both agree on
 If you get stuck or are not sure of your answer ask
another group
 If you get really stuck or don’t understand what the
Lecture Tutorial is asking as one of us for help
Concept Quiz—Earth’s Position
Assume Earth were moved to a distance from the Sun
twice that of what it is now. How would that change the
gravitational force it would experience from the Sun?
A.
B.
C.
D.
E.
It would be half as strong.
It would be one-fourth as strong.
It would be twice as strong.
It would be four times as strong.
It would not change.
MATH TOOLS 4.1
 The gravitational acceleration at the
surface of Earth, g, can be solved for by
using the formula for the gravitational force
and Newton’s second law.
 The m cancels.
 g is the same for all
objects at the same R.
Newton’s Law of Gravitation
g ~ 10 m/s2 “the acceleration of gravity” & g x m is your weight!
• Newton’s law of gravitation states: Two bodies attract each other with a
force that is directly proportional the product of their masses and is
inversely proportional to the square of the distance between them.
Gm
m
1 2
F
 2
grav
d
2


Nm

11
24


6
.
67

10
5
.
97

10
kg
m
object
2


kg

F

grav
6 2
6
.38

10
m
F
gm
grav




Concept Quiz—Gravity and Weight
Your weight equals the force between you and Earth.
Suppose you weigh 600 newtons. The force you exert on
Earth is:
A. 600 newtons.
B. much smaller than 600 newtons because your mass is
much less than Earth’s.
C. exactly zero, since only massive objects have gravity.
Concept Quiz—Earth and Moon
Earth and the Moon have a gravitational force between
them. The mass of the Moon is 1.2 percent of that of
the Earth. Which statement is incorrect?
A. The force on the Moon is much larger than that on
Earth.
B. The forces are equal size, even though the masses are
different.
C. The Moon has a larger acceleration than Earth.
CONNECTIONS 4.1
 Gravity works on every part of every body.
 Therefore, self-gravity exists within a planet.
 This produces internal forces, which hold the
planet together.
CONNECTIONS 4.1
 There’s a special case: spherically
symmetric bodies.
 Force from a spherically symmetric body is the
same as from a point mass at the center.
MATH TOOLS 4.2
 The velocity of an object traveling in a
circular orbit can be found by equating the
gravitational force and the resulting
centripetal force.
 This yields:
 You can solve for the period by noting that
 This yields
Kepler’s third law:
MATH TOOLS 4.3
 In order to leave a planet’s surface, an
object must achieve a velocity greater than
the planet’s escape velocity.
 Therefore, Earth’s escape velocity is
 Newton derived Kepler’s laws from his law
of gravity.
 Physical laws explain Kepler’s empirical
results:
 Distant planets orbit more slowly; the
harmonic law and the law of equal areas
result.
 Newton’s laws were tested by Kepler’s
observations.
CONNECTIONS 4.2
 The gravitational
interaction of three
bodies leads to
Lagrangian
equilibrium points.
 These are special
orbital resonances
where the object at
that point orbits in
lockstep.
 SOHO is near L1.
Lab This Week
•
•
•
•
•
Blackbody Curves and UBV Filters
What you need to know:
A Blackbody is a perfect emitter.
Stars are NOT blackbodies.
The Stefan-Boltzmann Law (Chapter 5): F = sT4