Gravity 01/13/2014
AST201
Week 2
Tues. Jan 14 – Lecture 3
Lecture Notes:
*do assignment 1 – due Friday
Time flows at different rates for any two people in motion relative to one another!
*moving clocks run slow
if Jackie is moving and you are not, her time goes slower
Observers in motion relative to one another also disagree about their lengths
moving makes things shorter
you could fit a 10ft ladder in a 9ft barn if it moved fast enough
Twin Paradox (only a paradox if you don’t have relativity to help you)
imagine you get in a spaceship and travel to the star Vega at 99.9% of the speed of light
Earth to Vega distance = 25 light years
Light year is the distance light travels in one year –not speed (speed of light)
LIGHT YEAR IS NOT TIME
How far is a light year? A: some giant number 9.5 trillion km There is nothing a light year away from the earth – sun is 8 light minutes away (would be somewhere
between our galaxy and the next one)
“highwaydrivingminute” if you go 100km/h, you travel 1.6km in a minute
1 highwaydrivingminute = 1.6km
Q: According to special relativity, if someone on earth measures Vega to be 25 light years away, you in your
ship headed to Vega at 0.999c will measure the distance to be: 25 light years
You on your ship will have the length contracted so you will think it will be less than 25 light years
Q: The person on earth sees you travel 25 light years at 0.999c they think your trip takes: a little more than
25 light years (if you travel just slower than 100km/hr, and have to travel 100km, it will take you just slightly
more than an hour)
Has nothing to do with relativity
Q: You on the ship measure the distance between Earth and Vega as only 1 light year. Thus, for you the trip
to Vega takes only: one year because your year is a light year
how fast are you going? 0.999c going 1 light year should take about a year
time travel is possible – you can always travel into other people’s future if you move very quickly – one way
trip into the future – cant go into the past, cant go to future then come back
http://www.scivee/tv/node/2415
Black holes
four fundamental forces of nature – everything in galaxy can be described with 4 fundamental forces of
nature
Strong nuclear force (hold atomic nuclei together) strongest
Electromagnetism (makes atoms cling to each other) eg. friction (infinite range)
Weak nuclear force (breaks atoms apart)
Gravity (makes masses attract one another) (infinite range) – barely exists but makes a huge contribution
Q: do stars on one side of our galaxy feel gravity from stars on the other side? A: yes
Tutorial
Alice is moving towards you at 50km/hr. you throw a ball in her direction at 50km/hr. what does she see the
ball doing? Speed change of position – rate of movement
Velocity – rate of change of position in a certain direction
Acceleration – change of speed – rate it increases or decreases
Frame of reference – point of view/what you see vs. what someone else sees
Two people have same reference if they are not moving relative to one another
(same place is two people moving at same velocity)
Words like “stationary” and “moving” have to be relative to something
Two key absolutes:
The laws of physics are the same in reference frames that are not accelerating but movement does not
matter
The speed of light is invariant (always measured to be the same) in a vacuum
In a vacuum means through space to make the statement correct
Speed=distance/time
Time=distance/speed
^if you don’t have a clock how do you tell the amount of time has gone by with the beanbag in the air? –
need distance and speed
would the person running and a stationary observer agree on the following?
ahow much distance the beanbag has travelled? A: no because stationary sees arc, runner sees straight
path
bhow much time the beanbag has spent in the air? A: yes because the speeds must be different
how would your answers to 2 change if the beanbag always travelled at same speed? – time would be
different
Time dilation
Time runs more slowly in the reference frame of anyone moving relative to you
The faster the other reference frame is moving, the more slowly time passes with it Jan 14 Reading 01/13/2014
Reading Notes: Jan 14 Reading 01/13/2014
Sections S3.1,S3.2 (only the part called “What is curved spacetime?”), S3.3, S3.4
Figures S3.1, S3.2, S3.3, S3.4, S3.12, S3.13, S3.15, S3.18, S3.19, S3.20, S3.21
Key Notes:
Two ways to think about gravity
Name the four fundamental forces of nature, rank them by relative strength, and identify what
role each one plays in the universe
Describe how forces are related to accelerations
Distinguish between Newtonian gravity and Einstein’s general relativity
Explain the Equivalence Principle and describe what it tells us about the nature of gravity
Describe how the presence of a mass deforms spacetime
Describe gravity in terms of spacetime curvature
S3 – Spacetime and Gravity
S3.1 – Einstein’s Second Revolution
If you launch two probes in opposite directions from a space station, they will meet as they orbit the earth
Einstein’sgeneral theory of relativity published in 1915
What are the Major Ideas of General Relativity?
The special theory of relativity applies only to situations in which we are not concerned with the effects of
gravity
The three dimensions of space and the one dimension of time together = an inseparable fourdimension
combination called spacetime
Einstein’s General Relativity theory – matter shapes the ‘fabric’ of spacetime in a manner analogous to the
way heavy weights distort a trampoline (the greater the mass, the greater the distortion of spacetime) Jan 14 Reading 01/13/2014
Since matter is within spacetime not placed on it, it is difficult to visualize
The distortions (based on mass) determine how other objects move through spacetime
The stronger the gravity, the more slowly time runs
Universe has no boundaries and no center but may have finite volume
Large masses that have rapid changes in motion/structure emit gravitational waves that travel at the
speed of light
Is All Motion Relative?
Special relativity tells us there is no answer to the Q: who is moving?
