# Gravity Lens Beam [Draft Paper]

Gravity Lensed Beamed Power for Interstellar Propulsion

Dani Eder [1]

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 ${\displaystyle \theta ={\frac {4GM}{rc^{2}}}}$ 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 ${\displaystyle \theta =5906/r}$ 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.
• Need to reference previous work by Robert Forward on laser-pushed lightsails focused by fresnel zone plate.
• 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.

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<References>

1. Author email: danielravennest@gmail.com.