Gravity Tractor - Example

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 ×109 = 107, 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

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.