-
-
---------------------------- 2216 - Einstein’s math and gravity lens.
-
- Two satellites intended for Europe’s equivalent to the United States’ GPS network, were placed into orbit incorrectly, causing them to travel around Earth in ellipses rather than circles. That was not ideal for the satellites’ originally intended navigational use, but scientists realized the wayward satellites were perfect for testing Einstein’s general theory of relativity.
-
- According to general relativity, gravity affects not just space, but also time. The deeper within a gravitational field you are, the slower time passes. So a clock at a higher altitude will tick faster than one closer to Earth’s surface, where Earth’s gravity is stronger. The satellites’ orbital mishap allowed the most precise test yet of this effect, known as a gravitational redshift.
-
- As the two misplaced satellites move in their elliptical orbits, their distance from Earth periodically increases and decreases by about 5,300 miles. Using the precise atomic clocks on the satellites, the scientists studied how that altitude change affected the flow of time. The clocks sped up and slowed down by tiny fractions of a second agreeing with the predictions of general relativity within a few thousandths of a percent.
-
- Einstein’s math was right again. The Hubble Space Telescope gave us another proof of his math. The telescope focused on a foreground cluster of galaxies 5.4 billion lightyears away. Directly behind this cluster at 9.7 billion lightyears distance was another galaxy. The image of the most distant galaxy appeared as an Einstein Ring as gravity bent the image around he nearer gravity cluster. The ring was 38 arc-seconds in diameter.
-
- Here is how the arc of the ring could be used to calculate the mass of the galaxy cluster that was inside the ring including the dark matter that was hidden there.. Here is how the mass of the cluster is related to the arc of the ring:
-
----------------------- Mass = a^2 * c^2 * (d*D) / 4 * G (d-D)
-
---------------------- where : a = angular diameter of the ring in radians.
-
---------------------- c = the speed of light meters/second
-
--------------------- d = distance to the farthest galaxy meters
-
--------------------- D = distance to the nearer galaxy cluster meters
-
--------------------- G = the gravitational constant m^3 / kg * sec^2
-
-
-
----------------------- Mass = a^2 * c^2 * (d*D) / 4 * G (d-D)
-
---------------------- a = 38 arc seconds = 38 / 206,265 arc seconds / radian
-
---------------------- a = 1.842 * 10^-4 radians
-
----------------------- a^2 = 3.39 * 10^-8 radians^2
-
---------------------- c = 3 * 10^8 meters / second
-
--------------------- d = 9.7 billion lightyears = 9.7 * 10^9 * 9.5 * 10^ 15 meters / LY
-
---------------------- d = 92.15 *10^24 meters
-
--------------------- D = 5.4 billion lightyears = 5.4 * 10^9 * 9.5 * 10^ 15 meters / LY
-
---------------------- D = 51.3 * 10^24
-
---------------------- (d * D) = 4,727 * 10^48 = 4.727 * 10^51 meters^2
-
---------------------- (d - D) = 40.85 * 10^24 = 4.085 * 10^25 meters
-
--------------------- G = 6.67 * 10^-11 m^3 / kg * sec^2
-
-
-
------------------------ Mass = a^2 * c^2 * (d*D) / 4 * G (d-D)
-
------------------------ Mass = (3.39 * 10^-8) * ( 9 * 10^16) * (4.727 * 10 ^51) / 4 * (6.67 * 10^-11) (4.085 * 10^25) kg
-
------------------------- Mass = (1.442 * 10^61) / (1.090 * 10^16)
-
---------------------------Mass = 1.333* 10^45 kg / 2 * 10^30 kg / solar mass
-
-------------------------- Mass = 6.67 * 10^14 solar mass
-
-
- The Solar Mass of the Galaxy Cluster is 6.67 * 10^14 the mass of our Sun. So, that would be the number of stars in the cluster if all were the size of our Sun, 667,000,000,000,000 suns
-
- So, Einstein’s math was correct showing that the immense gravity will bend light to act like a magnifying glass.
-
-
-
- Another way to measure the mass of the galaxy cluster is to measure the speed of a star, pr a galaxy in circular orbit around the center of the cluster.
-
- The average speed of galaxies in orbit in the cluster is 988 kilometers per second. The average radius of the orbits is 9.5 lightyears.
-
------------------------------ velocity squared = G * Mass / Radius
-
------------------------------ V^2 = G * M / R
-
------------------------------- (9.88 * 10^5)^2 m^2 / sec^2 = M * (6.67* 10^-11) m^3 / kg*sec^2 / (9.5 * 10^6) LY * (9.5 * 10^15) m / LY
-
- ------------------------------ (97.6 * 10^10) m^2/sec^2 = M * (6.67* 10^-11) m^3 / (90.25 * 10^21) m * kg * sec^2
-
-- ------------------------------ (8,808 * 10^31) kg m^3 = M * (6.67* 10^-11) m^3
-
--------------------------------- (1,321 * 10^42) kg * solar mass / 2 *10^30 kg = M
-
--------------------------------- M = 660 * 10^12 solar mass
-
--------------------------------- M = 6.6 * 10^14 solar mass
-
- Astronomers used the geometry of the arc of the Einstein ring and the speed of orbiting galaxies to measure the total mass of the cluster of galaxies. These calculations went further to prove the existence of Dark Matter, the unseen mass. More mysteries to be solved in order to understand the universe we live in. The biggest mystery is us being here trying to understand it.
-
- Other Reviews available:
-
- 1142 - Can Einstein’s equations pass the tests? His equations are alone in unifying space, time, mass, energy, motion and light.
-
- 929 - Einstein’s Legacy. If you can link the equations of General Relativity and Quantum Mechanics it would be a supertechifragilisticexpialedocious breakthrough in physics.
-
- 49 - Einstein is right again. Measurements with the Gravity Probe satellite.
-
- December 23, 2018.
----------------------------------------------------------------------------------------
----- 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
--------------------- Sunday, December 23, 2018 -------------------------
-----------------------------------------------------------------------------------------
No comments:
Post a Comment