CORRECTION: An earlier version of this post improperly converted radians to arcseconds, and some table entries were errors. [February 17, 2022]
Back of the envelope calculations using the Rayleigh criterion (R = λ/D) on the resolution necessary to see an inverted image on the surface of the moon (0.11 mm, due to the Schwarzschild radius projection) suggests that upon a 16-meter detector, gamma rays of wavelength 10-10 micrometers would be required for a sufficiently accurate experiment.
For example, the average distance to the Moon is 385,000 km (385,000,000 m). However, the detector must be farther than bMoon = 9 x 10 10 m. If a 16,000 meter separated pair of detectors were located at 1 x 1011 m (0.67 AU), and the image on the Moon to resolve is 0.11 mm, then:
Tan-1 (0.00011 m/100,000,000,000 m) = 1.1 x 10-15 radians = 2.3 x 10-10 arcseconds
The Rayleigh criterion R (in arcseconds) = 0.21 λ/D, where λ is the wavelength in micrometres and D is the size of the telescope in metres, or the smallest distance between two gamma ray detectors.
D = 16,000 m
R = 2.3 x 10-10 arcseconds
(2.3 x 10-10 x 16,000)/0.21 = 1.8 x 10-5μm (gamma rays)
= 1.8 x 10-11 m = 1.7 x 1019 Hz = 72 keV
Any experiment of this type with sufficient resolution and sensitivity would require gamma ray detection surface(s), outer space, etc.
There are ways around some issues pertaining to size (D): For example, using two 4 meter detectors, thousands of meters apart and detecting a fraction of the emissions – this could reduce the required frequency.
The resolution can be improved and the size D may be reduced, when used in conjunction with higher energy gamma rays, such as the decay of Technicium-99, which is used in nuclear medicine, has a half-life of six hours and produces 512 keV gamma rays.
Similar calculations can be made with respect to the Earth. Here are some preliminary Python scripts on the Moon and the Earth. The purpose of this experiment is to test orientability using gamma rays under extraordinary spatial constraints relative to the center of a gravitational field.
See experimental apparatus design parameters below for the Moon or the Earth, where gamma rays γ = 125 ± 50 keV, distance between apertures = 1 x 100±1 mm ≅ a, b = 7 ± 6 AU
|Location||Distance between Apertures||Distance to Detectors||Required Energy of Gamma Rays|
|Moon||~ 0.1 mm||~ 1 AU||~ 120 keV|
|Mars||~ 0.9 mm||~ 4 AU||~ 54 keV|
|Earth||~ 9 mm||~ 13 AU||~ 18 keV|