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Astronomy 1020-H
Stellar Astronomy
Spring_2016
Day-10
Great Blizzard of 2016 – Part 2
Course Announcements
•
•
SW-3 & 4 will be due soon-ish (Fri. Feb. 12)
First, 1st Quarter observing nights: Mon. @ 7:30pm
•
Exam-1: Friday Feb. 12 (ch. 1-4)
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
Color-Card Question
 Renaissance Astronomy
 Gravity Formula
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.
 Tides are a
consequence
of gravity.
 Something closer
to an object
experiences a
stronger gravitational
pull than something
else farther away.
 Gravitational objects create Roche limits
within which the effects from their tidal forces
can destabilize other objects.
 Planets, stars, and galaxies can be affected.
 Galaxies can be distorted with tidal tails.
 Moons of planets can have great internal
activity because of tides, perhaps allowing for
conditions for life.
MATH TOOLS 4.4
 The net tidal force is the difference in force
on the two sides of the planet.
 The Moon’s tidal forces on Earth are 2.2
times as strong as the Sun’s tidal forces
on Earth, resulting in greater lunar tides
than solar tides.
Exam - 1