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----------------- - 1826 - How big is our Solar System?
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- The Solar System is the Sun and 8 planets in a flat rotating disk. The Earth-Sun distance is called an Astronomical Unit (AU). The 4 giant planets are the farthest out from the Sun:
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------------------------ Jupiter ------------------- 5.2 AU
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------------------------ Saturn ------------------- 9.5
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------------------------ Uranus ------------------- 19.2
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------------------------ Neptune ------------------- 30.1
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- Beyond Neptune, at 30 times as far from the Sun as the Earth, is Pluto the first Dwarf Planet. The Solar System does not stop at 8 planets. Farther out we call them “Dwarf Planets” for lack of a better term. Pluto shares the space, 30 to 100 AU, with millions of rotating bodies called the Kuiper Belt of comets and asteroids, and Dwarf Planets
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- The most distant large Solar System object , found so far , is called Sedna. It was discovered in 2003 at a distance of 930 AU. It takes 11,400 years to orbit the Sun. Sedna is an icy rock about 1,400 miles in diameter. Sedna’s orbit extends 31 times as far as Neptune at its most distant.
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- Along with Sedna astronomers have identified 10 other large bodies orbiting beyond the Kuiper Belt. They all average a distance of 150 AU.
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- Unlike the closer planets that have nearly perfect circular orbits these distant objects have very elongated orbits.
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------Elongated Orbits ----------- closest -------------- farthest --------- orbit period
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--------------------- Sedna ---------- 76 AU --------- 930 AU ----------- 11,400 years
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-------------------- 2012VP113 ----- 80 -------------- 446 ----------------- 4,300
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- Sedna orbits like a long-period comet. Sedna’s orbit appears unanchored to the gravity of the 4 giant planets. The same is true of a 2014 discovery , 2012VP113 , had a similar elliptical orbit.
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- The suggestion to explain these perturbed elliptical orbits is that a “ super Earth” orbiting 250 AU could gravitationally explain things. ( computer modeling). The super-Earth would be 2 to 15 times the mass of the Earth.
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- We need more data. November 2015 another object V774104 has an orbit extending beyond Sedna’s.
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- Again, we need more data. In 2018 a Large Synoptic Surveyor Telescope ( LSST) will see first light on top of a mountain in Chile. The large telescope should bring us many new discoveries enlarging our understanding of our Solar System, with more data.
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- The hope is that if Planet “X” truly exists in our outer Solar System, LSST will find it. Maybe astronomers have already seen Planet X and don’t recognize it. People tend to see what they are looking for. Stay tuned , an announcement will be made shortly.
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- If we have more data we learn the distance and the period of orbit. Now we can calculate the mass that the object it is orbiting.
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- For example: The mass of the Sun can be calculated knowing the period of Earth’s orbit. This is Kepler’s 3rd law. The period of orbit squared is directly proportional to the radius of orbit cubed
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---------------------- p^2 = 4*pi^2 * a^3 / G * M
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---------------------- Mass = ( 4*pi^2/G) * a^3 / p^2
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---------------------- p = period of orbit = 1 year = 3.15*10^7 seconds
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--------------------- a = the average distance of orbit = 150 million kilometers = 1.5*10^11 meters
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--------------------- a = 93 million miles.
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-------------------- Mass = 5.9*10^11 a^3 / p^2
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-------------------- The mass is directly proportional to the cube of the distance of orbit and inversely proportional to the square of the period of orbit.
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------------------- Mass = 5.9*10^11 * ( 1.5*10^11)^3 / ( 3.15*10^7)^2
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------------------- Mass = 2.0 *10^30 kilograms
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- The mass of the Sun = 200,000,000,000,000,000,000,000,000,000 kilograms
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- The orbital velocity (v) for each of the planets decreases with distance ( r ):
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---------------------- v^2 = M * G / r
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----------------------- Mercury ----------------- 107,082 miles per hour
----------------------- Venus ------------------- 78,337
----------------------- Earth ------------------- 66,615
----------------------- Mars ------------------- 53,858
----------------------- Jupiter ----------------- 29,236
----------------------- Saturn ----------------- 21,675
----------------------- Uranus ---------------- 15,233
----------------------- Neptune --------------- 12,146
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- The orbital velocity is the balance between the pull of gravity and the push of centripetal force. The weaker the gravity the lower the orbital velocity needed to maintain this balance.
