User:Danielravennest/papers/Gravity Lens Beam



Gravity Lensed Beamed Power for Interstellar Propulsion

Dani Eder

Tirion Designs,

1309 Stroud Ave, Gadsden, AL 35903




 * Abstract


 * We consider the possibility of using the Sun as a gravitational lens to focus a high-power beam on a distant spacecraft. The beam energy is used to power a high exhaust velocity particle accelerator.  This relieves the spacecraft of needing an internal power supply for propulsion.  If the delivered energy is large enough, it can exceed the rest-mass energy of any fuel.  If the particle energy of the exhaust is relativistic, the exhaust mass can exceed the rest-mass in the fuel tank.  This has the potential for better performance than anti-matter concepts and modifies the normal Tsiolkovsky rocket equation because fuel used does not equal exhaust mass.

Notes for Text


 * The paper has not been written yet, but this section will hold notes for later inclusion


 * Light ray deflection angle $$\theta = \frac{4GM}{rc^2}$$ radians, where r is the impact parameter (undeflected miss distance from the object center), G is the universal gravitational constant, M is the mass of the body, and c is the speed of light. For the Sun, the gravitational parameter GM is 1.32 x 1020m3/s2, so the formula reduces to the convenient form $$\theta = 5906/r$$ where r is in meters.  Note that the radius to bend light 1 radian is exactly twice the Schwarzchild radius for a black hole of the same mass.


 * To avoid disturbances from the Sun's atmosphere, we choose an impact parameter of 109 meters, or 1.4 Solar radii. This gives a deflection of 5.9 x 10-6 radian, or 1.2182 arc-seconds, a value confirmed by eclipse tests of relativity nearly a century ago.  Since the deflection occurs equally all around the perimeter of the Sun, parallel light rays come to a focus at a distance of 1/deflection angle = 169,319 x impact parameter = 169.319 billion km = 1131.8 AU.


 * NBF article comments where idea was brought up and discussed


 * Need to reference previous work by Robert Forward on laser-pushed lightsails focused by fresnel zone plate.
 * Space Transport and Engineering Methods/Photon Engines


 * Calculate optimum combination of collector size at spacecraft and beam source behind Sun. Consider sail type reflector focusing to solar cells vs direct beam collection with large array.


 * Calculate maximum beam intensity for solar cells with beam frequency tuned to semiconductor bandgap, and allowing for doppler effects.


 * Find numbers for lightweight particle accelerators.


 * Extract relevant info from NBF discussion.


 * Do literature search for beamed power and interstellar travel.

__________

