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Satellites in various orbits above the earth exploded? 
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#1
Dec1713, 01:33 AM

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1) What would happen if artificial satellites in various orbits above the earth exploded? Where would the fragments go?
2) How do constituents of asteroid belts stay in their orbit? Why don't they change orbits? Why that particular distance? Thanks 


#2
Dec1713, 01:37 AM

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#3
Dec1713, 01:49 AM

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Why does the Earth stay in its orbit (around the sun) ? Why that particular distance? Why does the moon stay in its orbit (around the Earth) ? Why that particular distance? 


#4
Dec1713, 11:37 AM

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Satellites in various orbits above the earth exploded?
http://en.wikipedia.org/wiki/Asteroid_belt 


#5
Dec1713, 12:26 PM

Mentor
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Debris ejected forwards, in the direction of the initial orbit, will enter a higher energy orbit with a larger semimajor axis, as the explosion accelerates it and gives it the necessary energy to reach this orbit. Given enough energy from the explosion, the debris could either be ejected completely out of orbit of the Earth or its orbital velocity could be decelerated so much that it simply falls back into the atmosphere. 


#6
Dec1713, 12:31 PM

P: 222

My original questions come from my perception that certain conditions are necessary for an object to remain in orbit. I presumed the conditions to include altitude above the body they are orbiting. Is there a certain altitude which, above it, an object placed there will orbit, for every reasonably close altitude above it?



#7
Dec1713, 12:45 PM

Mentor
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#8
Dec1713, 01:44 PM

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#9
Dec1713, 03:35 PM

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It is possible to leave the energy unaltered if the original speed, added speed and new speed are the sides of an equilateral triangle. Which is possible if the added speed is less than twice the original speed. If the new speed happens to be horizontal like the old speed was, then the new orbit is also circular, and with the same semimajor axis, only plane differs. If the new speed is the same as the old speed, but no longer horizontal, then the new orbit is elliptical but has the same semimajor axis. 


#10
Dec1713, 04:05 PM

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You can check different equations here to see the posibilities: http://en.wikipedia.org/wiki/Orbital_speed 


#11
Dec1713, 05:30 PM

P: 222

Thanks everyone for the information.



#12
Dec1813, 06:22 AM

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For example, if you have two objects in a similar circular orbit, and one fires thrusters to move upwards, that will have the effect of making its orbit elliptical, first going higher then going lower than the original orbit. Paradoxically, if you boost forward in orbit, that has the effect of raising the orbit which increases its period, so over a whole orbit you will drop back relative to something ahead of you in the original orbit, and vice versa. If you look at the relative motion as a pair of objects move around an orbit, a forward boosted object will soon start to change towards upwards motion, then into backwards motion, then downwards in a loop, ending up coming round to forwards again at the original altitude but further back in the orbit. Similar looping motions apply for other small differences of velocity. In Newtonian mechanics, a particle which passes through a particular point in an orbit around a static spherical object and is in free fall will pass through the same point on its next orbit, if there is a next orbit (that is, unless it escapes completely or hits the atmosphere). The "same point" in this sense ignores the rotation of the Earth, so it will not necessarily occur above the same location on the Earth, and the time taken to get back to that point depends on the energy of the orbit, so particles given different energy by the same explosion will pass through the same point later (if they have not hit the atmosphere) but at different times. 


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