- 4016 - ASTRONOMY SIZE? - How Do Astronomers Determine the Size of Things?
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----------------------------------- 4016 - ASTRONOMY SIZE?
- Astronomers make reasonable assumptions
than do the math to learn more.
Astronomers want to learn the size of things because if you know how big
something is you can estimate how far away it is. If you how bright something is you can estimate
how far away it is. If you know how far
away it is you know how far back in time it is.
- Astronomy is like archeology. With each layer of the earlier Universe they
explore the more they learn about our history.
In this example below astronomers are looking at a Globular Cluster of
stars and they would like to know how big it is.
- A Globular Cluster is thousands of stars in a spherical shape like
an elliptical galaxy. The estimate is
that there is a million stars in the cluster.
The stars are in orbit about a common center. Let’s start out estimating that it is similar
to our galaxy. The average star is about
the size of our Sun. The orbiting speed
is about the same as the average speed of stars in our galaxy, 10 kilometers
per second, or 22,370 miles per hour.
The objective is to estimate how big it is. Our galaxy is 100,000
lightyears across. Is this cluster
bigger or smaller than our galaxy?
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- Let’s start with the conservation of
energy. We know the stars are in orbit
about a common center. Their orbiting
velocity represents some kinetic energy.
We know that gravity and the angular momentum of the orbiting stars are
in balance because the cluster is neither collapsing or expanding.
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- Kinetic Energy is equal to ½ the mass times
the velocity. The bigger the mass the
more the energy. The faster the velocity
the more the energy. Our estimates are
the mass is one Solar Mass and the velocity is 10 kilometers per second.
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-------------------- KE
= ½ m*v^2
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- Then there is the Potential Energy of gravity
that is holding the mass of stars in its spherical shape. The mass is spread across the volume of
stars. Let’s assume the balance of
gravities potential energy is at the half way point out from the center. We know the force of gravity is proportional
to the masses and inversely proportional to the square of the distance of
separation. The Constant of
proportionality is the Gravitational Constant, “G“.
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----------------- F
= G * M^2 / R^2
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----------------- Potential Energy = Force acting over a distance
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---------------- PE
= F * R
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----------------- PE
= G * M^2 / R
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- Note that the Kinetic Energy pulls in one
direction but the gravity at the middle pulls in both directions. But, everything is balanced. Kinetic Energy = ½ Potential Energy
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---------- KE
= ½ PE
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----------- ½ m*v^2
= ½ G * M^2 / R
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- The mass is equal to the number of stars, 1
million, or 10^6 times the mass of the Sun, one Solar Mass, Ms. The velocity equals 10^4 meters / second. G
= 6.67*10^-11 meters^3 /
kilogram*seconds^2. One Solar
Mass equals 2*10^30 kilograms.
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----------- ½ m*v^2
= ½ G * M^2 / R
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----------- ½ (Ms*10^6)*(10^4)^2 = ½ G
* (Ms*10^6)^2 / R
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----------- ½ *(10^4)^2
= ½ (6.67*10^-11) * (2*10^30*10^6) / R
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----------- R
= 13.34*10^17 meters
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---------- one lightyear = 9.46*10^15 meters.
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----------- R
= 140 lightyears
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- The Globular Cluster is 140 lightyears
across. It is 40 % larger in diameter
than our Milky Way Galaxy. This is a rough estimate given all the assumptions. It is a starting point and the more
astronomers learn the more they can compare different calculations and get a
better idea of the evolution of the Universe.
A history that is uncovered step by step.
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May
21, 2023 ASTRONOMY SIZE? 1123 4016
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------ “Jim Detrick” -----------
--------------------- --- Sunday, May 21, 2023
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