# Topic 3: Mapping the universeTopic 3: Mapping the universe

How far away are the stars? 3A

Parallax- The apparent change in something’s position based on line of sight

• Stars seem to shift their positions slightly against a background of fixed stars.
• The things closer to you seem to shift faster

E.g. running past a forest with a mountain background; the trees appear to move faster as you run, rather than the mountains.

Parallax angle is half the angle moved by the star.

• Closer star = bigger parallax angleàstar shift more = change in position is more identifiable
• Further star = smaller parallax angleàstar moves angle less = change in position is less identifiable
• ½ the angle is double the distance

60 arc minutes = 1 degree

60 arc seconds = 1 arc minute                                     à Thus, 3600 arc seconds = 1 degree (1 arc hour)

1 arc second = 1/3600 of a degree

Parsec- the distance to a star with a parallax angle of 1 arc second

• 1 parsec = 3 light years away

Parsec equation:  Distance = 1 / angle (arc sec)

Summer and winter example

At any two times 6 month apart, you can form an ISOCELES triangle to show the parallax angle:

At summer dawn, you are looking straight up to see a star. From the diagram below, in summer (July) the star is located to your left.

6 months later…

At winter sunset, you are looking straight up to see a star. From the diagram below, in winter (January) sunset the star is located more to the right.

If you draw to lines to the star, one line from summer and the other from January, an isosceles triangle will form. If you draw a line down the middle, the angle down the middle will be 90 degrees. The straight up lines will be equal to the parallax angle (theta).  So you can use simple maths and SOH CAH TOA to work out the length of the missing side, and you can use the equation to find the distance of the star.

Observed brightness + Luminosity

Luminosity depends on size and temperature of a star.

àBigger + hotteràmore energy given outàbrighter star

• Bigger star has a greater surface radiating energy
• Hotter star radiates more energy per second from its surface

Observed brightness is the intensity of light that reaches you.

àDepends on luminosity + distance from Earth.

• Closer to star = lights spreads over shorter distance à receiving more energyà brighter star
• Further star = lights spreads over larger distanceà receiving less energyà dimmer star

E.g. you are looking at two stars with the same luminosity, and therefore the same brightness. However, one is further way. The closer star looks brighter whilst the distant star looks dimmer. In reality, both starts have equal luminosity, but the observed brightness is different.

Huygens technique for measuring distance of stars

1. He studied Sirius (the dog), the brightest star
2. Placed a screen between sun and himself
3. Made small holes in the screen
4. Made smaller holes until the light rays that hit him was the same brightness/intensity as Sirius
5. Calculated the fraction of the sun visible to him
6. Calculated the brightness = 1/30,000 brightness of the sun
7. Then calculated the distance (Sirius is actually x500,000 distant than sun- he was wrong)

Problems with the method

• Subjectivity (opinion) in the measurements- he judged the brightness of the sun and through screen; only an assumption
• Assumed that Sirius and Sun were identical stars, and therefore had the same luminosity (radiating same amount of energy)
• Assumed that no light was absorbed when light was travelling e.g. by dust particles, screen,

How did it help the future?

• Showed stars lay at large distances – not close to us!
• Sun would look like star if we were further away

Developments

• Now we can use sensitive instruments to measure bigness
• We can use observed brightness to compare brightness of identical stars

How far away are galaxies? 3B

1 mega parsec- 1 million parsecs

• Cepheid method uses Mpc’s to measure distance to galaxies; however it can’t be used to measure distances beyond a few Mpc because it’s too far away to see whether the star may belong to a galaxy or isolated.

Cepheid Variables- pulsate in brightness and intensity (luminosity) over a well-defined period of time.

• g. star gets brighter, dimmer, brighter over the course of 3 days. This continues to happen in a regular cycle.

This revealed that stars are contracting and expanding, hence their size and energy (luminosity) varies.

The brightest Cepheid’s vary with the greatest luminosity.

• Greater luminosity = longer time between pulses (pulse period)
• There are 2 Cepheid stars with same observed brightness (doesn’t means that their luminosity is the same; one may be further) that pulse at different rates (longer/shorter periods).

