Extreme Points of a Great Circle - (Part 3, Great Circles)

The Northernmost and Southernmost Points of a Great Circle

If you travel from Amsterdam (P1 in Figure 1) to San Francisco (P2) or the other way around, then you first go towards the north for a while, and then towards the south for a while. All great circles except for the equator have a northernmost point (PN) and a southernmost point (PS). You can calculate them as follows.

Fig. 1: Northernmost and Southernmost Point on a Great Circle

Certain Direction from a Point - (Part 2, Great Circles)

Suppose you want to know where you go if you start from a particular town in a particular direction and keep going straight (along a great circle). You can calculate the coordinates of points along the route as follows:

Fig. 2. Mercator and Hondius

Definition of a Great Circle - (Part 1, Great Circles)

[Since great circle calculations are so important on all spheres (like Earth, planets, polar coordinates, etc.) I have to add here such a text. This follows mostly /1/]

Fig. 7. Arthur H. Robinson 1979

["Arthur H. Robinson (January 5, 1915 – October 10, 2004) was an American geographer and cartographer, who was professor in the Geography Department at the University of Wisconsin–Madison from 1947 until he retired in 1980. He was a prolific writer and influential philosopher on cartography.

One of Robinson's most notable accomplishments is the Robinson projection. In 1961, Rand McNally asked Robinson to choose a projection for use as a world map that, among other criteria, was uninterrupted,[9] had limited distortion, and was pleasing to the eye of general viewers.[10] Robinson could not find a projection that satisfied the criteria, so Rand McNally commissioned him to design one.

Robinson proceeded through an iterative process to create a pseudo-cylindrical projection that intends to strike a compromise between distortions in areas and in distances, in order to attain a more natural visualization. The projection has been widely used since its introduction. In 1988, National Geographic adopted it for their world maps but replaced it in 1998 with the Winkel tripel projection."]

Mars Atmosphere and Water

There seems to be often a discussion about the Martian atmosphere and water there. But it is not commonly understood what effects the low pressure has to water on Mars (and generally in space). Most of us have done some water chemistry in schools and it is usually known how water reacts to pressure and temperature so that it is either solid, liquid or vapor and that there exists so called triple point where all these phases meet. The following figure shows the general water phase diagram relative to the pressure and temperature.

Figure 1. Water Phase Diagram

In this diagram we can see that as the pressure gets lower we come to the triple point below which there is no more any liquid water available. In space where there is the zero pressure there is no liquid water possible, it boils instantly. Only solid and vapor is possible.

Since in any atmosphere (Earth and Mars) the pressure gets lower when we go higher it is more convenient to show this diagram inverted so that it shows the phenomena relative to the altitude. Below is such a diagram drawn for Earth or Mars.

Figure 2. Water Phase Diagram on Earth and Mars

In this diagram we can see on the left the "normal" situation on Earth (the space might be the more general situation). And we are very used to liquid water since it exists between 0 and 100 C degrees, and is the most common water phase here on Earth. But we seem to forget that Earth surface is just a small exception in the huge space.

When we move to the Mars (on the right in the diagram) we instantly notice that we have lost our liquid water since Mars mean surface pressure is almost exactly water's triple point. And that we cannot even find any liquid water if we go higher in the atmosphere since the pressure just gets lower. Also if we consider the typical low temperatures on Mars we see that any liquid water would be very rare there. Also if the typical liquid water range here on Earth is 0 to 100 C degrees, on Mars it might be just 5 C degrees in very low places and high Mars temperatures. So it is rather clear why there is no living plants possible on Mars without heated pressurized shelters.

In this diagram we can also see that the mean Mars surface is at about 35 km altitude compared to the Earth's atmosphere and we also know that nothing much usually lives naturally above 6 km here on Earth, top of the Mount Everest for example.

["There is very little native flora or fauna on Everest. There is a moss that grows at 6,480 metres (21,260 ft) on Mount Everest. It may be the highest altitude plant species. An alpine cushion plant called Arenaria is known to grow below 5,500 metres (18,000 ft) in the region"]


VIDEOS

YouTube video: "Water Boiling at Room Temperatures, Under a Vacuum"

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Apollo Mission Films (Part 14, Apollo Control Systems)

NASA made several films during the Apollo program about the physics, calculations and programming principles used to do the manned Moon trip. Compared to today's standards many of those are very detailed and give very good information about how the programs behind the successful missions were tailored. Most of films originated from MSC (Manned Spacecraft Center) Houston, Texas. This is a list of links I have found in YouTube (there might be more in various archives).

1950's Computer Language "George"

[The Laning and Zierler system (sometimes called "George" by its users) was one of the first operating algebraic systems, that is, a system capable of accepting mathematical formulae in algebraic notation and executing equivalent machine code.

The system accepted formulas in a more or less algebraic notation. It respected the standard rules for operator precedence, allowed nested parentheses, and used superscripts to indicate exponents.

It was among the first programming systems to allow symbolic variable names and allocate storage automatically. The system also automated the following tasks: floating point computation, linkage to subroutines for the basic functions of analysis (sine, etc.) and printing, and arrays and indexing. It could also solve automatically ordinary differential equations using Gills' variation of the 4th order Runge-Kutta Method, that was an inbuilt language feature.

Dr. J. Halcombe Laning

It was implemented in 1952-53 and published in 1954 for the MIT WHIRLWIND computer by J. Halcombe Laning and Neal Zierler. It was made during a time with similar UNIVAC A-2, IBM Speedcoding and a number of other systems that were proposed but never implemented.

The following text is a reprint of a MIT's summer session report 1954.]

LM Descent to the Moon - Part 7 - Crew Comments (1969)

(Apollo 11 LM - DOI to Touchdown Crew Debriefing, 1969)

[The following is a partial reprint of NASA's Apollo 11 crew interviews /1/ during their quarantine that took three weeks after their splash down. Apollo 11 CM splashed down on July 24, 1969.]

Figure 1. ARMSTRONG, COLLINS and ALDRIN.
The Apollo 11 mission, launched on July 16, 1969 and returned to Earth on July 24, 1969. Aboard the space craft were astronauts Neil A. Armstrong, commander; Michael Collins, Command Module (CM) pilot; and Edwin E. Aldrin Jr., Lunar Module (LM) pilot