- Almost all of the stars in the night sky appear as a single point of light. However, many of them are binary stars, two stars orbiting around a common center of gravity. In fact, if Jupiter were just a little bit bigger it would ignite solar fusion and our Solar System would be a binary star system.
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- This review is about a binary star system called LL Pegasi, 3,000 lightyears from is in the Constellation Pegasus the Winged Horse. The observation that tells us it is a binary system is that it is spraying spiral arcs of material out from its center. One or both of the stars is loosing material by throwing it out of the system like a revolving lawn sprinkler.
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- The spirals arcs are expanding outward at 31,000 miles per hour. This velocity moves the spiral arcs outward 272,000,000 miles every year. The space between the spirals is 800 years. This means that the binary orbit is 800 years and the spacing between the spirals is:
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-------------------------- 272*10^6 miles / year * 800 years = 217 billion miles
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- The spirals go out 6 shells so the time duration for these spirals to be created is :
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-------------------- 6 shells * 800 years = 4,800 years.
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- If each shell decreases in brightness according to this function how many shells can we see?
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------------------------- Brightness = 128* N^-3/2
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--------------------------- N is the number of shells. The brightness of the background is Magnitude 2. What is the maximum number of shells we will be able to see?
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--------------------------- 2 = 128* N^-3/2
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---------------------------- N^3/2 = 128/2 = 64
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---------------------------- N = ( 2^6) ^ 2/3 = 2^4 = 16
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- The maximum number of shells that we could see is 16 spiral shells.
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- 16 shells would cover the period 16 * 800 = 12,800 years for that many spirals to work their way out like a lawn sprinkler.
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- As the 2 stars get closer and closer together the tidal forces begin pulling the stars apart. The tidal force is the difference in the pull of gravity between your head and you feet. The gravity force of the Earth on you body is not enough for you to feel the difference (Other than old age shortening you the Earth’s tidal forces are not pulling you apart.) However, around every body there is a distance called the tidal radius within which a body will be torn apart. Its own gravitational forces will not hold it together.
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---------------------- Tidal radius = 2.44 R * ( D / d ) ^1/3
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--------------------- Tidal radius = R * ( M / m ) ^1/3
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- Let’s see how close the Moon would have to be before the Earth began tearing it apart?
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--------------------------- R = radius of the Earth = 6,378 kilometers
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-------------------------- D = the density of the Earth = 5,500 kilograms / meter^3
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-------------------------- d = the density of the Moon = 3,400 kilograms / meter^3
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------------------------- Tidal radius = 2.44 * 6378 * 5500 / 3400 ) ^1/3
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--------------------------- Tidal radius = 18.27 *10^3
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- Tidal radius is 18,270 kilometers. The Moon is 340,000 kilometers away and moving further away be 3 centimeters every year. We don’t have to worry about Earth’s tidal forces tearing the Moon apart, unless something changes.
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- What if the Earth had the gravity of a Blackhole and the Moon was a Red Supergiant Star? How far would the star have to be away to keep from being torn apart by the Blackhole’s tidal forces?
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---------------------- Tidal radius = R ( M / m ) ^1/3
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-------------------- m = mass of the star = 20 Solar Mass
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-------------------- M = mass of the Blackhole = 10 Solar Mass
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----------------------- R = radius of the Blackhole = radius of the orbit of Earth = 150,000,000 kilometers.
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----------------------- Tidal radius = 1.5*10^8( 10/20 ) ^1/3 = 1.19*10^8 kilometers
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- The star would have to be 74,000,000 miles away from the Blackhole in order to start being torn apart. The radius of the Blackhole is 37 miles.
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- What if the Blackhole was like the one at the center of our Milky Way Galaxy? It has a mass of 4,000,000 Solar Mass.
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------------------------- M = mass of the galactic Blackhole = 4*10^6 Solar Mass
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----------------------- Tidal radius = R ( M / m ) ^1/3
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---------------------- Tidal radius = 1.5 *10^8( 3*10^6 / 20 ) ^1/3
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----------------------- Tidal radius = .797*10^10
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- The tidal radius would be 4.9 billion miles , which is just beyond the orbit of Pluto.
- There goes Earth into pieces. An announcement will be made shortly, stay tuned.
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707-536-3272, Thursday, December 13, 2012
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