- 3471 - ASTRONOMICAL DISTANCES - how far back can we go? Astronomical DISTANCES - how to measure them? - Measuring distances in astronomy is a very difficult process. Many of the prior reviews have covered specific methods in some detail. In this review I have put several methods all together to step by step reach galaxies at the edge of the Universe.
----- 3471 - ASTRONOMICAL DISTANCES - how far back can we go?
- I have used half a dozen of the over two dozen distance measuring methods used by astronomers. We start with the simplest. Plain trigonometry.
-
- OUT TO 200 LIGHTYEARS: We start by measuring the angle to a nearby star in relation to its more distant background stars. Then six months later when the Earth is on the other side of the Sun we measure the angle again. The angle will change. The nearby star will have shifted relative to its background stars due to parallax.
-
- The same occurs when you extend your hand and view you thumb with one eye then the other and the background scenery shifts due to parallax. The sine of the parallax angle = the opposite side / hypotenuse. The opposite side of the right triangle is the distance between the Sun and the Earth and the hypotenuse is the distance to the star.
-
- PARALLAX EXAMPLE : The closest star is Proxima Centauri. The six month parallax angle was measured to be 0.76 arc seconds. There are 3600 arc-seconds in 1 degree. 0.76 arc-seconds = 2.11*10^-4 degrees. The sine of the parallax angle is 3.685*10^-6 The distance from the Sun to the Earth is 1.5*10^11 meters.
-
- Distance to Proxima Centauri = (1.5*10^11) / (3.685*10^-6) = 4.1*10^16 meters
1 lightyear = 9.46*10^15 meters Distance to Proxima Centauri = 4.3 lightyears, our closest star.
-
- Next we measure the brightness of the star in watts / meter^2 (F) where we know the distance (D). Now we can calculate the intrinsic luminosity (L) of the star.
-
--------------------- L = 4*pi * D^2 * F
-
--------------------- where: 4*pi * D^2 is the surface area of a sphere of radius D
-
-------------------- where: “F” is the Flux, or apparent luminosity, or brightness of the star that we measured.
-
------------------- where: “L” is intrinsic luminosity of the star.
-
- LUMINOSITY EXAMPLE: L = 4*pi*D^2 * F
-
------------------ where: F is the Flux we measured to be 1*10^-12 watts/m^2
-
------------------- where L = 3.8*10^26 watts, the same luminosity as our Sun.
-
----------------- therefore: D = 5.5*10^18 meters, or 581 lightyears
-
- OUT TO 100,000 LIGHTYEARS: Next we find a star in a more distant galaxy that is similar, and we can assume that it has the same intrinsic luminosity. We measure its Brightness, F and calculate the distance D using the same formula:
-
-------------------------------------- D^2 = L / 4*pi*F
-
- Next, rather than use a single star that we think is similar we measure the brightness of dozens of stars and plot them versus their temperature, or color. This plot is called the H-R diagram, the Hertzsprung - Russell diagram. Luminosity versus temperature plots the stars of various masses that are on the Main-Sequence which is a straight line on this H-R graph.
-
- Luminosities range from 10^-3 to 10^5 Solar Luminosities. Temperatures range from 30,000 Kelvin to 3,000 Kelvin, corresponding to colors from Blue to Red.. The size of the stars range from 0.1 to 10 Solar Radius.
-
- We do this straight line plot for stars in a galaxy where we know the distance (Hyades Cluster). Next, we create a similar plot for stars in a galaxy where we want to find the distance (Pleiades Cluster).
-
- Wien’s law is used to measure temperature by measuring the wavelength of maximum brightness. Temperature = 00029 m*K / wavelength max. Now we have two straight line Main-Sequence plots that shift in dimness for the more distant galaxy. The distance squared is equal to the shift in brightness.
-
- STAR CLUSTER EXAMPLE: The Hyades Cluster of stars can be measured using the parallax method to have a distance of 151 lightyears. We would like to calculate the distance to the Pleiades Cluster of Stars know as the Seven Sisters.
