- 3538 - MATH - calculating escape velocities? - How Fast Do You Have to Go to Escape the Galaxy? Velocities great enough to escape the Milky Way Galaxy and enter intergalactic space traveling at their escape velocity forever. What is the escape velocity to escape the Universe?
--------------------- 3538 - MATH - calculating escape velocities?
- How fast do you have to be going to escape the gravity of the Earth?
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----------------------- 6.96 miles per second
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--------------------- 25,056 miles per hour.
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- Just over 25,000 miles per hour and the traveler can permanently escape the grasp of Earth’s gravity. But, not the grasp of the Sun. How is escape velocity calculated?
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- The velocity needed to escape the gravity of a body is directly proportional to the mass of the body and inversely proportional to the radius to the center of the mass.
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----------------- (velocity)^2 = constant * Mass / radius
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- The constant needed to make this equation an equality is 2 times the Gravitational Constant, “G”.
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------------------ G = 6.67 * 10^-11 m^3 / (kg*sec^2)
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----------------- v^2 = 2 * G * M // r
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----------------- M = mass of the Earth
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------------------ M = 5.97*10^24 kilograms
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------------------- r = radius of the Earth
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------------------- r = 6.38 *10^6 meters
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------------------- v^2 = 2 * (6.67*10^-11) * ( 5.97*10^24) // ( 6.38*10^6)
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------------------- v^2 = 12.48*10^7
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------------------ v = 11.2 kilometers / meter
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----------------- velocity = 25,000 miles per hour.
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----------------------------- For the Moon the escape velocity = 2.4 kilometers / meter
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------------------ v ( Moon) = 5,370 miles per hour
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--------------------------------- For the Sun the escape velocity is:
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------------------- v ( Sun ) = 1,382,400 miles per hour.
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- How fast is the escape velocity from the Sun at the distance of the Earth?
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--------------- v(Sun at Earth) = 93,600 miles per hour
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- Our fastest rocket ships can only go 36,000 miles per hour. So, our rockets can escape the Earth but the can not go fast enough to escape the Sun. Astronomers have figured out how to use gravity to swing by the planet and slingshot the rocket at ever greater velocities.
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- When rockets get free from gravity traveling in outer space there speeds can gradually increase if they use more rocket fuel. But, fuel is heavy and rockets want to carry payloads not fuel.
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- How fast would these rockets have to get going in order to escape the gravity of the Milky Way? Are there stars in the galaxy going fast enough to escape the Milky Way?
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- The galaxy contains at least 200,000,000 suns and weighs over 2* 10^42 kilograms. Using averages for distances and mass distributions the escape velocity for the Galaxy is:
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---------------------- v( galaxy ) = 648,000 miles per hour.
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- Have astronomers ever found a star traveling this fast away from the center of the Galaxy?
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- Yes, in 2005, a blue star was discovered (spectral type “O”) in the Constellation Hydra the Sea Serpent traveling at:
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--------------------- v(star) = 1,558,800 miles per hour.
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- This star is 362,000 lightyears away from the center of the galaxy. At these speeds it must have left the center of the Galaxy some 80,000,000 years ago.
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- By 2011 astronomers have discovered 12 stars traveling at galactic escape velocities. One of these in the Constellation Puppis the Stern, very near the Dog Star, Sirius, is a Neutron Star traveling that fast. It’s velocity is 0.5% the speed of light. This star will leave our Galaxy in just a few million years.
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------------------ v(neutron star) = 3,353,167 miles per hour
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- How can these enormous stars possible obtain these enormous velocities?
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- Astronomers have two theories: One has to do with binary stars that fly too close to an enormous Blackhole, like the one at the center of our Galaxy. When the Blackhole captures one of the stars and pulls it in the Conservation of Momentum requires the companion star to be flung in the opposite direction with the same kinetic energy. This Conservation of Energy puts enormous velocity in the escaping companion star.
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- The second theory has to do with a massive supernova explosion that is asymmetric. If the explosion is lopsided and the explosion goes off in one direction the remnant Neutron Star could get shot away like a cannon ball. Again, the Conservation of Energy requires an equal and opposite reaction. If the massive star’s supernova explodes in one direction the Neutron Star flies off in the opposite direction at enormous velocities.
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- Velocities great enough to escape the Milky Way Galaxy and enter intergalactic space traveling at their escape velocity forever. What is the escape velocity to escape the Universe?
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- Light traveling at light speed creates the Observable Universe as it goes. But, space is expanding faster than the speed of light. And, light is getting redshifted to broader and lower energy wavelengths as it goes.
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- It appears that nothing can ever escape the Universe. An announcement will be made soon, stay tuned..
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April 10, 2022 1353 3538
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