Gravitational Interactions

1
Chapter 13

• Gravitational Interactions

2
Newton Gravity

• Newton did not discover gravityhe discovered
  that gravity is universal
• The same force that pulls an apple off of a tree
  holds the moon in orbit AND holds both the Earth
  and the moon in orbit around the sun
• The sun also revolves as part of a cluster of
  other stars around the center of our galaxythe
  Milky Way
• Newton was not able to explain how objects can
  exert forces on one another without coming into
  contact
• Scientists later discovered that masses create a
  gravitational field in space
• A gravitational force is an interaction between a
  mass and the gravitational field created by other
  masses

3
Gravitational Fields

• Force Field exerts a force on objects in its
  vicinity
• magnetic fields, electric fields, gravitational
  fields
• Gravitational Field the type of force field
  that surrounds massive objects
• g (the gravitational field vector) depends on two
  things
• Mass
• radius
• The gravitational field is a vector with a
  magnitude of g that points in the direction of
  the gravitational force
• g Fg/m

4
Gravitational Field Strength and Free Fall

• What is the acceleration of an object in free
  fall?
• 9.8 m/s2
• Near the Earths surface g 9.8 m/s2
• Gravitational field strength and free fall
  acceleration are equivalentbut they are not the
  same thing
• If you hang a mass from a spring scale, you can
  measure the gravitational field strength
• The mass is at rest there is no measurable
  acceleration

5
Finding Gravitational Field Strength
This equation shows that gravitational field
strength depends only on mass and distance. On
the surface of any planet the value of g depends
on the planets mass and radius. This also shows
that your weight (mgmass times gravitational
field strength) will vary with location!
6
Gravitational Field Strength

• Compared to its strength at the Earths surface,
  what is the strength of a gravitational field at
  twice the distance?
• Find the gravitational field strength of Mars.
  The radius of Mars is 3.38 x 106 m and the mass
  of Mars is 6.42 x 1023 kg

7
Gravitational Field Inside a Planet

• If you dropped a rock into a tunnel through the
  Earth, what would happen?
• It would gain speed until it reached the Earths
  center, and then lose speed the rest of the way.
  Its speed at the far end of the tunnel would be
  the same as its initial speed. It would then
  fall back and repeat the motion in cyclic
  fashion.
• The rock would make a round trip in approximately
  90 minutes (the same time that it takes a close
  orbit satellite to orbit the Earth)
• As the velocity of the rock increases when
  falling into the Earth tunnel, what happens to
  the acceleration?
• It decreases as the gravitational field
  decreases, and is zero at the Earths center.
  The falling body has its maximum velocity at the
  Earths center, where both the field and the
  acceleration are zero.

8
Weight and Weightlessness

• When you step on a bathroom scale, it does not
  actually measure your weight.
• The scale measures the downward force acting on
  the scale, the scale reading equals your weight
• If your friend pushes down on you while you stand
  on the scale the scale reading will go up.
• Your weight does not change the scale reading
  now equals your weight plus the applied force.
• Due to Newtons 3rd Law, the downward force you
  exert on the scale equals the upward (normal)
  force that the scale exerts on you.

9
Weight Weightlessness

• Suppose you are in an elevator standing on a
  scale, what happens to the reading when
• the elevator accelerates while traveling upward?
• The reading increases the upward acceleration
  adds to the normal (upward) force
• the elevator travels upward at a constant speed?
• The reading does not change there is no
  acceleration (force) acting other than the
  acceleration of gravity
• the elevator accelerates while traveling
  downward?
• The reading decreases the downward acceleration
  takes away from the normal (upward) force
• the elevator travels downward at a constant
  speed?
• The reading does not change there is no
  acceleration (force) acting other than the force
  of gravity
• the cable breaks and the elevator falls downward?
• The reading would be zero there is no longer a
  support force
• This condition is called weightlessnessit is not
  the absence of gravity it is the absence of a
  support force

10
Ocean Tides

• Ocean tides are caused by the differences in the
  gravitational pull of the moon on opposite sides
  of the Earth
• The ocean nearest the moon is pulled towards the
  moon, the main body of the Earth is also pulled
  towards the moonaway from the ocean on the other
  side therefore the Earths waters are elongated
  at both ends
• There are two sets of ocean tides each day (2
  high tides and 2 low tides)
• This is because the Earth is rotating
• Ocean tides do not occur at the same time each
  day because the moon appears in the same position
  in the sky every 24 hours and 50 minutes

11
Types of Tides

• Spring tides especially strong tides
• Occur when the moon, sun and
• Earth are in line
• The gravitational forces of the
• moon and the sun both contribute
• to the tides
• Occur during full moons and new moons
• Neap tides especially weak tides
• Occur when the gravitational force of the sun and
  the moon are perpendicular to each other with
  respect to the Earth
• Occur during quarter moons
  
• (you see a ½ moon)

12
Tides

• Why doesnt the sun contribute more to tides?
• Difference
• The sun is much farther away from the Earth
  therefore there is not as much difference between
  the distance from the sun to the near side of the
  Earth and the distance from the sun to the far
  side of the Earth
• Not as much difference in the gravitational pull
  of the sun

13
Eclipses

• Lunar Eclipse the Earth is directly between the
  sun and the moon
• Solar Eclipse the moon is directly between the
  sun and the Earth

14
Phases of the Moon
15
Phases of the Moon Tides

• Earth, moon, sun alignment is usually not perfect
  
• that is why we dont have eclipses every month
• Full moon when the Earth is between the sun and
  the moon
• New (dark) moon when the moon is between the
  Earth and the sun
• Spring tides occur during full and new moons
• Half moon when the moon is half way between a
  full moon and a new moon
• Neap tides occur during half moons
• Tides are also affected by the tilt of the
  Earths axis
• Although opposite tidal bulges are equal daily
  high tides are often unequal most of the time

16
Tides in the Earth the Atmosphere

• Earth is not a rigid solidmolten liquid covered
  with a thin solid crust
• Moon-sun tidal forces produce Earth tides as well
  as ocean tidesthe surface of the Earth rises and
  falls up to 25 cm per day
• The atmosphere of the Earth also experiences
  tides
• These magnetic tides regulate cosmic rays in the
  lower atmosphere

17
Black Holes

• 2 processes continually in stars
• Gravitationbrings solar material towards the
  center
• Thermonuclear fusionsimilar to a hydrogen bomb
  pushes solar material outward
• These two processes balance each other
• When the star runs out of hydrogen, gravitation
  will collapse the star
• The star will become a black dwarf (our sun will
  become one in 5 billion years) or a black hole
• Black hole a mass that has collapsed to such a
  large density that its large gravitational field
  prevents light (anything) from escaping
• Gravitational field near a black hole is enormous
• Gravitational field beyond the original radius of
  the star is not changed (the black hole is not
  any heavier than the original star)
• Black holes are more massive than a million suns