How to Measure Distances in the Universe - Revision history

WikiSysop: /* Redshifts */

2012-03-06T04:18:53Z

Redshifts

← Older revision		Revision as of 04:18, 6 March 2012
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	Train whistles sound lower pitched as they recede, due to the moving source of the sound waves. This is called the Doppler shift. Light waves from a galaxy that is moving away also appear longer in wavelength, lower in frequency, and therefore redder in color. This effect is called the redshift, and it provides a way for us to measure distances to galaxies.		Train whistles sound lower pitched as they recede, due to the moving source of the sound waves. This is called the '''Doppler shift'''. Light waves from a galaxy that is moving away also appear longer in wavelength, lower in frequency, and therefore redder in color. This effect is called the
			'''redshift''', and it provides a way for us to measure distances to galaxies.


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	Once Edwin Hubble had identified Cepheid variables in Andromeda galaxy, he could use the Period-Luminosity Relationship, discovered by Henrietta Levitt, to find the brightnesses of the stars. With that, and the inverse square law, he could measure the distance to the Andromeda galaxy, and to other galaxies in which Cepheid variables occurred.		Once Edwin Hubble had identified Cepheid variables in Andromeda galaxy, he could use the Period-Luminosity Relationship, discovered by Henrietta Levitt, to find the brightnesses of the stars. With that, and the inverse square law, he could measure the distance to the Andromeda galaxy, and to other galaxies in which Cepheid variables occurred.

	Hubble noticed a pattern in this new data. He noticed the greater the distance of the galaxy, the greater its redshift. Almost all the galaxies he measured appeared to be moving away from us, and the greater the distance of the galaxy, the faster it was going. His original measurements have been replaced by others of more accuracy, and extended out much farther. The relationship he discovered is called the Hubble Law.		Hubble noticed a pattern in this new data. He noticed the greater the distance of the galaxy, the greater its redshift. Almost all the galaxies he measured appeared to be moving away from us, and the greater the distance of the galaxy, the faster it was going. His original measurements have been replaced by others of more accuracy, and extended out much farther. The relationship he discovered is called the '''Hubble Law'''.

	Cepheid variables are not bright enough to use for distance measurements much beyond the 60 million light years of the Virgo Cluster. The Type Ia supernovae are so much brighter that we can see them billions of light years away. The Hubble Law holds, even at these distances; even looking back billions of years into the past, it was found that the distance of a galaxy is proportional to its redshift.		Cepheid variables are not bright enough to use for distance measurements much beyond the 60 million light years of the Virgo Cluster. The Type Ia supernovae are so much brighter that we can see them billions of light years away. The Hubble Law holds, even at these distances; even looking back billions of years into the past, it was found that the distance of a galaxy is proportional to its redshift.

	Now the redshift could provide the distance to any galaxy. The more distant the galaxy the greater the redshift. Distance could be measured in redshifts. A cluster of galaxies with an average redshift z = 0.01 means the galaxies are moving away at about 0.01th the speed of light. If it is has a redshift z = 0.02 it is moving away at twice that speed, and is twice as far away.		Now the redshift could provide the distance to any galaxy. '''The more distant the galaxy the greater the redshift'''. Distance could be measured in redshifts. A cluster of galaxies with an average redshift z = 0.01 means the galaxies are moving away at about 0.01th the speed of light. If it is has a redshift '''z = 0.02''' it is moving away at twice that speed, and is twice as far away.

	Astronomers measure the wavelength of light by analyzing the spectrum of a star or even an entire galaxy. When we look at a distant receding galaxy we see all the wavelengths of its spectral features increased by the same factor, 1+z. When z is small it is approximately v/c where "v" is the speed of the galaxy moving away, and "c" is the speed of light. However, matter cannot travel travel faster than the speed of light, and at larger z the speeds just get closer and closer to "c". We will look at how this works in more detail in a later unit when we explore the effects of relativity. For now, remember that the most distant galaxies appear to recede from us at nearly the speed of light, and that the more distant they are, the more its spectral features are reddened, shifted to longer and longer wavelengths.		Astronomers measure the wavelength of light by analyzing the spectrum of a star or even an entire galaxy. When we look at a distant receding galaxy we see all the wavelengths of its spectral features increased by the same factor, 1+z. When z is small it is approximately v/c where "v" is the speed of the galaxy moving away, and "c" is the speed of light. However, matter cannot travel travel faster than the speed of light, and at larger z the speeds just get closer and closer to "c". We will look at how this works in more detail in a later unit when we explore the effects of relativity. For now, remember that the most distant galaxies appear to recede from us at nearly the speed of light, and that the more distant they are, the more its spectral features are reddened, shifted to longer and longer wavelengths.

