

Once we know how magic works it's no longer magic; it becomes science.  Karthik [more] 



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#1




Some physics/math help
I'm a part of the Texas High School Aerospace Scholars program, an online science course that the Johnson Space Center is conducting. All of the lessons consist of an essay, math problem, and occasionally a graphic. The first lesson doesn't quite explain the math problem that well, and many of the other students are confused. I can't simply tell you the full question because I'm supposed to be doing this myself, but I just need clarification as to what it's asking for.
If an orbiting craft needs to reduce its perigee to a certain altitude from its current altitude, how would I find the change in velocity the craft must make? I'm provided with both the initial and final distances, along with the mile:fps change in velocity ratio for these altitudes. Two of the other students have mention the Braking Distance formula of Vf^2=Vo^2+2ad, but I don't see how to use it. Any help at all would be appreciated. Thanks much, Parker 
#2




Re: Some physics/math help
"I'm provided with both the initial and final distances, along with the mile:fps change in velocity ratio for these altitudes."
Sounds like to me it is a little more simple than they are making it out to be. If you have the ratio, you can figure out the initial and final velocities from that ratio table. Change in velocity is just the difference. Now if you need to calculate a rate of change of velocity (constant deceleration), then the equation your friends gave would be correct. I am not a Rocket scientist, but I was a Physics tutor in College. Without the exact details of the problem, that is about all I can help. If you would like some further assistance, feel free to PM me and I can discuss further. 
#3




Re: Some physics/math help
When we learned about satellite motion in my physics class last year, to find velocity at a certain altitude we used the equation
v = sqrt(G*m/r) Where G is the gravitational constant, 6.67x 10^11 Nm^{2}/kg^{2} m is the mass (kg) of the body/planet the satellite is orbiting, and r is the radius (altitude) of orbit in meters. You could use the given distances to find the velocity at each altitude, subtract your answers to find the change, and convert to the proper units. 
#4




Re: Some physics/math help
Quote:
This is true if you are definitely balancing centripetal Acceleration with gravitational pull. From the problem statement he gave though, it sounds like they gave him a table or ratio to calculate those values. 
#5




Re: Some physics/math help
The page says, "There is a change of 1 mile for every 2 feet per second (fps) change in velocity when you are below a 500mile altitude above the Earth." Sorry if I wasn't clear. I didn't mean they actually gave me two ratios.
I think it's much easier than it is made out to be, and others have mentioned that using that exact equation isn't even necessary. At the moment, I'm just stumped on the velocities. EDIT: DeltaV, change in velocity, is defined as (VfVo), correct? If so, would DeltaV or the 'a' in the above mentioned formula be the given ratio? Last edited by ParkerF : 12282008 at 08:12 PM. Reason: Small thought. 
#6




Re: Some physics/math help
Quote:
Say initial altitude is 500 miles and final altitude is 400 miles, the change in altitude would be 100 miles therefore the change in velocity would be: (100 miles)/(1 mile/2 fps)=200 fps change in velocity. 
#7




Re: Some physics/math help
Thanks for the help. I believe I've got it down now. Your information and a bit of help from JVN finally got me to understand the problem, and it is ridiculously simple. Now I just need to do my essay. .
Again, thanks a lot for your time and information, Parker P.S. I actually had the answer a few days ago when I had attempted it, but it felt too simple so I check the TAS forums to see many other students confused by it, hence the beginning of over thinking. 
#8




Re: Some physics/math help
If it walks like a duck, and talks like a duck could be a very clever animatronics display created by Disney Imagineers.... Sometimes it is just a duck.

#9




Re: Some physics/math help
Well, seeing as this is a great place to do so, I want to make sure I did this next problem correctly for selfassurance.
Quote:
f/m=a < New formula 12,000 lbs / 250,000 lbs =a .048 G =a .048 G * (32 fps/s) =a < Converting away from Gs (1.536 fps/s) =a t=v/a t=304 fps / (1.536 fps/s) t=197.916667 seconds t=197.916667 seconds / 60 seconds < Converting into minutes t=3.29861111 minutes If someone could spare their time to just check over this and let me know if I thought the problem through correctly, it would be greatly appreciated. Thanks very much, Parker Francis 
#10




Re: Some physics/math help
Long answer:
Your calculation is correct, but I would be careful with the use of English units in general. I would convert everything to SI units (Newtons, meters, etc.) simply because working with English units can be a bit tricky, particularly when doing calculations with Newton's 2nd law. The problem I see with your calculations is that you are mixing pounds as force and pounds as mass. Pound generally means force, but there is a unit called the Avoirdupois pound that refers to mass. When you use Fnet = ma, the calculation only works if the units for mass and force match, kilograms with newtons, for example. I know it sounds tedious, but when faced with a problem given in English units, I recommend converting your units to SI, use your equations to make your calculations, and then convert back for the answer. I tell my physics students that the extra brain wringing required to use English units in calculations ends up being much worse than doing the unit conversion twice. When you do the conversion, and you divide the force by the mass, your answer is in units of acceleration, as you would expect. In the case of this problem, you divide and get an answer in G's, which can be a bit awkward if you don't know how to deal with it. You handled it without a problem though, so congrats! short answer: Good work...you should think about limiting the number of decimal places you report in your final answer though Happy new year! Evan 
#11




Re: Some physics/math help
Thanks very much for looking over it, I'll keep what you said in mind. I stared at Google Calculator and the question for about 15 minutes straight before I decided to go with my attempt at converting the Gs and such. It's a very confusing concept for me, but I'm glad I got lucky.
Thanks again, Parker Francis Last edited by ParkerF : 01012009 at 03:27 PM. Reason: Sentence edit 
#12




Re: Some physics/math help
are you sure you got the first question right? When i worked it, I obtained a different fps using the ratio. How did you get your first answer?

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