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."]

LM Descent to the Moon - Part 6 - Programming (1971)

(Apollo Lunar-Descent Guidance, 1971)

[The following MIT / NASA's 1971 text, partial reprint of the reference /0/, describes the descent algorithms used in the Apollo Lunar Module computer program (Luminary version 099/1A, about 63,000 lines of YUL assembly code) and flown summer 1969. This paper actually describes an advanced version of the algorithm which was not used since the older version which was more tested at that time (1969) was good enough for the job. What so ever, the text gives a good glance to the manned planetary descent programming.]

Figure 1. Components of the Lunar-Descent Guidance System.

LM Descent to the Moon - Part 5 - Powered Landing Maneuver (1964)

(LEM Powered Landing Maneuver, 1964)

[This is a partial reprint of a 1964 technical paper from MIT/NASA, which explains the mathematics behind the 1960's lunar landings. See /1/ for details. LM was called LEM (Lunar Excursion Module) those days and the first landing was to be done summer 1969, 5 years after this paper was written. The strength of this algorithm is that it is real time adaptive to the variations of the parameters from different sources (and also errors). This algorithm was called "E Guidance" due to the E matrix used in it. The basic LM descent guidance logic was defined by an acceleration command which was a quadratic function of time and was, therefore, later termed "Quadratic Guidance". ]

Figure 0. Look angle "lambda" is relative to the thrust axis

Orbit Calculator (Circular)

Orbit Calculator

Planet Mercury Venus Earth   Moon Mars Jupiter Saturn Uranus Neptune Around which the satellite orbits. Currently using Mass kg Radius m Altitude [h] m km Speed [v] m/s km/s Period [T] s min

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Circular orbit variables

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Solar System Simulator

A handy solar system simulator is available from Solar System Scope. This simulator gives you a better view to our solar system and how the planets rotate around the sun. You can switch to realistic orbits or planet sizes as you wish, the simulation setup is on the left side.

Solar System Simulator snap shot

Press the following link to start the simulation and wait until the flash player loads fully and then click inside the window.

Link to: Solar System Simulator

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LEAMOR Manned Space Craft - Modular Transport Engine (Part 3)

PART 3: Modular Transport Engine (TE)

LEAMOR stabnds for Light Extended Apollo Mars Orbit Rendezvous.

As we already have figured out that the large spacecraft must be modular (since the lift vehicle can only lift a certain amount to the LEO at one time). See the previous part of this article series and we call these about 150 ton (lbs) building blocks as L-modules.

L-Modules about 150 000 lbs each, size about D5 x L11.75

LEAMOR Manned Mars Mission - Why Modular? (Part 2)

PART 2: Why the Manned Mars Mission Must be Modular?

Simply because the launch vehicle can only lift a certain amount at any time - and that size or mass will be the maximum module size - and the only way to get larger masses and structures is to bolt them together in the low Earth's orbit (LEO).

LEAMOR stabnds for Light Extended Apollo Mars Orbit Rendezvous.

SLS can lift about 150 .. 300 tons (lbs) to LEO

Delta-V Calculator (The Rocket Equation)

Delta-V Calculator

Before burn (Rocket mass incl. fuel m1) After burn (Rocket mass excl. fuel m2) Vex or Isp exhaust velocity specific impulse Delta-V change in velocity = Vex*ln(m1/m2)

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