	Not only could distances be measured, but since all distant galaxies are receding from us, and the more distant a galaxy, the faster the galaxy it goes, it appears that the universe is expanding!		Not only could distances be measured, but since all distant galaxies are receding from us, and the more distant a galaxy, the faster the galaxy it goes, it appears that '''the universe is expanding!'''

	Not only that, but if you follow their paths backwards, it seems that all galaxies would at some time have been in the same place, beginning at a singular event that we call the Big Bang!		Not only that, but if you follow their paths backwards, it seems that all galaxies would at some time have been in the same place, beginning at a singular event that we call the '''Big Bang!'''

	By the end of next week you will be able easily to measure the size of the visible Universe, and to follow the of galaxies backwards in time to the beginning of the universe.		By the end of next week you will be able easily to measure the size of the visible Universe, and to follow the of galaxies backwards in time to the beginning of the universe.

WikiSysop: /* Cepheid Variables */

2012-03-06T04:16:14Z

Cepheid Variables

← Older revision		Revision as of 04:16, 6 March 2012
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	Over 80 years ago, Henrietta Leavitt worked at Harvard College Observatory measuring photographs of Cepheid variable stars in the Small Magellanic Cloud, a compact galaxy that is a nearby companion to our Milky Way.		Over 80 years ago, Henrietta Leavitt worked at Harvard College Observatory measuring photographs of [http://imagine.gsfc.nasa.gov/docs/science/mysteries_l1/cepheid.html Cepheid variable stars] in the Small Magellanic Cloud, a compact galaxy that is a nearby companion to our Milky Way.


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	With their brightnesses known, distances to galaxies in which they resided could be determined by using the inverse square method. Edwin Hubble found Cepheid variables in the Andromeda Galaxy, which place it 2.5 million light years away. It's the most distant object you can see in the sky without a telescope. The light that made this image left the galaxy 2.5 million years ago.		With their brightnesses known, distances to galaxies in which they resided could be determined by using the inverse square method. '''Edwin Hubble''' found Cepheid variables in the '''Andromeda Galaxy''', which place it 2.5 million light years away. It's the most distant object you can see in the sky without a telescope. The light that made this image left the galaxy 2.5 million years ago.


	[[File:cepheid_variable_plate_similar_size.png\|600px\|center]]		[[File:cepheid_variable_plate_similar_size.png\|600px\|center]]

	<center>Hubble's original photograph on which he first identified a Cepheid variable (VAR!) in the Andromeda Galaxy</center>		<center>Hubble's original photograph on which he first identified a Cepheid variable ('''VAR!''') in the Andromeda Galaxy</center>

WikiSysop: /* Inverse Square */

2012-03-06T04:14:40Z

Inverse Square

← Older revision		Revision as of 04:14, 6 March 2012
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	Once the brightness of a specific type of star is known close up, we can tell the distance of similar stars by how much fainter they appear when farther away. The rule that applies is the Inverse Square Law.		Once the brightness of a specific type of star is known close up, we can tell the distance of similar stars by how much fainter they appear when farther away. The rule that applies is the '''Inverse Square Law'''.


