Transcript Gravitational redshift of Sirius B Equivalent velocity 80 km/s

A recap of the main points so far…
Observers moving uniformly with respect to each other
• do not agree on time intervals or distance intervals
• do not agree about the simultaneity or otherwise of
events
A moving clock appears to run slow – time dilation
A moving ruler appears short – length contraction
•A moving object has an increased relativistic mass
•Mass can be converted into energy (and vice-versa)
E = m c2
The Twins Paradox
Symmetry
As far as the observer on Earth is concerned, a
clock on the spaceship is running slow and
lengths are contracted in the direction of motion.
As far as the observer on the spaceship is
concerned, a clock left on Earth is running slow
and lengths are contracted in the direction of
motion.
The frames of reference are equivalent?
Hammer and feather on the moon
Underlying principles of General
Relativity
The Equivalence
Principle
No difference between a
steady acceleration and
a gravitational field
Gravity and Acceleration cannot be distinguished
V = a h/c
h
Equivalence principle – this situation should be the same
h
Gravitational
field
Consequences I. Gravitational Redshift
Size of effect (doppler
shift equivalent speed)
Earth
0.2 m/s
Sun
0.6 km/s
White Dwarf
70 km/s
Neutron Star 100,000 km/s
Black-hole
infinite
Gravitational redshift of Sirius B
Equivalent velocity 80 km/s
Corrections to GPS
Orbital radius 26,000 km
gh/c2 = 0.0000000026
Clocks “on the ground”
would lose about 0.2 ms
per day (actually a bit
less).
Clocks on the GPS
satellites run intentionally
slowly!
Lensing of distant galaxies by a foreground cluster
QSO 2237+0305
The Einstein cross
Abell 1689
Plus derived
Mass Map
Einstein Rings
Galaxies at 3, 6 and 11 billion light years away