ASTRONOMY 181

The SPECIAL Theory of RELATIVITY

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

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

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

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

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

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!!!

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!!!

Recall the Doppler shift…

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

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.

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 flashes @ 6 min/flash = 60 min Inbound: 10 flashes @ 6 min/flash = 60 min Total = 120 min = 2 hours

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 3 min for the trip back… Outbound: 10 flashes @ 12 min/flash = 120 min Inbound: 10 flashes @ 3 min/flash = 30 min Total = 150 min = 2.5 hours

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

EXAMPLE: A trip to Pluto Pluto is 5 light hours away. 0.8c 0.999999c Earth System 6.25 hr 5.000005 hr Rocket System 3.75 hr 25 minutes

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.

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

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

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

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.

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

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

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

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

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

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

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