Transcript Goal: To understand gravity

Goal: To understand gravity
Objectives:
1)
To understand who discovered what about
gravity.
2)
To learn about the Universal nature of gravity
3)
To explore the Gravitational Constant
4)
To understand how gravity is responsible for
Tides
5)
To understand how gravity changes when you are
inside of the earth
6)
To understand how gravity can lead to Black
Holes!
Next hour we will look at orbits
Who discovered gravity?
• Discuss with a neighbor
Newton Discovers
• Newton realized that gravity extended far
beyond the surface of the earth.
• Gravity extends to the moon, and even to
the other side of the universe.
• Gravity is truly universal.
• However, it does fall off with distance.
Inverse Square Law
• Is just how it sounds.
• As you get further away from an object, the force
of gravity drops as the distance squared.
• The moon is about 60 times further from the
center of the earth than we are.
• If the gravitational force on me is 950 N on the
surface of the earth then what is the force of
Earth’s gravity on me from the orbit of the
moon?
Putting it together
• Obviously, the more mass you have the
greater the gravitational force is on you.
• Also, the more mass the other thing has,
the greater the pull.
• So, that means the gravitational force is
proportional to
• mass 1 * mass 2 / distance squared
Gravitational Constant
• The only thing left out is a constant value
which gets everything exactly right.
• This constant is noted as G (not to be
confused with g).
• G = 6.67 * 10-11 N m2 / kg2
• So, the equation is:
Force = G * mass1 * mass 2 / (radius * radius)
• Where radius is the distance between the
CENTERS of the two objects
Tides
• What causes the tides?
Tidal forces
• Tidal forces are the result of a net difference in
the gravitational force on 2 sides of an object.
• So, the part of the earth facing the moon feels a
greater tug than the part away from it.
• This creates a net force for the parts of the earth
near to and far away (near to towards the moon,
and far away is away from the moon).
• At the parts of the earth in the middle, there is no
net force.
• So, material (water mostly) goes towards the two
points of greatest force. Thus the high tide!
Basic tidal facts
• For most places on the earth, there are 2 high
tides and 2 low tides a day.
• Since the earth rotates the position of the tides is
about 10 degrees in front of the moon, and on
the opposite side of the earth from that.
• Due to local coastlines, the sizes of the tides
vary, but average to be about 1-2 m in height.
• The moon also affects land! The land tide is
about 6 inches, but is so gradual we don’t feel it.
• Finally, since the moon orbits the earth, the time
of the tides changes by about 50 minutes each
day – the same as the rise/set times of the
moon.
http://csep10.phys.utk.edu/astr161/l
ect/time/tides.html
Tide from
the sun is
10% that
of the
moon, but
enough to
affect the
Magnitude
of the
tides.
Tidally locked!
• The moon is tidally locked. That means
that the position of the “high tide” for the
ground on the moon is locked roughly into
place.
But wait, there’s MORE!
• Since the bulge is pulled forward (due to
tidal friction), that bulge will tug on the
moon, and the moon on the bulge.
• This will result in a force which slows down
the earth’s rotation ( our days increase by
2 milliseconds per day per century).
• Since energy must be conserved, the
moon gains orbital energy, and gets 4 cm
further from the earth each year!
How do we know?
• Sorry hoax enthusiasts, but we know this
by shining laser light onto mirrors we
placed on the moon (i.e. we had to be
there to do this, sorry). By finding the time
it takes to come back, they can measure
the distance to the moon accurate to a few
millimeters.
Gravity inside an object.
• If you were to drill a hole to the center of
the earth, would the gravitational force
increase or decrease as you fell down the
hole?
Only to the inside
• Only the mass inside of you counts
(assuming symmetry)
• The mass inside of you falls a lot faster
than the radius squared law.
• So, the gravitational force on you goes
DOWN.
• In fact, in the center, the force is ZERO!
Black Hole
• A black hole is an object that is either so
massive or so dense that the escape
velocity on its surface is greater than the
speed of light.
• As Einstein discovered nothing can travel
faster than the speed of light.
• Therefore NOTHING, not even light can
escape from a black hole!
No escape!
• The radius at which the escape velocity is
exactly the speed of light is called the
Schwarzschild radius.
• The Schwarzschild radius is an event
horizon.
• An event horizon is a surface where if
something were to pass through it, it is
gone (event horizon = goodbye forever).
But there’s more!
• Mass warps space. Time is relative to
space. Therefore masses warp time also!
• Tobject = Tuniversal / (1 – rs / r)1/2
• Where rs is the Schwarzschild radius (the
radius of the event horizon of a black hole)
• rs = 1.5 km * Mass of object / Mass of our sun
Black hole astrophysics
• What would happen if we swapped our
sun for a black hole of exact equal mass?
• A) The earth would be sucked into the
black hole
• B) Time on the earth would slow down
• C) The earth would be slingshot out of the
solar system
• D) Nothing would happen to the orbit of
the earth or the clocks on earth.
Black hole astrophysics
• What would happen if we swapped our
sun for a black hole of exact equal mass?
• D) Nothing would happen to the orbit of
the earth or the clocks on earth.
• Black holes are not vacuum cleaners.
They obey gravity just like everything else.
• In fact it is harder to run into a black hole
because it is so frikkn small (diameter of 3
km for one the mass of out sun).
Can we “see” black holes?
• Nope, light can’t escape.
• However, we do see them indirectly by watching
stars or accretion disks in orbit around them.
• In fact we find lots of them out there.
• In the center of every galaxy there seems to be
one.
• Ours has a 2.6 million solar mass black hole
(which is small, many galaxies have a black hole
which is over a billion solar masses)
Death of black holes?
• Turns out that black holes can die!
• This is because of Hawking radiation.
• What is this? Well… Long winded answer
coming up that won’t be on the test but is
kinda cool!
Conclusion
• We have examined the universal nature of
gravity.
• We have also seen how gravity causes
tides as well as black holes.