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1. Homework Statement
The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13164 ft/sec. Determine the corresponding values of and . Use g = 32.23 ft/sec2 as the acceleration of gravity on the surface of the earth and R = 3959 mi as the radius of the earth.
I have uploaded an image of the solution.
2. Homework Equations
3. The Attempt at a Solution
r = 16388 miles
I've found r' = 9050.85 ft/s and θ' = 0.00011047 rad/s
But I cannot for the life of mt figure out why I can get θ'' or r''.
For r''
ƩF^{r} = ma_{r} = m(r''  rθ'^{2}) = Gmm_{E}/r^{2}
r'' = Gm_{E}/r^{2} + rθ'^{2}
= 3.439x10^{8}ft^{4}/lbfs^{4}+ 4.095x10^{23} lbf=s^{2}/lbf)/ 16388miles*5280) + (16388miles*5280)*0.0001047^{2}
r'' = .93236 ft/s^{2}
It says this is wrong and I've at a loss for where my mistake is.
Likewise for θ''
ma_{θ} = m(rθ''+2r'θ') = 0
Mass cannot equal zero, therefore the summation in the brackets must be equal to zero
θ'' = 2r'θ/r
= _2*9050ft/s*(133.63°(π/180))
θ'' = .0004879
This is also incorrect.
Any help would be appreciated. Thanks.
The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13164 ft/sec. Determine the corresponding values of and . Use g = 32.23 ft/sec2 as the acceleration of gravity on the surface of the earth and R = 3959 mi as the radius of the earth.
I have uploaded an image of the solution.
2. Homework Equations
3. The Attempt at a Solution
r = 16388 miles
I've found r' = 9050.85 ft/s and θ' = 0.00011047 rad/s
But I cannot for the life of mt figure out why I can get θ'' or r''.
For r''
ƩF^{r} = ma_{r} = m(r''  rθ'^{2}) = Gmm_{E}/r^{2}
r'' = Gm_{E}/r^{2} + rθ'^{2}
= 3.439x10^{8}ft^{4}/lbfs^{4}+ 4.095x10^{23} lbf=s^{2}/lbf)/ 16388miles*5280) + (16388miles*5280)*0.0001047^{2}
r'' = .93236 ft/s^{2}
It says this is wrong and I've at a loss for where my mistake is.
Likewise for θ''
ma_{θ} = m(rθ''+2r'θ') = 0
Mass cannot equal zero, therefore the summation in the brackets must be equal to zero
θ'' = 2r'θ/r
= _2*9050ft/s*(133.63°(π/180))
θ'' = .0004879
This is also incorrect.
Any help would be appreciated. Thanks.
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