2. ASTRONOMY 181

3. The SPECIAL Theory of RELATIVITY

4. Postulate 1
All physical laws must be equivalent when described in INERTIAL reference frames.

5. Postulate 2
The speed of light must be measured to be the same by all observers in inertial reference frames.

6. Consider two planets that are very distant from each other...

7. They may communicate using pulses of light ….say, 3 min apart

8. A rocket ship traveling between the planets would see the flashes…but how far apart?
From the point of view of the rocket crew, it could be that the flashes appear 6 min apart

9. Let’s assume that the rocket has its own beacon that flashes when they see a flash…
From the point of view of the rocket, they must flash every 6 min
From the point of view of the observer , the flashes are simultaneous…3 min apart!!!

10. The reverse situation: signals are sent from right to left…
From the point of view of the rocket, they must flash every 1.5 min
From the point of view of the observer , the flashes are simultaneous…3 min apart!!!

11. Recall the Doppler shift…

12. AS IT APPROACHES US WE WOULD SEE A FLASH EVERY 3 MIN
If the rocket flashes every 6 min:
AS IT APPROACHES US WE WOULD SEE A FLASH EVERY 3 MIN
AS IT RECEEDS US WE WOULD SEE A FLASH EVERY 12 MIN

13. If the rocket travels from one planet to the other and back again emitting a total of twenty flashes, 10 out and 10 back at a rate of 1 every 6 min, the flashes can be used to time the trip.

14. Outbound: 10 flashes @ 6 min/flash = 60 min
From the point of view of the rocket, flashes are emitted every 6 min for the whole trip…
Outbound: 10 6 min/flash = 60 min
Inbound: min/flash = 60 min
Total = 120 min = 2 hours

15. Outbound: 10 flashes @ 12 min/flash = 120 min
From the point of view of the planet, flashes are emitted every 12 min on the way out and every min for the trip back…
Outbound: min/flash = 120 min
Inbound: min/flash = 30 min
Total = 150 min = 2.5 hours

16. TIME DILATION!!! 2 hours have passed on the rocket
2.5 hours have passed on the planet
TIME DILATION!!!

18. EXAMPLE: A trip to Pluto
Pluto is 5 light hours away.
0.8c c
Earth System
6.25 hr hr
Rocket System
3.75 hr
25 minutes

19. In this course, we have learned:
How the length of the earth year is known.
How the shape and size of the earth is known.
How the motion of the earth is known.
How the mass of the earth is known.
How the length of the periods of the planets are known.
How the mass of the planets are known.
How the chemical composition of celestial objects is known.
Where many of the elements come from.
How the evolution of stars is known.

20. How do we know the SIZE of our UNIVERSE? How do we know the AGE
TWO IMPORTANT QUESTIONS REMAIN…
How do we know the SIZE
of our UNIVERSE?
How do we know the AGE

21. Remember that, looking out into space is looking backward into time.
OUR ESTIMATION OF THE AGE OF THE UNIVERSE DEPENDS ENTIERLY ON OUT ESTIMATION OF HOW LONG IT WOULD TAKE THE UNIVERSE TO GET THIS BIG

22. So, how big is the universe….
A QUICK REVIEW:

23. Radar Ranging:
We measure distances in our solar system by bouncing radio waves off planets, for example.
Geometry helps us to interpret the results.
Within one light-hour.

25. Parallax:
The distances to objects are determined by observing apparent shifts with respect to background objects.
100 light-years

26. Main-Sequence Fitting:
We know the distance to the Hades Cluster in our own galaxy.
Comparing the luminosity of main sequence stars in Hades to the main-sequence stars of other clusters in our galaxy allows us to infer their distances.
100,000 light-years

28. Cepheid Variables: There is a period-luminosity relation for Cepheids.
Studying this relationship for Cepheids nearby allows us to determine the luminosity of Cepheids in other, nearby galaxies.
10,000,000 light-years

31. Distance Standards:
Luminosities of white dwarfs in nearby galaxies are determined.
There is a rotational period-luminosity relation for galaxies allowing us to determine the luminosities of more distant galaxies. (Tully-Fisher Relation)
10,000,000,000 light-years

36. Abell 1835 IR 1916: Virgo Cluster: Red shift Factor 11

37. IMPORTANT Time Dilation Distance Luminosity Relation
Distance Standards
Stellar Parallax
Cepheid Variables

38. NEXT TIME:
The END
OF THIS COURSE
AS WE
KNOW IT…