1. Gravity Flashcards
What does Newton’s law of gravity predict about planet orbits?
That they orbit the sun in elliptical trajectories
What is Kepler’s first law?
That all planet orbits are ellipses
What is Kepler’s second law?
Planets sweep out equal areas in equal times
This is due to the conservation of angular momentum
What is Kepler’s third law?
The square of the orbital period, P is equal to the cube of the semi major axis, R_a
What is the perihelion of a planet?
The point at which it is closest to the sun
What does Newton’s law of gravity fail to predict?
The precession of the perihelion of planets due to gravitational interaction
How is the observation of the precession of the perihelion accounted for?
- Most of it due to gravitational pull from different planets e.g. Jupiter
- Einstein’s GR says the planets move along geodesics in space-time geometry
What is a “prograde” perihelion?
A precession in which the direction of the perihelion is in the direction of orbital motion
State Einstein’s equivalence principle
Intertial and gravitational masses are the same thing
Describe how the equivalence principle can be applied to the motion of light in frame K and K’ for horizontal motion
Frame K (at rest): Light moves along a horizontal line
Frame K’ (Accel. upwards): Light has some deflection below the horizontal line
Equiv. principle: K’ frame is the same as a new frame at rest which is in a gravitational field
What does an observer notice about light that travels vertically upwards in frame K vs K’?
Frame K (rest): No change in freq.
Frame K’ (Const accel): Observed freq has changed due to gravitational redshift
How is Newton’s field equation obtained?
- Take the gradient of the potential -GM/r, and F = M grad V.
- Use Laplace on Green function
Explain how you translaste between Newton’s field equation and Einstein’s equations
Laplace = curvature
Potential = space time metric
Mass density = Energy density
What are the two principles of special relativity
- Laws of nature are the same in all intertial frames
- Speed of light is the same in all inertial frames
Briefly explain the concept of time dilation for a clock in Frame K
Clocks that are moving run slowly
- Clock in K measures cT = cT
- Clock in K’ measures cT’ = γcT
- Time elapsed in K’ is longer
What do measurements of the time or distance depend on ?
The observer
What are invariants and why are they useful
Things that are the same in all frames of reference
What is the metric of special relativity?
Minkowski invariant
(x’-ct’)(x-ct)
Explain why the phase of a wave is an invariant quantity
The phase counts the number of waves in any wave train and all observers must agree on this
Describe the Minkowski s-t geometry
Inside cone is time like
Along the cone is light like
Outside cone is space like
Future is above the past
State the values of the velocity invariant for space, light and time like trajectories
> 0 is space like
=0 is light like
<0 is time like
When is a set “space like”?
If at every point, every vector tangent to it is space like
When is a set “time like”?
If there is at least 1 vector tangent to it that is time like
Give examples of space and time like sets
Space: A plane - ct = ct’ = 0 and sphere -c^2 t^2 + x^2 + y^2 = -R^2
Time: A plane - x= x’ = 0 and sphere -c^2 t^2 + x^2 + y^2 = +R^2
What is the Minkowski metric?
The covariant η_(μν) type (0,2) tensor. 00=1, 11=22=33 = 1q
What is the name of the sign convention for the covariant tensors
The signature and we use (-, +, +, +)
Explain the similarities and differences between a vector and a tensor
- They both have a magnitude
- A tensor hcan have several directions whereas a vector just has one
What is the proper time?
The time measured by an observer who is moving along the trajectory
How do free particles travel?
In straight lines at constant speeds (N1)
Describe how massive and massless particles move in Minkowski space
Massive particles move along time like trajectories
Massless particles move along null (light) like
What is the stress-energy-momentum tensor
The source of the gravitational field in general relativity which replaces the mass of Newton’s theory
In the continuity equation, what do the values of mu represent
mu = 0 is the conservation of mass
mu = i are the N-S equations
State the similarities and differences between the stress energy momentum tensor and the electromagnetic field tensor
Both symmetric, type (0,2) and conserved
- EM field is also traceless
