Sunday, May 21, 2023

4016 - ASTRONOMY SIZE? -

 

-    4016  -   ASTRONOMY   SIZE?   -    How Do Astronomers Determine the Size of Things?

-


-

-----------------------------------   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?

-

-    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.

-

-    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.

-

--------------------  KE  =  ½ m*v^2

-

-  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“.

-

-----------------  F  =  G * M^2 / R^2

-

-----------------  Potential Energy =  Force acting over a distance

-

----------------  PE  =  F * R

-

-----------------  PE  =  G * M^2 / R

-

-    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

-

----------  KE  =  ½ PE

-

-----------  ½ m*v^2  =  ½ G * M^2 / R

-

-    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.

-

-----------  ½ m*v^2  =  ½ G * M^2 / R

-

-----------  ½ (Ms*10^6)*(10^4)^2  =  ½ G * (Ms*10^6)^2 / R

-

-----------  ½ *(10^4)^2  =  ½  (6.67*10^-11) * (2*10^30*10^6) / R

-

-----------  R  =  13.34*10^17 meters

-

----------  one lightyear =  9.46*10^15 meters.

-

-----------  R  =  140 lightyears

-

-    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.

-   

May 21, 2023             ASTRONOMY   SIZE?                 1123           4016  

-------------------------------------------------------------------------------------------                                                                                                                      

--------  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”  -----------

--------------------- ---  Sunday, May 21, 2023  ---------------------------------

-

 

 

 

 

               

 

 

No comments:

Post a Comment