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/sci/ - Science & Math

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2230912 No.2230912 [Reply] [Original]

I've got a few math problems that I need to confirm I did correctly :) Can someone make sure I did these right?


1st:

The shuttle must reduce its velocity at a pre-calculated point in orbit in order to return to Earth. For this maneuver, the shuttle is turned into an attitude with the Orbital Maneuvering System (OMS) nozzles pointing into the direction of the velocity. The shuttle must perform the burn to change its orbit so that the perigee, the point in the orbit that is closest to Earth, is inside the Earth's atmosphere. The opposite of perigee is apogee.

De-orbit maneuvers are usually done to lower the perigee of the orbit to 60 miles (or less). The shuttle is captured and re-enters as it passes into the atmosphere at this altitude. There is a change of 1 mile for every 2 feet per second (fps) change in velocity when you are below a 500-mile altitude above the Earth.

Determine the feet per second change in velocity (delta-V) the shuttle will need to make if it is at an altitude of 236 miles above the Earth at apogee and 220 miles above the Earth at perigee, and needs to drop the perigee to an altitude of 60 miles. The units for this math problem are feet per second.

perigee = 220.
220- 60 = 160 miles needed to descend.
160*2 = 320FpS change in velocity. ( 1 mile : 2 Fps)

>> No.2230923
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2230923

Scia, I remember the variables when you posted the question. No need to go anon.

>> No.2230930

>>2230912
I guess that drops the perigee to 60 miles, if that's what the question is asking. I think it is.

>> No.2230933

Part 2:
Assuming the orbiter's OMS engines have a combined force (thrust) of 12,000 lbs and the shuttle has a weight of 250,000 lbs (with a full cargo bay), compute the length of the burn in minutes using the velocity from part 1.

f = ma (force equals mass times acceleration) and t = v/a (time equals velocity divided by acceleration)

Your acceleration will be in G's, where 1 G = 32 feet per second per second (this is how far an object travels due to the force of gravity in a vacuum). The units for this math problem are minutes and seconds.

12000 = 250000A (F=MA)
A = 20 + (5/6)
Time = Velocity / Acceleration
(acceleration needs to be in G's) (20+(5/6)) / (32 Fps^2) = (125/192) G's

Time = (320 FpS) / ((125/192))G's = 491.52 Seconds = 8 minutes, 11.52 Seconds

>> No.2230945

Thanks to everyone in advance, I am scared to ask /b/ for help...

>> No.2230959

>>2230930
yah, that's what it's asking

>> No.2230976

>>2230945
Scared? Pssh. I don't understand that point of view very much. You have NO HOPE of anyone there helping you anyway.

>> No.2230987

>miles
>feet per second

all of my hate

Orbital speed

<div class="math">v=\sqrt{\mu (\frac{2}{r}-\frac{1}{a})}</div>

mu is the standard parameter for earth

>> No.2231721

>>2230912

Wait, I recognize this..


HAS?

>> No.2231833

Where does this shit come from? Seriously, as much as I had eurofags and their unitism, who the fuck uses fps and miles for orbital mechanics?

Anyway your first part is right. Your second part is wrong. It's easy to check on google calculator, which gives 3.45 minutes:
http://www.google.com/search?q=%28250000+pounds+*+320+feet%2Fs%29%2F12000+pounds+force

You did a couple things wrong. a=f/m; the 20 5/6 number you got is m/f. You said you wanted to change the acceleration unit to g's, but maybe you meant you wanted to change it from g's to f/s^2. I suggest you always keep your units explicit. It helps you catch your errors. When your answer ends up with the right units, it's a good sign you did everything right.