-
- We measure the brightness and temperature of 50 stars in the Hyades Cluster and plot a Main-Sequence line. The relative brightness ranges from 0.1 to 50. The temperature ranges from 4000 to 8000 Kelvin.
-
- Next, we do the same thing for 50 stars in the Pleiades Cluster. The Main-Sequence straight line is shifted to 7.5 times dimmer than the straight line for the Hyades Cluster. That means that it is the square root of 7.5 further distant away.
2.75 times 151 lightyears = 415 lightyears away for the Pleiades Cluster.
-
- OUT TO 100,000,000 LIGHTYEARS: Among the stars in a galaxy of known distance we find pulsating stars called Cepheids. The period of pulsation of these Cepheid Stars is directly proportional to their intrinsic luminosity, L. Once we calibrate this relationship we find Cepheids in a more distant galaxy. Measuring the periods of pulsation we can determine their intrinsic luminosity, measure their brightness and calculate their distance:
-
--------------- D^2 = L cepheid / F * 4*pi
-
- CEPHEID EXAMPLE: 50 Cepheids are measured with pulsations from 1 to 100 days. The brightness measured and the luminosities calculated because the distance is known. Luminosities range from 1000 to 30,000 Solar Luminosity. The straight line plot has the equation: Luminosity = 320*(Period) + 575. To measure the distance to the M100 galaxy in the Coma Berenices three Cepheid Stars are found to have periods of:
-
------- Periods -----Solar ------- Luminosity ------- Brightness----- Distance
------- Days ----- Luminosity------- watts -------- watts/meter----- MLY
-
------- 30 --------- 10,300------- 3.9*10^30 ----- 9.3*10^-19 -------- 61
-
------- 8 --------- 3,100--------- 1.2*10^30 ----- 3.8*10^-19 -------- 53
-
------- 19--------- 10,300------- 3.9*10^30 ------ 8.7*10^-19 -------- 51
-
- Note that our calculations vary by 55 + or - 5 million lightyears. The galaxy is probably only a few hundred lightyears across so the error in our distance measurement is + or - 10%. These are not very accurate distance measurements.
-
- Besides the Cepheids in the Large Megellanic Cloud galaxy another fortunate occurrence happened in 1987. A supernova exploded. Previous pulsations before the explosion had created a shell of gas around the star. When the star exploded the ultraviolet light took 240 days to reach the shell and light up the gas.
-
- The radius of the ring was measured to be 0.858 arc seconds. That distance would be the speed of light * the 240 days = 6.2*10^15 meters. The sine of the angle 0.858 arc seconds = 4.12^10^-6. The distance to the star is calculated to be 1.5*10^21 meters, which is 150,000 lightyears. This gives astronomers a better calibration on the luminosity of the Cepheids and the luminosity of the supernova.
-
- OUT TO 10,000,000,000 LIGHTYEARS: Next we find a supernova explosion in a galaxy still farther away. To know the intrinsic luminosity it must be a certain type of supernova, called a white dwarf supernova. Supernovae are much brighter than Cepheid stars and can be measured at much greater distances.
-
- The peak luminosity of the supernova is 10^10 Solar Luminosity and it remains above 10^8 for 150 days. A typical Cepheid star is 10^4 Solar Luminosity. We can measure the brightness of Cepheids out to 100 million lightyears.
-
- Using the inverse distance squared formula this means we can measure supernova out to 10^11 lightyears, 100 billion lightyears. The Observable Universe is 10^10 or 10 billion lightyears. Therefore, astronomers should be able to measure distances out to the edge of the Universe.
-
- OUT TO 13,700,000,000 LIGHTYEARS: After measuring the distances to many galaxies, Edwin Hubble noted the correlation of distance with recession velocity. Recession velocities were measured using the redshift of the galaxies light spectrum.