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	'''An Example'''		<center>'''An Example'''</center>



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	'''More Examples'''		<center> '''More Examples''' </center>

WikiSysop: /* Parallax */

2012-03-06T04:13:41Z

Parallax

← Older revision		Revision as of 04:13, 6 March 2012
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	Since the sky is a great hemisphere, we can think of it in degrees, the horizon being 0 and overhead being 90 degrees up. Each little degree may be divided into 60 tiny arcminutes. Each arcminute may be divided into 60 even smaller arcseconds. If a star shifts one '''arcsecond''' when the Earth moves one astronomical unit through space, its angle of parallax is one arcsecond, and the star is one '''parsec''' distant, about 3'''.26 light years away'''.		Since the sky is a great hemisphere, we can think of it in degrees, the horizon being 0 and overhead being 90 degrees up. Each little degree may be divided into 60 tiny arcminutes. Each arcminute may be divided into 60 even smaller arcseconds. If a star shifts one '''arcsecond''' when the Earth moves one astronomical unit through space, its angle of parallax is one arcsecond, and the star is one '''parsec''' distant, about '''3.26 light years away'''.

WikiSysop at 04:13, 6 March 2012

2012-03-06T04:13:15Z

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			== Lasers and Radio Signal Timing==

	~~== Lasers ==~~

			Distances to the '''Moon''' are measured by '''timing a pulse of laser light''' reflected from mirrors placed on the surface by Apollo astronauts in the 1960's and 1970's. A laser pulse travels 400,000 kilometers from the Earth to the Moon in 1.3 seconds. Send the pulse out, and 2.6 second later it comes back to you.
	Distances to the Moon are measured by timing a pulse of laser light reflected from mirrors placed on the surface by Apollo astronauts in the 1960's and 1970's. A laser pulse travels 400,000 kilometers from the Earth to the Moon in 1.3 seconds. Send the pulse out, and 2.6 second later it comes back to you.


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	Distances to Sun and planets are measured by timing radio signals from man-made satellites orbiting around those planets. The images of Saturn returned by the Cassini satellite take about 1 hour and 23 minutes to travel 1,300,000,000 kilometers to reach us.		Distances to '''Sun and planets''' are measured by '''timing radio signals''' from man-made satellites orbiting around those planets. The images of Saturn returned by the Cassini satellite take about 1 hour and 23 minutes to travel 1,300,000,000 kilometers to reach us.

	Within the solar system we measure distances by comparison to the Earth-Sun distance, and use the Astronomical Unit as the measuring stick. Since the Earth's orbit is an ellipse, astronomers prefer to define the "AU" for an imaginary planet that would orbit in the Sun in a circle in the same time it takes for Earth to orbit in its ellipse. For most purposes this means that the AU is the average distance from the Earth to the Sun. It is precisely		Within the solar system we measure distances by comparison to the Earth-Sun distance, and use the [http://neo.jpl.nasa.gov/glossary/au.html Astronomical Unit] as the measuring stick. Since the Earth's orbit is an ellipse, astronomers prefer to define the "AU" for an imaginary planet that would orbit in the Sun in a circle in the same time it takes for Earth to orbit in its ellipse. For most purposes this means that the AU is the average distance from the Earth to the Sun. It is precisely

	<center>		<center>
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	Triangulation has been used to measure distances for thousands of years. Greek astronomers used it to try to determine distances of the Moon and Sun. Kepler used it to find distances to the planets. Surveyors use it to locate to locate property boundaries and plan construction. You could use it for something as simple as finding the height of a telephone pole without climbing it, tape measure in hand.		'''Triangulation''' has been used to measure distances for thousands of years. Greek astronomers used it to try to determine distances of the Moon and Sun. Kepler used it to find distances to the planets. Surveyors use it to locate to locate property boundaries and plan construction. You could use it for something as simple as finding the height of a telephone pole without climbing it, tape measure in hand.

	A simple example in astronomy occurs when we measure the direction to an object seen when the Earth is first on one side of its orbit, and then again six months later when Earth is on the other side.		A simple example in astronomy occurs when we measure the direction to an object seen when the Earth is first on one side of its orbit, and then again six months later when Earth is on the other side.
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	The triangle with the sides A, B, and C is a "right" triangle. That's one that has a "right" or 90 degree angle. The right angle is marked in the figure; it's the one that is at the Sun.		The triangle with the sides A, B, and C is a "right" triangle. That's one that has a "right" or 90 degree angle. The right angle is marked in the figure; it's the one that is at the Sun.

