Resolution of the planet Mars

Dr. Neville Thomas Jones, Ph.D.


There seems to be some fundamental flaw in the almost universally-accepted astronomical data regarding the size of, and distance to, Mars. For instance, on the 29-09-2003, the "Starwatch" column on page 22 of the UK's Guardian newspaper reported that Mars was 72,000,000 km away from us, and that it subtended an angle of 19.4 - 20 arcseconds.

If Mars has a radius 0.5327 times that of the World (Encyclopaedia Britannica) and was really 72,000,000 km away, then it would indeed subtend the stated angle. However, the lower limit of human sight, corresponding to the wavelength for peak spectral sensitivity, 560-nm (Hecht and Williams, J. Gen. Physiol., 5, 1-34), is given by Born and Wolf as 24 arcseconds (Principles of Optics, sixth edition, p. 415). Now it should be noted that Born and Wolf's tome is widely recognized as the foremost work on optics and that their figure of 24'' represents an absolute minimum. In fact, the angular resolution of the human eye is usually taken as being about 1 arcminute (3 times bigger than the angular extent claimed for Mars' disc at the time in question).

If someone holds a pound coin between their finger and thumb and walks away from you, there will come a point when you can no longer see the coin. I.e., its angular dimension is too small for the optical instrument you are using (your eye in this case) to resolve. Exactly the same is true of a football, a hot air balloon or a planet. Mars is not emitting visible light any more than the coin is.

If the coin were a light, and that light flashed, then you would probably see the flash, but you would be unable to determine the outline of the coin.

Mars is an object. A big object, fair enough, but nevertheless still an object. We see it because light is reflected off it, just the same as we see the pound coin between our friend's finger and thumb. It is sunlight that is reflected off the coin and it is sunlight that is reflected off Mars. Thus Mars is simply an illuminated object, like the coin, like a football, like blades of grass, etc.

The smallest object that can be resolved by an optical instrument of circular entrance pupil is well-established and is given by something called the Rayleigh resolution criterion. This, in turn, depends upon only two things: the diameter of the aperture and the wavelength of the light. Distance does not come into it, for what we are talking about.

The eye is an optical instrument which obeys the Rayleigh resolution criterion. There is no question about this. Let's take the wavelength as 560-nm, corresponding to the peak spectral sensitivity of cones in the human retina. Let's take the maximum pupil aperture, which corresponds to a fully dilated (i.e., dark-adapted) pupil. This gives us the very maximum chance of resolving the object (i.e., of determining its shape). What is the smallest illuminated object that we can resolve under these conditions? The answer to this question has been shown to be 24 arcseconds. This means that at the distance quoted to Mars, the claimed diameter of Mars is (well) below this limit. If the distance of 72,000,000 km is correct, then Mars' diameter must be bigger. Conversely, if the diameter is correct, then the distance to this planet must be much less. Possibly (almost certainly, in my opinion), both distance and diameter are greatly exaggerated.

This point is based upon standard diffraction theory. It is all the more convincing if one bears in mind the fact that you do not need a totally dark-adapted eye to see Mars. It is (relatively) very large. It does not necessarily need to be bright (and indeed can be partially obscured by cloud). The angular resolution of the human eye under these circumstances, and at this wavelength, is one arcminute. The point? Secular data does not add up. Either the distance to Mars is wrong, or the size of Mars is wrong, or both.

The only effect that does tend to slightly increase the size of Mars is the spreading of its point spread function by the Earth's atmosphere. This is true only to a very small extent. It is a statistical effect and is important only for long-exposure images in telescopes. The response time of the cones in the fovea of the human eye make this spreading almost completely non detectable. (Through a telescope the only thing you will notice because of this is a slight blurring of features on Mars.) I repeat, then, that the accepted distance to Mars and the accepted diameter of Mars would make it completely indistinct to an unaided human eye. On the contrary, it was a very sizeable nighttime object. Something is wrong. That something is the secular data regarding Mars, for what we actually observed during the latter part of 2003, even if going out from a brightly-lit room and looking at Mars without waiting for our eye to adapt and for the pupil to fully dilate, was a distinct, sizeable orange disk.



Based upon this data, Mars would have been a point of orange light against a black backdrop to the unaided human eye, rather than the extremely brilliant disc that we could all very easily see (this was a few weeks after its closest approach). Since the eye has been extensively studied in terrestrial laboratories, and since Fraunhoffer diffraction theory is very well established, it seems obvious, from the simple observation of any one of us, that earthly data regarding Mars is significantly incorrect.