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-------------------- Gravity Force G * m * M / r^2
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--------------------- Force = mass * acceleration
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---------------------- F = m*a
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-------------------- acceleration = a = v^2 / r
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------------------ Centripetal Force = m * v^2 /r
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-------------- An orbiting object balances the centripetal force trying to throw it out into space and the gravity force trying to pull it back to the center of gravity.
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--------------------m*v^2 / r = G M m / r^2
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------------------- v^2 = G * M / r
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- Here are the escape velocities of the 8 Solar System planets. This is the velocity of a rocket ship that can escape the velocity of the planet.. The more massive the planet the harder it is to escape its pull of gravity.
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--------------------- (Velocity)^2 = 2 * G * M / R
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--------------------- M is the mass
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--------------------- R is the radius
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----------------------- Mercury ----------------- 9,900 miles per hour
----------------------- Venus ------------------- 23,300
----------------------- Earth ------------------- 25,000
----------------------- Mars ------------------- 11,250
----------------------- Jupiter ----------------- 133,000
----------------------- Saturn ----------------- 79,400
----------------------- Uranus ---------------- 48,000
----------------------- Neptune --------------- 53,000
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- For example: The escape velocity for the Moon: The Potential Energy due to position ( r = distance to center of gravity ) is balanced with the Kinetic Energy of the velocity of the rocket ( v ).
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------------------------ K.E. = P.E.
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------------------------ K.E. = ½ m * v^2
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------------------------ P.E. = G * M * m / r
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------------------------ M = 7.4*10^22 kilograms
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------------------------ r = 1.7*10^6 meters
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------------------------- ½ m * v^2 = G * M * m / r
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----------------------- (Velocity)^2 = 2 * G * M / r
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- --------------------- (Velocity)^2 = 2 * (6.67+10^-11 m^3/kg*s^2) * (7.4*10^22 kg) / ( 1.7*10^6 m)
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------------------------ Velocity = 2.4 km / sec
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------------------------ Velocity = 5,368 miles per hour.
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- The rocket has to have an escape velocity of 5,368 miles per hour to escape the gravity of the Moon. It has to have a velocity of 25,000 mph to escape the gravity of Earth. This math has our confidence in data gathering for our Solar System.
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- But, it is not working for the Galaxy. The more distant solar systems from the center of the Galaxy are orbiting at the about the same velocity. The more distance the less gravity the centripetal force needed is less and they should be orbiting at a slower speed. Not so. They are all orbiting the Galaxy center at the same speed. The math for escape velocity and orbital velocity does not work. What’s wrong?
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- In order to explain this observation astronomers have created Dark Matter. A halo of mass that is outside the Galaxy disk with 10 times the mass of what is inside in the disk. The mass interacts with gravity but does not interact with electromagnetic radiation, therefore, it is “ Dark”
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- There is other evidence for Dark Matter but those are other reviews listed below. We are searching to discover Planet X and for identifying the massive particles that make up Dark Matter. Who says there is not more to learn. Can we learn fast enough to survive?
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- Request these Reviews to learn more:
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- #1157 - The mysteries of our Solar System. Uranus is the only planet that has its rotating axis on its side.
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- #1150 - What is new and extreme in our Solar System? Neptune has winds that reach 1,500 miles per hour. Earth is the only planet, so far, that has an atmosphere with free oxygen. We can breath easier.
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- #1524 - Discovering new solar systems.
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- #1507 - Geological history of the Solar System.
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- #15 - The Sun and the planets in Six easy Pieces. Lots of math.
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- --------------------------------------------------------------------------------------
----------------- RSVP, Pass it on to whomever is interested. ----------------
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email comments, corrections, request for copies or Index of all reviews
- to: ------- jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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----- 707-536-3272 -------------------- Thursday, February 11, 2016 -----
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