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A 2 Pages Term Paper on ICBM motion using Kepler's law and circular motion

Kepler’s Laws

     Johannes Kepler (1571-1630), the German assistant and successor to Tycho Brahe, was a Copernican from his twenties on, and was destined to bring about acceptance of the heliocentric concept. That is, he believed the sun rather than the earth was the center of the planetary system. (CVC website)

Kepler’s Laws are summarized as follows:

LAW 1: The orbit of a planet/comet about the Sun is an ellipse with the Sun's center of mass at one focus.

LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time.

LAW 3: The squares of the periods of the planets are proportional to the cubes of their semi-major axes.

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     Intercontinental Ballistic Missiles, or ICBM for short, are highly sophisticated, long-range missiles that are capable of destroying targets from a range of 8000 nautical miles. “MIRV, Multiple Independently Targeted Reentry Vehicles, capability was a great advance in the building of ICBMs. This gave almost total certainty that if one side had ABMs, Anti-Ballistic Missiles, some warheads would still find their targets. Warheads also became smaller without sacrificing power so more could be launched with the same rockets. MIRVs are targeted taking into account surface winds that could change the path of the warheads. They detonate in what is called a "foot-print" or a defined area where the warheads are supposed to explode.” (History website)

     The advances in not only missile technology, but in all motion-guided or remotely controlled arsenal, was made possible by the three laws given above that govern the path decisions taken by scientists developing the former. The earth is an ellipse and any target, which is not at a visual distance, becomes a candidate for gravitational and heliocentric calculations to be highly accurate in order for it to successfully reach its target. ICBMs rely heavily on circular motion principles where acceleration, velocity and radius are interrelated:
|a| = |v|2 / r , Any time we find a particle in uniform circular motion it has an acceleration of magnitude |v|2 / r with a direction always perpendicular to the velocity. ” (w3c org website)

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     Ballistic missiles follow a trajectory that includes boosting, midcourse and terminating (BMDO website) In boosting, the flight of the missile takes place in which it is thrusting to gain acceleration. For 3-4 minutes the rocket is climbing against the earth’s gravity and sometimes even exiting the earth’s atmosphere. This phase is where the laws of science govern each and every moment of the missile and the success of the flight depends on the motion guidance and tracking control already put in the development of the ICBM. As the average weight of each ICBM comes around 30,000 pounds and a length of 70 feet, the mass that has to be monitored has to be kept in view. The designing phase of any ICBM is the most crucial and takes a long time testing and re-testing of all possible deviations to be eradicated.

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W3c org website:
URL verified on 1st December 2001.

History website:
http://journalnow.koz.com/servlet/wsj_ProcServ/GID=00134000000973801971170201&PG=00139000000976409295005917, URL Verified on 1st December 2001.

CVC website:

http://www.cvc.org/science/kepler.htm, URL Verified on 1st December 2001.

BMDO website:

http://www.acq.osd.mil/bmdo/bmdolink/html/basics.html, URL Verified on 2nd December 2001.


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