-
-
-------------------- 2541 - BINARY STARS - used to calculate mass?
-
- Just kidding!!!! Two stars are better than one because their interaction can be observed and can introduce laws of physics that we can not see with only one star.
-
- Fortunately about half the stars in the Universe are companion stars. They are binary or triple star systems rather than being single, lonely stars like our Sun. For example, Astronomers observe a binary star system. One of the stars is a White Dwarf. That means it is a Neutron Star and we know its mass initially must be 1.44 Solar Mass.
-
- This is because at that particular mass the electron degeneracy pressure holding the star from collapsing gives way and all the electrons and protons collapse into a core of neutrons. The other star observed is a hydrogen burning star like our Sun but it is loosing mass to the orbiting Neutron star at the rate of 10^14 kilograms per second. If all this mass is turned into radiation as it collapses into the Neutron Star how bright does the Neutron Star become?
-
- If the infalling mass is transformed into energy than it must follow:
-------------------------- Einstein’s formula: E=mc^2.
-
------------ mass = m = 10^14 kilograms per second
-
------------ c^2 = 9 * 10^16 meters^2 per second^2.
-
------------ Energy = E = 9*10^30 kilograms meters^2 / second^2 per second.
-
- If all this Energy is in the form of radiation, or luminosity then:
-
--------------- E = L = 9^10^30 joules / second.
-
- Another law of physics is the luminosity is proportional to the forth power of temperature. The hotter the object the brighter it becomes. Anything proportional can be turned into an equality with the right constant of proportionality.
-
----------------- L = Constant * (temperature)^4
-
- In this case the Constant is equal to the surface area of the sphere times Stephen-Boltzman’s Constant.
-------------- Constant = (4*pi^radius^2) * (5.67*10^-8 watts / Kelvin^4)
-
-------------- The radius of a Neutron Star is 6.1 miles , or 10 kilometers.
-
------------- L = 9*10^30 joules / second = 4*pi*(10^4)^2 *5.67*10^-8 watts / Kelvin^4 * T^4
-
------------ T^4 = .1268*10^32 Kelvin^4
-
-------------------------------------- T = 60,000,000 Kelvin
-
- The temperature at the surface of the Neutron Star is 60,000,000 degrees Kelvin. This temperature is equivalent to energy in the photons of radiation by another Constant, Boltzman’s Constant = 1.38*10^-23 Joules / Kelvin
-
--------------- Photon Energy = Constant * Temperature
-
-------------- PE = k * T
-
------------- PE = 1.38*10^-23 Joules / Kelvin * 60*10^6 Kelvin
-
-------------- PE = 82.8 *10^-17 Joules
-
-------------- 1 Electron volt = 1.6*10^-19 Joules.
-
--------------------------------------- PE = 5170 electron volts.
-
-------------- 5170 electron volts is the photon energy of X-rays.
-
- The wavelength of X-rays can also be calculated by the photon energy being inversely proportional to wavelength. The smaller the wavelength the higher the energy. In this case the Constant is the speed of light times Planck’s Constant of Action.
-
------------ Photon Energy of = PE = h * c / wavelength.
-
------------ wavelength = 6.63*10^-34 joule*seconds * 3*10^8 meters / second / 82.8 *10^-17 Joules
-
----------- wavelength = 0.24 nanometers, which is the wavelength of X-rays.
-
- We cannot see the illumination from this White Dwarf companion star unless we use an X-ray telescope.
-
- Astronomers observe another binary where one star is a Pulsar Star and a companion that is not visible. They are both orbiting a common center of gravity in 42 minutes. The Pulsar is emitting pulses with each revolution so astronomers can calculate its velocity to be 11 kilometers / second, or 25,000 miles per hour. The companion star them must have a velocity of 770 kilometers per second, or 1,700,000 miles per hour.
-
- Knowing the velocities and the period we can calculated the radius to the common center of gravity. Circumference = 2*pi*r. Distance = velocity * time.
-
----------- Radius of the Pulsar = v * period / 2*pi
-
----------- Radius of the Pulsar = 11 km/sec * 42 minutes * 60 seconds / 2*pi
-
----------- Radius of the Pulsar = 4400 kilometers
----------- Radius of the Companion = 770 km/sec * 42 minutes * 60 seconds / 2*pi
-
----------------------------- Radius of the Companion = 309,000 km
-
- The period ,”p”, of the orbiting bodies squared is proportional to the major axis ,“a”, between them cubed. The distance between the bodies is (4400 kilometers plus 309,000 kilometers) = 313,400 kilometers.
-
----------- p^2 = 4*pi^2 * a^3 / G ( Mp+Mc)
-
------------ p = 42 minutes = 2,250 seconds
-
------------ a = 313,400 kilometers = 3.13*10^8 meters
-
------------ G = 6.67*10^-11 m^3/kg*sec^2
-
------------------------------- Mp = mass of the Pulsar which is a Neutron Star.
Neutron Stars have a mass of 1.44 Solar Mass.
-
------------ Mc = the mass of the companion star.
------------(2.25*10^3)^2 = 39.48 * (3.13*10^8)^3 / 6.67*10^-11 ( Mp+Mc)
-
------------ Mp + Mc = 28.3 * 10^29 kilograms
-
---------- Solar Mass = 2*10^30 kilograms
-
----------------------------------- Mp + Mc = 1.42 Solar Mass.
-
- The angular momentum of the two bodies must be the same so the mass * velocity of both bodies must be the same:
-
-------------- Mc * Vc = Mp * Vp
-
------------- Mc = 1.44 * 11 km/sec / 770 km/sec
-
-------------------------------------- Mc = 0.02 Solar Mass.
-
- Both calculations tell us that the Neutron Star as a very small companion orbiting it only 2% the size of our Sun and probably a Brown Dwarf, because it is not big enough to be a hydrogen burner.
- In these two examples of observing binary stars we have used to laws of physics to calculate masses, surface temperatures, luminosities, and the frequency of radiation.
-
- How neat is that ?
-
- December 13, 2019 2541 1118
----------------------------------------------------------------------------------------
----- 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” -----------
- https://plus.google.com/u/0/ -- www.facebook.com -- www.twitter.com
--------------------- Tuesday, December 17, 2019 --------------------
-----------------------------------------------------------------------------------------
No comments:
Post a Comment