Is there gravity in space?
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Is there gravity in space?
Why do objects fall at a rate of 9.8 m/s2?
• What makes them fall?
• Would this rate change on a larger planet?
• Why?
Newton’s Laws and Forces
• What are they?
– Law of balanced forces (constant velocity)
– Law of unbalanced forces F = ma (acceleration)
– Law of force pairs
• What is force?
• A push or a pull
• Is ag (9.8 m/s2) a force?
• No. It is acceleration in response to a force.
Newton’s Big Idea
• Did Newton discover gravity?
• NO! He discovered gravity is universal. Everything pulls on everything else in the universe in a way that only involves mass and distance. Gravity is not unique to earth.
Why was this so important?
• Since the object is accelerating, an invisible force must be present
• The force is acting at a distance.
• The force not limited to earth.
• Newton wondered if the force extended as far out as the moon. This could explain why the moon moved in a curved path around the earth!
By such reasoning, Newton came to
the conclusion that any two objects in the Universe exert
gravitational attraction on each
other, with the force having a
universal form.
2
21
d
mGmF
Is there gravity in space?
• Myth: there is no gravity in space• Fact: gravity is everywhere.• When you stand next to another person, there is
gravitational force. Why don’t you feel it?• Your relative masses are too small so you only sense
gravity in relationship to the earth. You feel this as weight.
• Gravity is the weakest of the four fundamental forces.
• The other three are electromagnetic, strong nuclear, and weak nuclear force.
Newton’s Law of Universal Gravitation:
• Law of Universal Gravitation - there is a force of attraction between any two objects with mass.
• The greater the mass the greater the force
• The force decreases as the square of the distance increase
2
21
d
mGmF
Newton’s Law of Universal Gravitation
F = Force of attraction (N)
G = 6.67 x 10-11 Nm2/kg2
m1 = mass of object one (kg)
m2 = mass of object two (kg)
d = distance between the centers of the two objects (m)
2
21
d
mGmF
Accepted Values
• G = 6.67 x 10-11 Nm2/kg2 This is the Gravitational Constant
• me = mass of the Earth
(5.97 x 1024 kg)
• re = radius of the Earth
(6.37 x 106 m)
Ex. A What is the force of attraction between a 6 kg object and a 20 kg object separated by a distance of 5 m?
(6.67 x 10-11 Nm2/kg2 )(6 kg) )(20 kg)
F = [(5m)2]
F = 3.20 x 10-10 N
Repeat this problem changing masses and then distancesEx. A What is the force of attraction between a 6 kg object and a 20 kg object separated by a distance of 5 m?
(6.67 x 10-11 Nm2/kg2 )(6 kg) )(20 kg)
F = [(5m)2]
F = 3.20 x 10-10 N
• To solve for these kinds of problems, substitute small numbers for masses and distance. Disregard the G.
• What happens to gravitational force if mass of one object is doubled?
• Force is doubled
• What happens to gravitational force if mass of both objects is doubled?
• Force is 4 times as great
How does mass affect Gravitational Force?
How does distance effect Gravitational Force?
• What happens to gravitational force if the distance between objects is doubled?
• The force decreases to 1/4th as much
• What happens to gravitational force if the distance between objects is tripled?
• The force decreases to 1/9th as much
• What happens to gravitational force if the distance between objects is ten times as much?
• The force decreases to 1/100th as much
Ex. B The gravitational force between two masses is 8 N? How does the force change if both of the masses are doubled and the distance tripled?
Ex. B The gravitational force between two mass is 8 N? How does the force change if both of the masses are doubled and the distance tripled?
• 3.55 N
Ex. C Calculate the distance between two objects with identical masses of 400 kg if the gravitational force between them is 2.45 x 10-11 N?
Ex. C Calculate the distance between two objects with identical masses of 400 kg if the gravitational force between them is 2.45 x 10-11 N?
d = Gm1m2
F
Ex. C Calculate the distance between two objects with identical masses of 400 kg if the gravitational force between them is 2.45 x 10-11 N?
d = Gm1m2
F
6.67 x 10-11 Nm2/kg2 )(400 kg) )(400 kg)
d = (2.45 x 10-11 N)
Ex. C Calculate the distance between two objects with identical masses of 400 kg if the gravitational force between them is 2.45 x 10-11 N?
d = Gm1m2
F
6.67 x 10-11 Nm2/kg2 )(400 kg) )(400 kg)
d = (2.45 x 10-11 N)
d = 4.36 x 105 m
Example D: What is the force of attraction between you and your closest neighbor in this class?
• 1 kg = 2.2 pounds
• Assume you are spheres and your centers are 0.75 meter apart.
