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Math for calculating orbital rendezvous manovers


alpha tech
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OK so i have been looking for a way to mathematically figure out how to rendezvous with anther spacecraft with out using the map as a challenge and i have been reading on Wikipedia on orbital rendezvous, and i think i have come to an partial understanding of it but i am not sure. so here is what i know that i have to do. first i have to go either higher or lower than the target, phasing orbits, and then at a certain moment i have to speed up to catch up with the target when in a matching intersection, and then after the burn i have to point retrograde on target mode on navball and fire at closest approach when i get to the separation distance. now here is the article that i have been reading and i partially understand it except for the ARC-TAN, SINE, TAN. https://en.wikipedia.org/wiki/Orbit_phasing

so its just the arc tan, sine and tan that get me off cause i have no idea what they are

 

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TAN and SIN are trigonometric functions. TAN describes the ratio of the legs of a right triangle given an angle of said triangle. Similarly, SIN describes the ratio of one leg and the hypotenuse given an angle. The specific sides involved can be gotten from the mnemonic "SOH-CAH-TOA" where O=opposite leg, A=adjacent leg, and H=hypotenuse, relative to the angle (by convention, theta).

ARCTAN is an inverse trig function. Given a ratio of sides (refer again to SOH-CAH-TOA), ARCTAN returns an angle.

You can find these functions on any scientific calculator.

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Another note:

Unless I'm wrong (in which case, please correct me), most phone calculators that have trig functions write arcsin, arccos, and arctan as sin-1, cos-1, and tan-1. I think some graphing calculators (TI-84, TI-nSpire, etc) do this too, but I can't confirm it.

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On 5/15/2017 at 1:18 PM, 0111narwhalz said:

TAN and SIN are trigonometric functions. TAN describes the ratio of the legs of a right triangle given an angle of said triangle. Similarly, SIN describes the ratio of one leg and the hypotenuse given an angle. The specific sides involved can be gotten from the mnemonic "SOH-CAH-TOA" where O=opposite leg, A=adjacent leg, and H=hypotenuse, relative to the angle (by convention, theta).

ARCTAN is an inverse trig function. Given a ratio of sides (refer again to SOH-CAH-TOA), ARCTAN returns an angle.

You can find these functions on any scientific calculator.

OK i knew they were trig functions but i had no idea what they did or how to use them i have a TI-84

for this do i have to use sin(O*H) or what

and you saying if i have two sides and do the inverse i can get an angle with ARCTAN

 

On 5/15/2017 at 7:42 PM, TotallyNotHuman_ said:

Another note:

Unless I'm wrong (in which case, please correct me), most phone calculators that have trig functions write arcsin, arccos, and arctan as sin-1, cos-1, and tan-1. I think some graphing calculators (TI-84, TI-nSpire, etc) do this too, but I can't confirm it.

yes i have seen the Tan -1 an sin -1 on my calculator

and just to ask if their is a more simpler explanation for these cause i kind of get the ratio between two sides but other than that i am totally lost like the inverse i know that has to deal with the opposite regression or something like that. but functions i get them but the explanation of what they are or how to explain them is way beyond me. i took algebra 1 but other than that i have no clue.

 

Edited by alpha tech
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1 hour ago, alpha tech said:

and you saying if i have two sides and do the inverse i can get an angle with ARCTAN

Exactly that, if you have two sides, resp. the ratio of their lengths, you can get the angle with arctan, in the same way as you can get the ratio of these sides by taking tan of the angle.

1 hour ago, alpha tech said:

and just to ask if their is a more simpler explanation for these cause i kind of get the ratio between two sides but other than that i am totally lost like the inverse i know that has to deal with the opposite regression or something like that. but functions i get them but the explanation of what they are or how to explain them is way beyond me. i took algebra 1 but other than that i have no clue.

arctan is the inverse function of tan, i.e. arctan = tan^-1.

What does inverse function mean? If I have a function f mapping x to y, then f^-1 maps y to x (provided that no more than one x is mapped to y).

What does this mean for tan? tan maps angles in (-pi/2,pi/2) resp. (-90°,90°) (depending on your notation of angles) to values in the real numbers, and arctan maps real numbers to angles in (-pi/2,pi/2) resp. (-90°,90°). For example tan(pi/4) = tan(45°) = 1, and arctan(1) = pi/4 = 45°.

Or take a look at this graph

280px-Tangent_one_period.svg.png

tan maps values on the horizontal axis (usually called the x-axis) to values on the vertical axis (usually called the y-axis), arctan does the inverse: it maps values on the vertical axis to values on the horizontal axis.

Edited by Tullius
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