-
- Plotting distances of 200 to 1,600 million lightyears versus receding velocities measured from 25,000 to 35,000 km/sec. resulting in a straight line with a constant slope of 22,000 km/sec per million lightyear. This is known as Hubble’s Constant. It defines the rate of expansion of the Universe. Galaxies will be traveling faster by 22,000 km/sec, (49,000 miles per hour) for every million lightyears distant they are away from us.
-
- HUBBLE EXAMPLE: We know the hydrogen emissions line in the light spectrum is at 656.3 nanometers. We measure this in three different galaxies and it has shifted to the red end of the spectrum. Redshift = z = (measured wavelength - 656.3) / 656.3
For redshifts much less than 1 the velocity = speed of light * z. The receding velocity divided by 22,000 km/sec per million lightyears gives the distance in million lightyears.
-
---------------Emission ----- Redshift ------- velocity ------------ Distance
----------- Wavelength --------- z ----------- million mph-------- lightyears
-
------------659.6 nm --------- .005 ----------- 3.4 ------------------ 690,000
-
------------664.7 nm --------- .013 ----------- 8.6 ---------------- 1,750,000
-
------------6679.2 nm ------- .035 ----------- 23.4 ---------------- 4,760,000
-
- The last amazing thing about the Hubble Constant for the expansion of the Universe is that lightyears are also time as well as distance. And, if we run time backwards we can determine when the expansion started.
-
- The reciprocal of the Hubble Constant will give us the age of the Universe, assuming the expansion rate has always been the same:
-
------------- 1/ 22,000 km/sec/ MLY = 1.36*10^10 years. The age of the Universe is 13.6 billion years. And, the distance to the edge of the Observable Universe is 13.6 billion lightyears.
-
- Well, now you have extended your knowledge to the edge of he Universe. Well done.
The James Webb Space Telescope will see 10 times further ito the history of the universe. There is more to come. Stay tuned.
-
February 19, 2022 ASTRONOMICAL DISTANCES 863 2532 3471
----------------------------------------------------------------------------------------
----- Comments appreciated and Pass it on to whomever is interested. ---
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
----------------------------- Saturday, February 19, 2022 ---------------------------
------------- 3471 - ASTRONOMICAL DISTANCES - how far back can we go?
-
- I have used half a dozen of the over two dozen distance measuring methods used by astronomers. We start with the simplest. Plain trigonometry.
-
- OUT TO 200 LIGHTYEARS: We start by measuring the angle to a nearby star in relation to its more distant background stars. Then six months later when the Earth is on the other side of the Sun we measure the angle again. The angle will change. The nearby star will have shifted relative to its background stars due to parallax.
-
- The same occurs when you extend your hand and view you thumb with one eye then the other and the background scenery shifts due to parallax. The sine of the parallax angle = the opposite side / hypotenuse. The opposite side of the right triangle is the distance between the Sun and the Earth and the hypotenuse is the distance to the star.
-
- PARALLAX EXAMPLE : The closest star is Proxima Centauri. The six month parallax angle was measured to be 0.76 arc seconds. There are 3600 arc-seconds in 1 degree. 0.76 arc-seconds = 2.11*10^-4 degrees. The sine of the parallax angle is 3.685*10^-6 The distance from the Sun to the Earth is 1.5*10^11 meters.
-
- Distance to Proxima Centauri = (1.5*10^11) / (3.685*10^-6) = 4.1*10^16 meters
1 lightyear = 9.46*10^15 meters Distance to Proxima Centauri = 4.3 lightyears, our closest star.
-
- Next we measure the brightness of the star in watts / meter^2 (F) where we know the distance (D). Now we can calculate the intrinsic luminosity (L) of the star.
-
--------------------- L = 4*pi * D^2 * F
-
--------------------- where: 4*pi * D^2 is the surface area of a sphere of radius D
-
-------------------- where: “F” is the Flux, or apparent luminosity, or brightness of the star that we measured.
-
------------------- where: “L” is intrinsic luminosity of the star.
