Finite element method

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In 12 months 2013, c ommercial retails, shoebox residences and mass market properties continued to be the celebrities of the property market. Models are snapped up in report time and at document breaking prices. Builders are having fun with overwhelming demand and patrons need more. We feel that these segments of the property market are booming is a repercussion of the property cooling measures no.6 and no. 7. With additional buyer's stamp responsibility imposed on residential properties, buyers change their focus to commercial and industrial properties. I imagine every property purchasers need their property funding to understand in value. A gravity tractor (GT) is a spacecraft that deflects another object in space, typically a potentially hazardous asteroid that might impact Earth, without physically contacting it, using only its gravitational field to transmit the required impulse. The tractor spacecraft could either hover near the object being deflected or orbit near it. The concept has two key advantages: namely that essentially nothing need be known about the mechanical composition and structure of the asteroid in advance and that the relatively small amounts of force used enable extremely precise orbit manipulation and determination.

Advantages

A number of considerations arise concerning means for avoiding a devastating collision with an asteroidal object, should one be discovered on a trajectory that were determined to lead to Earth impact at some future date. One of the main challenges is how to transmit the impulse required (possibly quite large), to an asteroid of unknown mass, composition, and mechanical strength, without shattering it into fragments, some of which might be themselves dangerous to Earth if left in a collision orbit. The GT solves this problem by gently accelerating the object as a whole over an extended period of time, using the spacecraft's own mass and associated gravitational field to effect the necessary deflecting force. Because of the universality of gravitation, affecting as it does all mass alike, the asteroid would be accelerated almost uniformly as a whole, with only tidal forces (which should be extremely small) causing any stresses to its internal structure.

A further advantage is that a transponder on the spacecraft, by continuously monitoring the position and velocity of the tractor/asteroid system, could enable the post-deflection trajectory of the asteroid to be accurately known, ensuring its final placement into a safe orbit.

Limitations

Limitations of the tractor concept include the exhaust configuration. With the most efficient hovering design (that is, pointing the exhaust directly at the target object for maximum force per unit of fuel), the expelled reaction mass hits the target head-on, imparting a force in the exact opposite direction to the gravitational pull of the tractor. It would therefore be necessary to use the orbiting-tractor scheme described below, or else design the hovering tractor so that its exhaust is directed at a slight angle away from the object, while still pointing "down" enough to keep a steady hover. This requires greater thrust and correspondingly increased fuel consumption for each m/s change in the target's velocity.

Issues of the effect of ion propulsion thrust on the dust of asteroids have been raised, suggesting that alternative means to control the station keeping position of the gravity tractor may need to be considered. In this respect, solar sails have been suggested.

According to Rusty Schweickart, the gravitational tractor method is also controversial because during the process of changing an asteroid's trajectory the point on Earth where it could most likely hit would be slowly shifted across different countries. It means that the threat for the entire planet would be minimized at the cost of some specific states' security. In Schweickart's opinion, choosing the way the asteroid should be "dragged" would be a tough diplomatic decision.

Example

To get a feel for the magnitude of these issues, let us suppose that a NEO of size around 100 m, and mass of one million metric tons, threatened to impact Earth. Suppose also that

• a velocity correction of 1 cm/s would be adequate to place it in a safe and stable orbit, missing Earth

• that the correction needed to be applied within a period of 10 years.

With these parameters, the required impulse would be: V × M  = 0.01 [m/s]×10⁹ [kg] = 10⁷ [N-s], so that the average tractor force on the asteroid for 10 years (which is 3.156×10⁸ seconds), would need to be about 0.032 newtons. An ion-electric spacecraft with a specific impulse of 10,000 N-s per kg, corresponding to an ion beam velocity of 10 km/s (about twenty times that obtained with the best chemical rockets), would require 1,000 kg of reaction mass (Xenon is currently favored) to provide the impulse. The kinetic power of the ion beam would then be approximately 317 W; the input electric power to the power converter and ion drive would of course be substantially higher. The spacecraft would need to have enough mass and remain sufficiently close to the asteroid that the component of the average gravitational force on the asteroid in the desired direction would equal or exceed the required 0.032 N. Assuming the spacecraft is hovering over the asteroid at a distance of 200 m to its centre of mass, that would require it to have a mass of about 20 metric tonnes, because due to the gravitational force we have

$m_2=\frac{F{r}^2}{G{m}_1}=\frac{0.032[N]\times (200[m]{)}^2}{6.674\times 10^{-11}[N{m}^{2}k{g}^{-2}]\times 10^9[kg]}\approx 19200kg$

Considering possible hovering positions or orbits of the tractor around the asteroid, note that if two objects are gravitationally bound in a mutual orbit, then if one receives an arbitrary impulse which is less than that needed to free it from orbit around the other, because of the gravitational forces between them, the impulse will alter the momentum of both, together regarded as a composite system. That is, so long as the tractor remains in a bound orbit, any propulsive force applied to it will be effectively transferred to the asteroid it orbits. This permits a wide variety of orbits or hovering strategies for the tractor. One obvious possibility is for the spacecraft to orbit the NEO with the normal to the orbit in the direction of the desired force. The ion beam would then be directed in the opposite direction, also perpendicular to the orbit plane. This would result in the plane of the orbit being shifted somewhat away from the center of the asteroid, "towing" it, while the orbital velocity, normal to the thrust, remains constant. The orbital period would be a few hours, essentially independent of size, but weakly dependent on the density of the target body.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

• National Geographic, February 17, 2007
• New Scientist, November 9, 2005
• B612 Foundation

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