- #1

- 21

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The equation is as follows:

(I'm new here, so I didn't know the best way to input an equation.)

Any help that could be provided would be very much appreciated.

- Brandon

- Thread starter dBrandon/dC
- Start date

- #1

- 21

- 0

The equation is as follows:

(I'm new here, so I didn't know the best way to input an equation.)

Any help that could be provided would be very much appreciated.

- Brandon

- #2

LeonhardEuler

Gold Member

- 859

- 1

[tex]P=\int_{0}^{\pi}2\rho Gmdr^{2}a\sin{a}\dot ( \ln{\sqrt{r^{2}+d^{2}-\cos{a}} +r} -\frac{r}{\sqrt{r^{2}+d^{2}-\cos{a}}})da\left|^{r=6.275*10^6}_{r=6.175*10^6}[/tex]

Integrating the "a" part seems like it should be a nightmare, though. You could do a substitution u=-cos(a) if it wasn't for that a sitting outside. It's probably not expressible in elementary functions. Could you just evaluate it numerically?

- #3

AlephZero

Science Advisor

Homework Helper

- 6,994

- 292

[tex]\int \frac{a \sin a\, da}{(b^2 - \cos a)^{3/2}}[/tex]

is an elliptic function of the 3rd kind according to http://integrals.wolfram.com.

My knowledge of elliptic functions doesn't extend to knowing if your definite integral equals something nice, but at least that's a start.

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