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Orbit (follow up) - SlideRule - 12-31-2014 02:40 PM


a follow on posting for the ORBITS post (indirectly related)

form the Preface of Orbital Flight Planning by H.E. Blackwell, Ph.D.
This material is designed for students Interested in the area of space flight planning, who after training, may serve as flight planning aides. Flight planning aides are individuals who will assist engineers and scientists in the planning of orbital specs missions. With the development of the NASA space shuttle and its earlier successful missions, the time will come shortly when orbital flight missions will become a routine and nearly continuous activity. Space station construction is likely to be the first significant activity of the shuttle, along with the deployment of strategic and scientific experiments. Extensive commercial use of orbital flight is expected to follow.
With orbital flight becoming much more common, the need for routine flight planning activities increases. There are significant tasks in the planning of flights that can be performed by individuals with less than an engineer's background. Those tasks will be performed by the flight planning aide.
The objective in the training procedure for a flight planning aide is to provide an output, in a short period of time, that is capable of performing engineering type calculations and analyses. To perform useful and significant calculations, it is not necessary that one know the details and background of all operations. That is true for tasks other than calculations. While it is hoped that calculators and computers do not retard us in ability to add, multiply and reason, they do allow many of us who bore to error with the task of addition to become painlessly highly accurate. Some of us are curious about process and insist upon a thorough understanding. The flight planning aide student will be capable of performing certain operations without understanding their bases, and hopefully have a curiosity that will be required for learning extension. It is on that basis that this training material has been put together in a directed learning approach.
For this material, a calculator is necessary. Calculators and computers, along with the pencil, will certainly be the professional tools of the flight planning aide. Use of the calculator, common now in the general population, is emphasized first in the workbook in order to proceed quickly toward programming and eventual use of the computer. A strong objection might be made on the emphasis put in handling a particular calculator, the Hewlett-Packard 67. That we have done. Any programmable calculator with a good guide to its use, however, will be appropriate for the given exercises. Texas Instruments has such a calculator, though it uses algebraic logic, and there are others. Although we have described the HP keyboard and made specific reference to the HP handbook, any calculator may be used with the understanding that its operations must be thoroughly understood, through use of its calculator guide or owner's handbook. The first requirement for the flight planning aide student, therefore, is to be able to learn the use of the calculator. A strong mathematical inclination is also thought necessary.
But we have attempted to integrate learning activities. Flight planning vocabulary and orbital flight relations are introduced in the beginning and are used while facility with problem solving and the first major objective use of the calculator, is learned. To do this as we have, primary calculator instruction must come from the manufacturer or elsewhere. The learning tasks proceed through the solving of problems, as relatively more complex problems are quickly introduced into the calculator and programming exercises.
Teaching beginning students through such a problem sequence has long been a fascination of mine, but difficult to effect in traditional college sequential course curriculum. An information scattering technique is used, one I use in lecture and believe to be quite useful in inputing data to the learner that is not to be immediately used. But too much non-useful written information can be inhibitive. This written material contains only purposeful information with the hope that curiosities will be aroused to the point of asking questions and seeking further knowledge. The teaching-learning philosophy of Mr. Davis, in teaching such a course in flight planning, has been quite similar to my own.

NASA (NTRS) - Introduction to orbital flight planning

The HP67/HP97 Users' Library Solutions booklet, SPACE SCIENCE, as well as HP-41C Users' Library Solutions booklet, Physics (#6 Delta- V-Orbit Simulator) is applicable.



RE: Orbit (follow up) - Dwight Sturrock - 12-31-2014 04:44 PM

I like the phrase "though it uses algebraic logic,". Nice slam there.
Now that we often use computers, not only do we use algebraic logic,
We are reduced to clutter:


Which is ugly, inelegant and complicated.

RE: Orbit (follow up) - Paul Dale - 12-31-2014 11:23 PM

Edit: Ignore this, I don't know my operator precedence as Walter points out below.

(12-31-2014 04:44 PM)Dwight Sturrock Wrote:  We are reduced to clutter:


Which is ugly, inelegant and complicated.


\[\large e^{\frac{1^x}{x}}-\pi\]


- Pauli

RE: Orbit (follow up) - walter b - 12-31-2014 11:57 PM

(12-31-2014 04:44 PM)Dwight Sturrock Wrote:  We are reduced to clutter:


Which is ugly, inelegant and complicated.

Hmmmh. I vote for
\[\large {\frac{e^{1^x}}{x}}-\pi\]

RE: Orbit (follow up) - Dwight Sturrock - 01-01-2015 12:42 AM

Wolfram Alpha interprets e^1^x/x-pi like Walter did.

Octave interprets it as e^1^x/x-pi as (e^1)^x/x-pi, which is different than Wolfram-Alpha.

I would interpret it as Pauli did. Always used RPN calcs in college for math and electronics courses, never had problems with precedence.

Seems like I was always checking my MatLab inputs & outputs against my RPN calc to be sure we were talking the same language.

RE: Orbit (follow up) - RMollov - 01-01-2015 07:24 AM

(12-31-2014 11:57 PM)walter b Wrote:  
(12-31-2014 04:44 PM)Dwight Sturrock Wrote:  We are reduced to clutter:


Which is ugly, inelegant and complicated.

Hmmmh. I vote for
\[\large {\frac{e^{1^x}}{x}}-\pi\]

I vote for that too. And the brackets are redundant.

RE: Orbit (follow up) - RMollov - 01-01-2015 07:35 AM

(01-01-2015 12:42 AM)Dwight Sturrock Wrote:  Octave interprets it as e^1^x/x-pi as (e^1)^x/x-pi, which is different than Wolfram-Alpha.
... and wrong.

RE: Orbit (follow up) - Thomas Klemm - 01-01-2015 02:25 PM

(12-31-2014 02:40 PM)SlideRule Wrote:  NASA (NTRS) - Introduction to orbital flight planning

That's an interesting workbook. Thanks for sharing.

For small eccentricities (e), the true anomaly may be found from the formula,
\[\Theta=M+2e\sin M+\frac{5}{4}e^2\sin 2M+\frac{e^3}{12}(13\sin 3M-3\sin M)\]
p. 48

While it's clearly not the focus of the book to understand all the formulas but to apply them to real world problems you still might be wondering how they were found.
A few years ago I posted the somewhat related article Sunrise and Sunset wherein I referenced a paper where you can find the derivation of that formula:

Wir setzen also im weiteren
p. 158