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differentiation

this feels like it should be easy but i am failing miserably at this.

I get given three equations.

E=-(gmn)/(2r)

v = squareroot[gn/r]

E' = -(v^3)2ap

i have to find a or p as a function of g,m,n and r.

E, v, p and r are dependent on time.
(v = r')

i have tried every single permutation of differentiation and substitution for the past 40 hours and still cannot do this.

please give me an idea of what the **** to do,

thanks
Reply 1
Avatar for mqb2766
mqb2766
21
Original post by KloppOClock
this feels like it should be easy but i am failing miserably at this.

I get given three equations.

E=-(gmn)/(2r)

v = squareroot[gn/r]

E' = -(v^3)2ap

i have to find a or p as a function of g,m,n and r.

E, v, p and r are dependent on time.
(v = r')

i have tried every single permutation of differentiation and substitution for the past 40 hours and still cannot do this.

please give me an idea of what the **** to do,

thanks


Do you have a picture of the original question?
qqq.png
Original post by mqb2766
Do you have a picture of the original question?


yeah sorry for the poor paint job
Reply 4
Avatar for mqb2766
mqb2766
21
Original post by KloppOClock
qqq.png


The first part says use (15), so just differentiate that using the chain rule?
Original post by mqb2766
The first part says use (15), so just differentiate that using the chain rule?


qa1.png
i got this already, but i dont get how to use this to get rho or A as a function of GM, r and Me ?
Original post by mqb2766
The first part says use (15), so just differentiate that using the chain rule?


to be honest, i dont think i understand the question right. how can i find A as a function of variables when it is a given constant ? im not sure what im actually meant to be working out
Reply 7
Avatar for mqb2766
mqb2766
21
Original post by KloppOClock
qa1.png
i got this already, but i dont get how to use this to get rho or A as a function of GM, r and Me ?


I think the 2nd part is totally separate from the first part. Do you not just sub v into 18?
Original post by mqb2766
I think the 2nd part is totally separate from the first part. Do you not just sub v into 18?


idk what im meant to be finding. i already have dE/dt as a function of dr/dt. after that part in the second box im not sure what im meant to be getting.

by subbing in that v, i get dE/dT as a function of rho, A and E
Original post by KloppOClock
qqq.png


How is EhE_h different from EE ? Partial derivative ??

What do these letters represent?
Original post by KloppOClock
idk what im meant to be finding. i already have dE/dt as a function of dr/dt. after that part in the second box im not sure what im meant to be getting.

by subbing in that v, i get dE/dT as a function of rho, A and E


I'm just about calling it a day, but I suspect that the aim is to get you to have dE/dt in two different forms and then equate them to get an expression for dr/dt. So I think the second part is simply subbing v into (18). The only part that sounds a bit confusing is why they have
h = r - R
There doesn't seem to be an h in the expressions, but I may be misunderstanding the notation.

Will look again in the morning.
dE/dt = de/dr * dr/dt
Original post by RDKGames
How is EhE_h different from EE ? Partial derivative ??

What do these letters represent?


theyre the same pretty sure
Original post by KloppOClock
theyre the same pretty sure

Eh and E are similar, as Eh is total energy of the satellite at a hight and E is the total energy so where you have H=rh-re , rh is the radius of the orbit and re is the radius of the earth
(edited 5 years ago)
so you have de/dt = Gmm/r^2 * dr/dt
then equate this to (18)
also are you sure this is everything, i feel im not getting the full picture

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