• For two people at 150 pounds:
(6.67 x 10-11 Nm2/kg2 )(68.2kg) )(68.2 kg)
F = (0.75m)2
F = 5.52 x 10 -7 N
Example E: What is the force of attraction between you and the earth?
What would you use for m?
The mass of the earth: 5.97 x 1024 kg
What would you use for d?
The radius of the earth: 6.37 x 106 m
(6.67 x 10-11 Nm2/kg2 )(5.97 x 1024 kg) )(68.2 kg)
F = [ (6.37 x 106 m)2 ]
F = 670 N
The force between you and the earthF = 670N m = 68.2 kg
• Most of the force is dependent upon?
• Mass of the earth
• Do you know what else this value describes?
• Your weight!
• F = ma
• Use your mass and F between you and earth. Solve for a.
• Did you get 9.8 m/s2 ? WEIRD!!!!!
Example F: What is the force of attraction between you and the earth if you are 8.00 x 104
m above the surface?
What would you use for d?
The radius of the earth + height above surface:
6.37 x 106 m + 8.00 x 104 m
(6.67 x 10-11 Nm2/kg2 )(5.97 x 1024 kg) )(68.2 kg)
F = [ (6.37 x 106 m + 8.00 x 104 m)2 ]
F = 650 N
Remember when you were on the surface your weight was 688N! You just lost weight!
The force between you and the earthwhen you are high above:F = 650N m = 68.2 kg
• F = ma
• Use your mass and F between you and earth. Solve for a.
• Why is it no longer 9.8 m/s2 ?
• You have increased the distance between Earth and you, and therefore the affects of gravitational attraction are less!
Weightlessness: Does it exist?
• True weightlessness does not exist.
• In order to be truly weightless you would have to be infinitely far from all other objects with mass, since this is not possible, all objects have weight.
Weightlessness
• Astronauts are said to be weightless but in actuality they are in freefall toward the Earth just as their spaceship is. Hence they are both accelerating at the same rate so you have the appearance of weightlessness.
• The misnomer (wrong name) came about due to the fact that if you attempted to weigh them the scale would register a value of zero since both are in free fall
• Therefore, the astronauts would weigh zero but would not have a weight of zero.
Remaining slides are FYI
Applications of the Law of Universal Gravitation The inverse square law
• Calculate the gravitational field, ie. “g”
• In relation to earth, this is only 9.8 m/s2 when on the surface of the earth. When doing calculations where objects are falling out of buildings use 9.8m/s2
because it is “close enough” but if objects are in the atmosphere we must account for distance
• Would your weight be greater at sea level or on the top of Mt. McKinley?
Acceleration due to Gravity
• When the weight of the satellite (msg) is set equal to the gravitational attraction between the earth and the satellite (Gmsme/d2), the mass of the satellite will cancel out telling us that the acceleration due to gravity at any point can be calculated.
Acceleration due to Gravity
2d
mGmgm
ses
We know:
Using the Law of Universal Gravitation
can give us our weight.
We know Fw = ma
Therefore :
Acceleration due to Gravity
G = 6.67 * 10-11 Nm2/kg2
m2 = mass of the celestial body at the center of rotation (kg)
d = distance between the centers of the two objects (m)
gGm
d
2
2
2r
mGmgm
ses
G vs g
• How is G different from g?• G is a constant. It is the same everywhere in the
universe. It describes the proportionality between force, distance, and mass.
• g is changing. It is a measure of the local gravitational field (equivalent to the local acceleration due to gravity). On earth it is 9.8m/s2. Referred to as gravitational acceleration or gravitational field. (Also can be measured in N/kg)
What is a Field?
• A field is a region in which a suitable detector experiences a force.
• A suitable detector for a gravitational field is an object with a very small mass.
• There are other “fields” besides gravity. Can you think of any others?
Sample problem
• A satellite orbits at a point 8.65 x 107 m from the center of the earth. Calculate the acceleration due to the gravitational field given the earth’s mass of 5.98 x 1024kg
• g = .0535 m/s2 or Nkg
A satellite orbits at a point 8.65 x 107 m from the center of the earth. Calculate the acceleration due to the gravitational field given the earth’s mass of 5.98 x 1024kg
(6.67 x 10-11 Nm2/kg2 )(5.98 x 1024 kg) )
g = [ (8.65 x 107 m)2 ]
g =
When would it equal 9.8m/s2?
• When the object is on the surface of the earth.
• Try it: given radius of earth as 6.37 x 106
WHAT IS THE DIFFERENCE BETWEEN THESE TWO EQUATIONS?
FGm m
d
1 2
2 gGm
d
2
2
This formula describes the force of gravitational attraction between two objects
FGm m
d
1 2
2
This formula describes the acceleration due to the Force of Gravity. It measures the gravitational
field exerted by a massive object.
gGm
d
2
2
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