Sunday, 7 February 2016

70) “From Washington’s Rock in New Jersey, at just a 400 foot elevation, it is possible on a clear day to see the skylines of both New York and Philadelphia in opposite directions at the same time covering a total distance of 120 miles! If Earth were a ball 25,000 miles in circumference, both of these skylines should be hidden behind over 800 feet of Earth’s curvature.

On a clear day, refraction.

They took their time to mention that we're talking about a clear day. Note also the discolouring on the image. I'm not going to spend much more time on pointing out refraction.

You know what? We will describe how to falsify the refraction explanation. 

·                     Three monochromatic high-power lasers; preferably, one red, one green and one blue, because primary colours. Ultraviolet lasers are also an option.
·                     A frequency generator of sufficient power.
·                     Three synchronised detectors.
·                     Other stuff that's not important enough to list.
If you're wondering about the frequency generator and synchronisation, it is because of a trick that allows you to detect dim objects.

So, what is the point? Well, we know that the refractive index depends on the wavelength. A widespread of lasers allows for monochromatic light of different wavelengths, so that one can directly falsify or confirm that prediction.

Ideally, the setup is such that the lasers are aligned in parallel from New York City to Bear Mountain. With a lot of effort, one can place the detectors such that they detect the lasers. If you're afraid of a fake signal, use a music song to regulate the laser. Yes, that can be done, and while it complicates the data analysis it is also extremely powerful as a way of detection.

What will you find? Well, if the refractive theory is true, then the differently coloured lasers will have detectors at different locations. It's that simple.

So far, this has been confirmed. The essence of the experiment isn't that hard - it basically uses lasers to determine the refraction, which can depend on various atmospheric conditions. And would one find this?

Atmospheric effects deleteriously impact free space laser communications. Beam wander, distortion and beam bending can affect pointing and tracking in particular. Mirages are an example of these effects. In June 2006, a campaign was conducted across the Chesapeake Bay by the Naval Research Laboratory to quantify effects of mirages at the marine layer. We imaged a series of lights positioned strategically on a tower across the bay, at Tilghman Island, approximately ten miles away from NRL's Chesapeake Bay Detachment (NRL-CBD). Recorded images were subject to displacement and distortion as functions of temperature, humidity, dew point, and other meteorological parameters. Results from the experiment will be presented and phenomenology discussed. [doi:10.1117/12.800782]

False claim

The distances from Washington Rock are roughly 40 km to Manhattan Island and 80 km to Philadelphia (and not "120 miles").

Looking out from Washington Rock however, you can only look in one direction, which is southeast. Neither New York (NE) nor Philadelphia (SW) lie in this direction.

Let's run the math anyway. Elevation is roughly 510 feet (155m) and not 400 feet. Even if it was in that direction and using the calculation from  #69, Manhattan should be perfectly visible from that vantage point (horizon at 45km).

The drop from the horizon to Philadelphia is roughly an extra 100m. With Philadelphia at 12m elevation, even buildings higher than 88m in Philadelphia should be visible. Factoring in refraction (depending on weather conditions), you would be able to see even more. A rough guessing value for refraction under normal conditions is 0.13 times the expected total drop as seen from sea-level:

Total drop for 80km distance (from sea-level) is roundabout 500m. So that gives you an extra 65m through refraction (with minimum standard value). That means, even buildings in Philadelphia that are only 23m high should come into view under average conditions.

Again, and just in case you're interested, here's a recent study that explains why the refraction coefficient (k)  can be far higher than the standard +0.13, even up to +16 near the ground on hot summer days:

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