You know that the star with the longer pulse period has the highest luminosity and is therefore   must be further away (because otherwise the observed brightness wouldn’t be equal; it would be brighter for the star with higher luminosity)

Measuring distances

Part 1

1. Find Cepheid + distance of it
2. Measure brightness
3. Work out luminosity
4. Plot graph of luminosity against period (linear relationship)

Part 2

1. Look for Cepheid in cluster/galaxy (roughly same distance)
2. Measure observed brightness + period of variation
3. From looking at the period, read luminosity of the graph.
4. Use luminosity + observed brightness to work out distance (external formula)

How are stars distributed in space? 3C

The light from the Milky Way comes from a strip of starlight.

• Further from strip = less stars visible
• Milky Way is a disc shape and has spiral layout

Herschel

Wanted to determine shape of the galaxy:

1. Counted stars in one direction
2. Moved telescope and counted more
3. Complete circle
4. Drew a map of the stars observed

The greater the no. of stars in one direction = greater distance to the edge in that direction.

Assumptions

• He assumed he could detect all the stars in the direction he was looking at (proved wrong when bigger telescoped were introduced)
• Assumed he could see to the end of the galaxy (proved wrong in future when scientists discovered that dust made it difficult to see all the stars at the centre of the galaxy)

The Great Debate

Nebula- blobs/ spirals showing faint patches of light

• Could be gas clouds, cluster of stars

Globular clusters- spherical clusters of stars

 Shapley Curtis The spiral nebulae are INSIDE of the Milky Way because: –          Globular clusters are only 100,000 light-years away and seem to lie in the sphere around the Milky Way. –          Nebulae= cloud/ dustànearby Spiral nebulae are OUTSIDE the galaxy. They are their own individual galaxies and are separate from the Milky Way. The universe is one giant galaxy – 100,000 parsecs across Our galaxy is smaller- only 10,000 parsecs across Sun + Solar system are away from the centre of the galaxy Sun + Solar system are at the centre of the galaxy, or very near.

Shapley + Curtis were both right.

Hubble proved Shapley’s point when he was studying the Andromeda nebula and spotted a faint Cepheid. He calculated that it was 1 million light years away- this was too far away to be part of the Milky Way, thus the Andromeda must be its own galaxy, indicating that there are many more galaxies out there.

What else is ‘out there’- and where is it? 3D

Objects studied by astronomers

• Asteroids- small rocky body’s orbiting the sun.
• Comet- consists of a nucleus of ice and dust
• Planetary nebula- formed when dying sun-like star throws off its outer layers of hot gas
• Supernova- The explosive death of a massive star whose energy output causes its expanding gases to glow brightly for weeks or months
• Supernova remnant- glowing, expanding gaseous remains of a supernova explosion
• Quasar- galaxies containing black holes that draw in materials from its surroundings, which heats it up and allows it to emit vast amounts of radiation

Learning from Supernovae

Supernovae explosions are monitored by measuring how their light output varies over time. If they are nearer to death, their light output will be less, and will therefore look dimmer.

Some supernovae always reach same peak luminosity; astronomers use these supernovae to work out the distances to galaxies where the supernovae are observed.

Observing distant galaxies 3E

Red shift

Galaxies are moving away from us

• Star spectra shows that when a galaxy moves away from us, the wavelength of light gets bigger, and thus the light becomes redder; the light has shifted towards the red end of the spectrum= REDSHIFT

If a galaxy is moving closer to us, the light it gives off gets squeezed together, which makes it appear bluer than it actually is. If the galaxy is moving away from us the light gets stretched out, which makes it appear redder than it really is. If the star is also going faster all the time, or accelerating, this effect is even greater.

• If the light is “red shifted” the star is moving away from us. If it is “blue shifted”, it is moving closer.

By seeing how much light has been red shifted (this is easy to measure), you can work out the recession velocity (how fast it is moving away).

More distant galaxy = greater red shift = greater speed of recession à LINEAR relationship

The fact that the galaxies are moving away suggests that space itself is expanding. This indicates that perhaps:

• The universe was smaller in the past
• The universe exploded from a single point (Big Bang)

The Big Bang theory has become a widely expected model of the universe and has enabled scientists to determine the age of the universe (14, 000 million years ago).

Hubble Constant Law

The value of the Hubble constant was originally 500 km/s per Mpc- however; this value was too highà disputes + uncertainties. Now it has been officially announced that the value is 70 km/s per (use this value for HC in the exam!)

• g. Find distance to galaxy with a speed of 475 km/s.

Rearrange equation: 475/70= 6.5 km