	In a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side next to the angle. In this case, we'd say		In a right triangle, the '''tangent''' of an angle is the ratio of the side opposite the angle to the side next to the angle. In this case, we'd say


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	You measure angle AC to be 89 degrees. Type 89 into your calculator and press tan to find that the tangent of angle 89 degrees is 57.3. "A" in our equation is just 1 astronomical unit:		You measure angle AC to be 89 degrees. Type 89 into your calculator and press '''''tan''''' to find that the tangent of angle 89 degrees is 57.3. "A" in our equation is just 1 astronomical unit:


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	== Parallax ==		== Parallax ==

	Parallax is the same as triangulation. We measure how much the direction to a distant object changes when it is observed from opposite sides of Earth's orbit. Distant stars provide a background for measuring the closer ones.		'''Parallax''' is the same as triangulation. We measure how much the direction to a distant object changes when it is observed from opposite sides of Earth's orbit. Distant stars provide a background for measuring the closer ones.

	When out on an evening's stroll, and a nearby tree seems to go by quickly as we walk, while the distant Moon seems to stand still overhead, we're experiencing parallax. When Earth moves from one side of the Sun to the other, a nearby star will appear to shift against the background of distant stars. The greater the shift, the closer the star.		When out on an evening's stroll, and a nearby tree seems to go by quickly as we walk, while the distant Moon seems to stand still overhead, we're experiencing '''parallax'''. When Earth moves from one side of the Sun to the other, a nearby star will appear to shift against the background of distant stars. The greater the shift, the closer the star.


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	Since the sky is a great hemisphere, we can think of it in degrees, the horizon being 0 and overhead being 90 degrees up. Each little degree may be divided into 60 tiny arcminutes. Each arcminute may be divided into 60 even smaller arcseconds. If a star shifts one arcsecond when the Earth moves one astronomical unit through space, its angle of parallax is one arcsecond, and the star is one parsec distant, about 3.26 light years away.		Since the sky is a great hemisphere, we can think of it in degrees, the horizon being 0 and overhead being 90 degrees up. Each little degree may be divided into 60 tiny arcminutes. Each arcminute may be divided into 60 even smaller arcseconds. If a star shifts one '''arcsecond''' when the Earth moves one astronomical unit through space, its angle of parallax is one arcsecond, and the star is one '''parsec''' distant, about 3'''.26 light years away'''.

WikiSysop: /* Cepheid Variables */

2012-03-06T04:08:29Z

Cepheid Variables

← Older revision		Revision as of 04:08, 6 March 2012
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	With their brightnesses known, distances to galaxies in which they resided could be determined by using the inverse square method. Edwin Hubble found Cepheid variables in the Andromeda Galaxy, which place it 2.5 million light years away. It's the most distant object you can see in the sky without a telescope. The light that made this image left the galaxy 2.5 million years ago.		With their brightnesses known, distances to galaxies in which they resided could be determined by using the inverse square method. Edwin Hubble found Cepheid variables in the Andromeda Galaxy, which place it 2.5 million light years away. It's the most distant object you can see in the sky without a telescope. The light that made this image left the galaxy 2.5 million years ago.


	[[File:cepheid_variable_plate_similar_size.png\|600px\|center]]		[[File:cepheid_variable_plate_similar_size.png\|600px\|center]]

	<center>Hubble's original photograph on which he first identified a Cepheid variable (VAR!) in the Andromeda Galaxy</center>		<center>Hubble's original photograph on which he first identified a Cepheid variable (VAR!) in the Andromeda Galaxy</center>


	[[File:cepheid_variable_in_andromeda.jpg\|600px\|center]]		[[File:cepheid_variable_in_andromeda.jpg\|600px\|center]]

WikiSysop: /* Inverse Square */

2012-03-06T04:07:21Z

Inverse Square

← Older revision		Revision as of 04:07, 6 March 2012
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			<center>
			Intensity = 1 / (Distance)<sup>2</sup>
			</center>

	~~Intensity = 1 / (Distance)2~~		<center>
			1/4 = 1 / (Distance)<sup>2</sup>
	1 /4 = 1 / (Distance)2		</center>

			<center>
	Distance = 2		Distance = 2
			</center>

			<center>
	2 x 1,000,000 ly = 2,000,000 ly		2 x 1,000,000 ly = 2,000,000 ly
			</center>


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	The oldest and most distant Type Ia supernova ever seen is SN 1997 11.3 billion ly away !!!		The oldest and most distant Type Ia supernova ever seen is SN 1997 11.3 billion ly away !!!