^ the situation is different if one of the reference frames is accelerating rather than traveling at constant
velocity
motion is no longer relative with acceleration
whenever you feel weight (not weightless) its due to equivalence principle
you cannot tell the difference between being in a room on earth vs. in a room accelerating through space
equivalence principle allows us to treat all motion as relative – leads to general relativity
S3.2 – Understanding Spacetime
What Is Curved Spacetime?
Same concept of twodimensional flat surface being curved but fourdimensional spacetime can also be
curved
Cannot visualize curvature of threedim. space or fourdim. Spacetime
Shortest distance between two points on a flat plane is always a straight line – cannot be applicable to
Earth’s surface because it is curved
Great circle – any circle around the earth’s surface that has its center at the center of Earth (full
diameter)
Space and spacetime have a flat geometry (rules of geometry on a flat plane)
Spherical geometry, saddleshaped geometry Jan 14 Reading 01/13/2014
Geometry of the universe is a mix of all three types but has to edges or center
“straight” lines in curved spacetime – if the straightest possible path is truly straight=flat region, if it is curved
=shape of curve is the shape of spacetime
Einstein’s equivalence principle – if you are floating freely, then your worldline is following the straightest
possible path through spacetime. If you feel weight, then you are not on the straightest possible path
all orbits must therefore represent paths of objects that are following the straightest possible path through
spacetime ▯shapes and speeds of orbits reveal geometry of spacetime ▯new view of gravity
S3.3 A New View of Gravity
Newton's law of gravity claims that every mass exerts a gravitational attraction on every other mass no
matter how far away they are from each other "action at a distance"
Einstein's equivalence principle allowed explanation of action of gravity w/o requiring any longdistance
force
What is gravity?
General theory of relativity removes idea of action at a distance by stating Earth feels no force tugging on it
in its orbit, allowing straightest possible path through spacetime
What we perceive as gravity arises from the curvature of spacetime
Rubber Sheet Analogy
No friction in space
Rubber sheet represents spacetime in region where it has flat geometry radial distances between circles
shown are all same. If you rolled a marble across sheet, it would roll in straight line at constant speed;
Newton's first law of motion (objects move at constant velocity when not affected by gravity or any other
forces)
Spacetime around sun Sun is heavy mass causing sheet to curve and form bowllike depression. Circles
more widely separated near bottom of bowl, showing gravity becomes stronger and curvature of spacetime
becomes greater as we approach Sun's surface (weakens near center). If you rolled a marble across sheet,
it would not go straight b/c sheet is curved, so it'd follow straightest possible paths given curvature of sheet
path would depend on speed + direction it was rolled with. Marbles rolled slowly/close to center would
follow elliptical/circular orbits around center, marbles rolled farther/faster could loop around center on
unbound parabolic/hyperbolic paths
General relativity states depending on speed + direction, planets/objects in space can follow
circular/elliptical/unbound parabolic/hyperbolic orbits (same shapes Newton's universal law of gravitation
allows) Jan 14 Reading 01/13/2014
Rather than orbiting b/c of mysterious force exerted on them by Sun, planets orbit b/c they follow straightest
possible paths allowed by shape of spacetime around them. Central mass of Sun not
grabbing/communicating w/ them or influencing motion in anyway. Instead, it's dictating shape of spacetime
around it
A mass like Sun causes spacetime to curve, curvature of spacetime determines paths of freely moving
masses like planets
Weightlessness in Space
Astronauts in space Earth curves spacetime in way that makes satellites go round they're following
straightest path as well as the spacecraft
Must launch spaceships at escape velocity to escape bowlshaped region around Earth (marble shot fast
enough to roll out of bowl + onto flatter region surrounding); astronauts would only feel weight when
deviating from straightest path
Limitations of the Analogy
It's a 2D representation of a 4D reality
3 important limitations:
Rubber sheet is supposed to represent universe, but doesn't make sense to place Sun upon universe
(masses should be within sheet) Jan 14 Reading 01/13/2014
Doesn't allow to show fact that planets o not all orbit Sun in precisely same plane, just that they're different
distances/higher or lower elliptical orbits
Doesn't show time part of spacetime, each orbit of Sun Earth returns to same place in space relative to Sun
but to a time a year later. (moves forward in time, stationary in space relatively)
What is a black hole?
Greater curvature of spacetime = stronger gravity. 2 ways to increase gravity;
Lager mass causes greater curvature (Newton's law of gravity increasing mass of object increases
gravitational attraction)
Leave its mass alone but increase its density by making it smaller inside (Newton surface gravity on object
of specific mass grows stronger as object shrinks in radius)
If object becomes so small with same mass it can become a bottomless pit a hole in the observable
universe (black hole)
Newton's laws don't envision possibility of holes in universe
Black hole place where spacetime is so curved nothing that falls into it can ever escape
Event horizon boundary that marks "point of no return", b/c events that occur within its boundary can have
no influence on observable universe
How does gravity affect time?
Gravity affects time as well as space (arises from curvature of spacetime)
Astronauts in still spaceship will have same flashing time, when spaceship accelerates astronauts are no
longer weightless; astronauts are constantly changing reference frames. Astronaut in front of ship's
reference frames are always carrying them away from point at which back astronaut's watch flashes
back's light takes longer to reach you than if still. Opposite for back.
Time runs slower at back of accelerating spaceship and faster at front
Equival
More
Less
