Math Help

[Greaper]

Hello,
 The Delta Glider 3 is a COOOOOLL craft!!!
 Have been tinkering with the auto pilot Ascent program, my world has dozens of space stations all around
Sol System and beyond.
 My question is simple.
I need a walk through with the
LAUNCH AZIMUTH math.
This is the way I thought the formula should be solved but the numbers don't add up.
I do belive these are the numbers for the DG3 at KSC to mir.

Launch Azimuth=arcsin(cos(Desiered-orbital-inclanation)/cos(Launch-Latitude))

 LA=arcsin(cos(178.81)/cos(40.80))
                 
                   (   .9997 ) / (  .7569 ) ---Cos of each  value then divided.
                   
                    arcsin( 1. 3172  )------arcsin=90 / 1.3172.   This was a wild guess at solving the formula.
                         
                       LA=68.32'       -------I am after the number 42'

So was I close or did I miss the mark compleatly? Most other algebraic math is easy once you know the rules
 to solving the formula.
Could some one exsplain the rules  so I may use ascent Autopilot to get to other stations?
 the above e-mail is no longer valid.
greaper@myexcel.com is the right one.
 Thank you.
 Grm. Reaper

Post Edited ( 06-18-04 06:50 )

[DanSteph]

Hello Greaper, welcome

sry can't help you at this time, I worked 18 hours non-stop,
I'm exhausted, I must go to bed. (7am here)

Cya

Dan



Post Edited ( 06-18-04 06:50 )

[Greaper]

Hello,
 That was quick! No problem!
It is  10:45 PM here in colorado.
 At your conveniance.  Unfortunetly I seam to have more time on my hands than exspected.
 Think I'll take a spin around the naberhood. ;o)
18hours?? that is brutale!!!!!
  I hope it was volentary, and not some bosses idea of a bad joke.
Grm. Reaper

[DocHoliday]

Hello Grim,

I'm not too big on math. But the inclination for Mir looks weird. 178,81 degrees? How did you get that? And cos
(178.81) gives you a negative result..

Hm, anyway, I'm to beat to think right now. I suggest you download Soyuz Guidance MFD and the Progress V1.11
addon. There are good .pdfs and a some Excel sheets on the subject. You should find them on library.avsim.net or
www.orbithangar.com. I'm pretty sure that should get your covered. If not, ask again, there are some pretty smart
people around here that might help you further.

Cheers,

[Simonpro]

Hi there,
Afraid you've got a couple of things wrong:
Launch Azimuth=arcsin(cos(Desiered-orbital-inclanation)/cos(Launch-Latitude))
This formula is correct.

LA=arcsin(cos(178.81)/cos(40.80))
(  .9997 ) / ( .7569 ) ---Cos of each  value then divided.
Completely incorrect.
First: Mir is not in a retrograde orbit. Mir orbited with an inclination of around 52 degrees I think.
Second: KSC is not at a latituude of 40. It is situated at a latitude of about 28 degrees!
Third: Cos 178.81 is not .9997, it is -0.9998.
Fourth: Cos 40.80 is not 0.7569, it is 0.756995 you are rounding off incorrectly.
                   
arcsin( 1. 3172  )------arcsin=90 / 1.3172.   This was a wild guess at solving the formula.
Indeed it is a wild guess. Arcsin is the inverse of sin. i.e: sin(30)=0.5 and arcsin(0.5)=30
There should be a button on your calculator to compute this, something like Sin^-1
                         
LA=68.32'       -------I am after the number 42'
The arcsin calculation and the incorrect variables mean this answer is incorrect.

Finally, please please use radians, not degrees! It doesnt really matter in this problem but if you use degrees for
some other problems in orbital mechanics you will encounter severe problems.

This should enable you to find the correct value.

[Greaper]

Hello,
 Thanks for the heads up.
Only the most basic of algibra was taught to me when I went threw school
 Meny years ago.
As far as the base values I thought I was using the cords from the DGIII scenerio.
 Momentary laps of ressone,
 I shall give it a go. It was late when I made the post and early when found.
Grm. Reaper
"second star to the right and straight on till morning."



Post Edited ( 06-18-04 19:23 )

[DanSteph]

oh btw to include a smiley you just need to include the keyword next
to the smiley image in the smiley help page (this button ->



(click on "quote this message in your reply" to see my message with the smiley tag I used)


Dan



Post Edited ( 06-18-04 15:17 )

[freespace2dotcom]

 

[DocHoliday]

As far as the base values I thought I was using the cords from the DGIII scenerio.

Ah, then you probably fell for that inclination trick. The inclinations througout orbiter (default MFDs at least) are
relative to the ecliptic, not the equator. So if you use them directly, you will get the error in the amount of earth's tilt
with relation to the ecliptic.

Cheers,
Janez

[Simonpro]

Still wont be 178 degrees, though - it *might* be 78, however :p

[DocHoliday]

I know that inclination was the first thing I noticed. That was a pure mixup on Greaper's part I guess.

[Greaper]

Hello,
 My approch was to use know numbers and answer's to the math and try
<Not very succesivly this time.>:wall: differnt aproches to solve the problem.
With to no avail. Numbers got mixed or not read correctly so basicly garbage in garbage out.
Never used the windows science caculeter or any other advance math caculeter.
I didn't catch the -0. on the first   and I rounded to far on the second.
Didnt know to add instead of dived but did see the arcsin =90
Fumboling in the dark. Some times their is light other times one must ask for gidance.
 Thank all of you for your replies and helpful suggestions.
Grm. Reaper