	== Distance to the Magellanic Clouds ==		== Distance to the Magellanic Clouds ==

WikiSysop: /* Parallax */

2012-03-06T04:05:28Z

Parallax

← Older revision		Revision as of 04:05, 6 March 2012
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			<center>
	tangent of the angle BC = A/B		tangent of the angle BC = A/B
			</center>

			<center>
	B = A / tan(BC)		B = A / tan(BC)
			</center>


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			<center>
	tan(BC) = BC/206265		tan(BC) = BC/206265
			</center>

			<center>
	B = A x 206265 / BC		B = A x 206265 / BC
			</center>


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			<center>
	Distance in parsecs = 1 / Parallax in arcseconds		Distance in parsecs = 1 / Parallax in arcseconds
			</center>


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			<center>
	Distance = 1/ 0.75 = 1.33 parsecs		Distance = 1/ 0.75 = 1.33 parsecs
			</center>

			<center>
	Distance =1.33 x 3.26 = 4.3 light years		Distance =1.33 x 3.26 = 4.3 light years
			</center>


	The only star this nearby is Proxima Centauri, the nearest star to us beyond the Sun. It's visible only with a good telescope from the southern hemisphere, a non-descript red dot among hundreds of thousands of other stars in the sky. When we see this star at night, we are seeing it as it was 4.3 years ago because the light took that long to reach us. It is set apart from all the others by having the largest parallax of any star. Because it is so close, its motion relative to the Sun in our galaxy carries it past us at an unusually fast clip. Year to year it moves across the sky with the combined back and forth motion of its parallax, and the steady drift of its proper motion through the galaxy.		The only star this nearby is Proxima Centauri, the nearest star to us beyond the Sun. It's visible only with a good telescope from the southern hemisphere, a non-descript red dot among hundreds of thousands of other stars in the sky. When we see this star at night, we are seeing it as it was 4.3 years ago because the light took that long to reach us. It is set apart from all the others by having the largest parallax of any star. Because it is so close, its motion relative to the Sun in our galaxy carries it past us at an unusually fast clip. Year to year it moves across the sky with the combined back and forth motion of its parallax, and the steady drift of its proper motion through the galaxy.

WikiSysop: /* Triangulation */

2012-03-06T04:03:38Z

Triangulation

← Older revision		Revision as of 04:03, 6 March 2012
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	<center>Distance = 150,000,000 x tan(89) kiolmeters</center>		<center>Distance = 150,000,000 x tan(89<sup>o</sup>) kiolmeters</center>

	<center>Distance = 150,000,000 x 57.3</center>		<center>Distance = 150,000,000 x 57.3</center>

WikiSysop: /* Triangulation */

2012-03-06T04:02:24Z

Triangulation

← Older revision		Revision as of 04:02, 6 March 2012
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			<center>
	Tangent of the angle AC = B/A		Tangent of the angle AC = B/A
			</center>


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			<center>
	B = A x Tangent of the angle AC		B = A x Tangent of the angle AC
			</center>


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			<center>
	Distance = A x tan(89)		Distance = A x tan(89)
			</center>

			<center>
	Distance = 1 x 57.3 astronomical units		Distance = 1 x 57.3 astronomical units
			</center>


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	Distance = 150,000,000 x tan(89) kiolmeters		<center>Distance = 150,000,000 x tan(89) kiolmeters</center>

			<center>Distance = 150,000,000 x 57.3</center>

	Distance = ~~150~~,~~000~~,~~000 x 57.3~~		<center>Distance = 8,593,494,245 kilometers</center>

	~~Distance = 8,593,494,245 kilometers~~


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	8,593,494,245 /300,000 = 28,644 seconds		<center>8,593,494,245 /300,000 = 28,644 seconds</center>