# differentiation

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#1
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
0
1 year ago
#2
(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?
0
#3
0
#4
(Original post by mqb2766)
Do you have a picture of the original question?
yeah sorry for the poor paint job
1
1 year ago
#5
(Original post by KloppOClock)
The first part says use (15), so just differentiate that using the chain rule?
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#6
(Original post by mqb2766)
The first part says use (15), so just differentiate that using the chain rule?

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 ?
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#7
(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
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1 year ago
#8
(Original post by KloppOClock)

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?
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#9
(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
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1 year ago
#10
(Original post by KloppOClock)
How is different from ? Partial derivative ??

What do these letters represent?
0
1 year ago
#11
(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.
0
1 year ago
#12
dE/dt = de/dr * dr/dt
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#13
(Original post by RDKGames)
How is different from ? Partial derivative ??

What do these letters represent?
theyre the same pretty sure
0
1 year ago
#14
(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
Last edited by homemadeclock; 1 year ago
0
1 year ago
#15
so you have de/dt = Gmm/r^2 * dr/dt
then equate this to (18)
0
1 year ago
#16
also are you sure this is everything, i feel im not getting the full picture
0
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