-
- LUMINOSITY EXAMPLE: L = 4*pi*D^2 * F
-
------------------ where: F is the Flux we measured to be 1*10^-12 watts/m^2
-
------------------- where L = 3.8*10^26 watts, the same luminosity as our Sun.
-
----------------- therefore: D = 5.5*10^18 meters, or 581 lightyears
-
- OUT TO 100,000 LIGHTYEARS: Next we find a star in a more distant galaxy that is similar, and we can assume that it has the same intrinsic luminosity. We measure its Brightness, F and calculate the distance D using the same formula:
-
-------------------------------------- D^2 = L / 4*pi*F
-
- Next, rather than use a single star that we think is similar we measure the brightness of dozens of stars and plot them versus their temperature, or color. This plot is called the H-R diagram, the Hertzsprung - Russell diagram. Luminosity versus temperature plots the stars of various masses that are on the Main-Sequence which is a straight line on this H-R graph.
-
- Luminosities range from 10^-3 to 10^5 Solar Luminosities. Temperatures range from 30,000 Kelvin to 3,000 Kelvin, corresponding to colors from Blue to Red.. The size of the stars range from 0.1 to 10 Solar Radius.
-
- We do this straight line plot for stars in a galaxy where we know the distance (Hyades Cluster). Next, we create a similar plot for stars in a galaxy where we want to find the distance (Pleiades Cluster).
-
- Wien’s law is used to measure temperature by measuring the wavelength of maximum brightness. Temperature = 00029 m*K / wavelength max. Now we have two straight line Main-Sequence plots that shift in dimness for the more distant galaxy. The distance squared is equal to the shift in brightness.
-
- STAR CLUSTER EXAMPLE: The Hyades Cluster of stars can be measured using the parallax method to have a distance of 151 lightyears. We would like to calculate the distance to the Pleiades Cluster of Stars know as the Seven Sisters.
-
- We measure the brightness and temperature of 50 stars in the Hyades Cluster and plot a Main-Sequence line. The relative brightness ranges from 0.1 to 50. The temperature ranges from 4000 to 8000 Kelvin.
-
- Next, we do the same thing for 50 stars in the Pleiades Cluster. The Main-Sequence straight line is shifted to 7.5 times dimmer than the straight line for the Hyades Cluster. That means that it is the square root of 7.5 further distant away.
2.75 times 151 lightyears = 415 lightyears away for the Pleiades Cluster.
-
- OUT TO 100,000,000 LIGHTYEARS: Among the stars in a galaxy of known distance we find pulsating stars called Cepheids. The period of pulsation of these Cepheid Stars is directly proportional to their intrinsic luminosity, L. Once we calibrate this relationship we find Cepheids in a more distant galaxy. Measuring the periods of pulsation we can determine their intrinsic luminosity, measure their brightness and calculate their distance:
-
--------------- D^2 = L cepheid / F * 4*pi
-
- CEPHEID EXAMPLE: 50 Cepheids are measured with pulsations from 1 to 100 days. The brightness measured and the luminosities calculated because the distance is known. Luminosities range from 1000 to 30,000 Solar Luminosity. The straight line plot has the equation: Luminosity = 320*(Period) + 575. To measure the distance to the M100 galaxy in the Coma Berenices three Cepheid Stars are found to have periods of:
-
------- Periods -----Solar ------- Luminosity ------- Brightness----- Distance
------- Days ----- Luminosity------- watts -------- watts/meter----- MLY
-
------- 30 --------- 10,300------- 3.9*10^30 ----- 9.3*10^-19 -------- 61
-
------- 8 --------- 3,100--------- 1.2*10^30 ----- 3.8*10^-19 -------- 53
-
------- 19--------- 10,300------- 3.9*10^30 ------ 8.7*10^-19 -------- 51
-
- Note that our calculations vary by 55 + or - 5 million lightyears. The galaxy is probably only a few hundred lightyears across so the error in our distance measurement is + or - 10%. These are not very accurate distance measurements.
