# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Where lies the hole in the Polar Cusp?**

**From:**Frank Reed

**Date:**2021 Dec 7, 07:15 -0800

David Pike, you wrote:

"It mentions the ‘Hole’ which appears around noon each day. One of the few 'Comments', if you can unload them, asks 'How do you know when it’s Noon at the Pole at the Summer Solstice?'. "

Of course there is no local noon on any date, solstice or not, at the (exact mathematical) geographic pole because there is no longitude. But the "so-called" polar cusp does not occur at the geographic pole. It exists hundreds of miles from the pole on the side of the Earth facing the Sun. So local noon is well-defined in the vicinity of the polar cusp.

Also, setting aside the polar cusp, even for observers very close to the geographic pole, one can always dispense with these sorts of questions simply by pointing out that no observer can ever be at the "exact" pole because it is a mathematical point. If you're one nautical mile from the pole, then compass directions are meaningful as usual. Then at the north pole local noon occurs when the Sun is due south. Alternatively, local noon occurs when the longitude of the point on the globe directly beneath the Sun (the Sun's GHA, in navigator jargon) is identical to the observer's longitude. It may not be observable in any useful way, but it's defined.

And:

"From a celestial point of view, might the Polar Cusp affect atmospheric refraction when the body is opposite side of the Pole to the observer?"

Here's a NASA press release from 2018 on these sub-orbital rocket experiments: https://www.nasa.gov/feature/goddard/2018/science-on-the-cusp-sounding-rockets-head-north. And here's another from last week: https://www.nasa.gov/feature/goddard/2021/science-at-the-cusp-nasa-rocket-to-study-mysterious-area-above-the-north-pole. The increase in atmospheric density at 250 miles altitude is described as "large" and it is, from a certain point of view. They describe a 50% increase in density. But of course this is the highly rarefied ionosphere. The density at that altitude is so low that satellites orbit up there for years without difficulty. Atmospheric drag at this altitude is real, and the International Space Station, for example, requires periodic re-boosts. In fact, 400km is a sort of "sweet spot". It's low enough that it's still relatively cheap to launch to, and it's high enough so that atmospheric drag has a typical time scale of about a year. These days, drag is counted as a "good thing". It guarantees that derelict satellites will come down within a few years.

As noted in the press releases, one question they're interested in answering is whether the increase in density at 400km demands an increase in pressure (and therefore density) at lower altitudes to support the weight of that extra mass in the high atmosphere. But let's be clear here: the amount of gas in a cubic meter at 400km altitude is approximately a trillion times less than at sea level. At sea level, with standard temperature and pressure, one cubic meter of air has a mass of about 1.2kg (and remember, 1 cubic meter of water has a mass of 1000kg). That varies by a factor of roughly 100 depending on solar activity. Clearly the factor 1.5 described for the polar cusp region is quite modest compared to the variation experienced in the 11-year solar activity cycle. In any case, the upper atmosphere is simply irrelevant to refraction at sea level or at "flying" altitudes in the atmosphere. We can treat everything above the stratosphere as insignificant detail.

Frank Reed

PS: Decades ago, launching ballistic rockets from Norway with "scientific payloads" was generally understood as testing the radar systems of the Soviets during the Cold War. In fact the science was a useful cover story on the more critical intelligence payload. Whether there is any of that mixed motivation (and funding) today is not clear. But given current international tensions, I would not be surprised.