Transcript Universal Gravitation

Universal Gravitation
Physics
Warm-Ups
What is Newtonian
Synthesis?
Same laws of physics
that apply to Earth, also
apply to the heavens
Warm-ups
A physics student has a mass of 70 kg
and is separated from Earth by a
distance of 6.60 x 106 m. What is the
force of gravity between the physics
student and Earth, if the mass of the
Earth is 5.98 x 1024 kg?
686 N
Warm-Ups
 Suppose that two objects attract each
other with a gravitational force of 16 units.
If the mass of both objects was doubled,
and if the distance between the objects
was doubled, then what would be the new
force of attraction between the two
objects?
 It would not change
Warm-ups
If the mass of the moon is 7.34 x
1022 kg, the radius is 1.74 x 106
m, and G = 6.67 x 10-11 Nm2/kg2,
what is g on the moon?
1.62 m/s2
Speed of an Object in Circular
Orbit
 V = √ Gm/r
V
: speed of object in orbit
 G : 6.67 x 10-11 Nm2/kg2
 m : mass that the object is orbiting
 r : distance between two objects
(orbiting object and mass that it is
orbiting)
Example Problem
If the mass of the sun is 2 x 1030 kg
and the distance between mars and
the sun is 2.28 x 1011 m, what is the
orbiting speed of mars around the
sun?
2.42 x 104 m/s
Period of Orbiting Object
T = 2*pi*r √r/Gm
r
: distance between 2
objects
 G : 6.67 x 10-11 Nm2/kg2
 m : mass that object is
orbiting
Example Problem
For the previous example
problem, find the orbiting
period of mars around the
sun.
5.9 x 107 s
Satellite Warm-UP
The mass of the Earth
is 6 x 1024 kg and the
radius of the Earth is
6
6.4 x 10 m. What is the
value of g 1000 km
above Earth?
7.31 m/s2
Weightlessness
Why do astronauts
orbiting in space feel
weightless?
Weightlessness
Astronaut and spaceship
are free falling at the same
rate of acceleration (g) and
the normal force on the
astronaut is 0
Weightlessness
How does a spaceship stay
in orbit if it is free falling?
Given a fast enough initial
velocity and misses the
Earth because it is curved
Einstein’s Theory of Gravity
Gravity is not a force, but an
effect of space itself
A mass causes space to be
curved, an other masses are
accelerated because of the way
they follow this curved space
Einstein’s Theory of Gravity
Called General Theory of
Relativity
During an eclipse, light was
deflected by the sun, which
provided evidence for this
theory
Moon of Saturn Problem
Mimas, a moon of Saturn,
has an orbital radius of 1.87
8
x 10 m and an orbital
period of 23 hours
(convert). Find the mass of
Saturn.
5.65 x 1026
Gravitational Field
Strength
Gravitational force per
unit mass on an object
g = Fg/m
Units: Newton/kg
Gravitational Field Strength
Lines of
force
directed
inward
Gravitational Field Strength
The gravitational field strength is 7.83
N/kg at the altitude of the space
shuttle. (a) How much does an 80 kg
astronaut weigh on the shuttle? (b)
How much did the astronaut weigh on
earth? (1 N = .22 lbs.)
a) 137.8 lb b) 172.5 lb
Review for Quiz
Work in groups to finish
back of review handout , pg.
188 (#6,7), and pg. 196 (#52)
Have me check off your
paper when your group is
done