-
- Besides the Cepheids in the Large Megellanic Cloud galaxy another fortunate occurrence happened in 1987. A supernova exploded. Previous pulsations before the explosion had created a shell of gas around the star. When the star exploded the ultraviolet light took 240 days to reach the shell and light up the gas.
-
- The radius of the ring was measured to be 0.858 arc seconds. That distance would be the speed of light * the 240 days = 6.2*10^15 meters. The sine of the angle 0.858 arc seconds = 4.12^10^-6. The distance to the star is calculated to be 1.5*10^21 meters, which is 150,000 lightyears. This gives astronomers a better calibration on the luminosity of the Cepheids and the luminosity of the supernova.
-
- OUT TO 10,000,000,000 LIGHTYEARS: Next we find a supernova explosion in a galaxy still farther away. To know the intrinsic luminosity it must be a certain type of supernova, called a white dwarf supernova. Supernovae are much brighter than Cepheid stars and can be measured at much greater distances.
-
- The peak luminosity of the supernova is 10^10 Solar Luminosity and it remains above 10^8 for 150 days. A typical Cepheid star is 10^4 Solar Luminosity. We can measure the brightness of Cepheids out to 100 million lightyears.
-
- Using the inverse distance squared formula this means we can measure supernova out to 10^11 lightyears, 100 billion lightyears. The Observable Universe is 10^10 or 10 billion lightyears. Therefore, astronomers should be able to measure distances out to the edge of the Universe.
-
- OUT TO 13,700,000,000 LIGHTYEARS: After measuring the distances to many galaxies, Edwin Hubble noted the correlation of distance with recession velocity. Recession velocities were measured using the redshift of the galaxies light spectrum.
-
- Plotting distances of 200 to 1,600 million lightyears versus receding velocities measured from 25,000 to 35,000 km/sec. resulting in a straight line with a constant slope of 22,000 km/sec per million lightyear. This is known as Hubble’s Constant. It defines the rate of expansion of the Universe. Galaxies will be traveling faster by 22,000 km/sec, (49,000 miles per hour) for every million lightyears distant they are away from us.
-
- HUBBLE EXAMPLE: We know the hydrogen emissions line in the light spectrum is at 656.3 nanometers. We measure this in three different galaxies and it has shifted to the red end of the spectrum. Redshift = z = (measured wavelength - 656.3) / 656.3
For redshifts much less than 1 the velocity = speed of light * z. The receding velocity divided by 22,000 km/sec per million lightyears gives the distance in million lightyears.
-
---------------Emission ----- Redshift ------- velocity ------------ Distance
----------- Wavelength --------- z ----------- million mph-------- lightyears
-
------------659.6 nm --------- .005 ----------- 3.4 ------------------ 690,000
-
------------664.7 nm --------- .013 ----------- 8.6 ---------------- 1,750,000
-
------------6679.2 nm ------- .035 ----------- 23.4 ---------------- 4,760,000
-
- The last amazing thing about the Hubble Constant for the expansion of the Universe is that lightyears are also time as well as distance. And, if we run time backwards we can determine when the expansion started.
-
- The reciprocal of the Hubble Constant will give us the age of the Universe, assuming the expansion rate has always been the same:
-
------------- 1/ 22,000 km/sec/ MLY = 1.36*10^10 years. The age of the Universe is 13.6 billion years. And, the distance to the edge of the Observable Universe is 13.6 billion lightyears.
-
- Well, now you have extended your knowledge to the edge of he Universe. Well done.
The James Webb Space Telescope will see 10 times further ito the history of the universe. There is more to come. Stay tuned.
-
February 19, 2022 ASTRONOMICAL DISTANCES 863 2532 3471
----------------------------------------------------------------------------------------
----- Comments appreciated and Pass it on to whomever is interested. ---
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
----------------------------- Saturday, February 19, 2022 ---------------------------
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