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given the major axis length, minor axis length, at the given angle THETA. what's the formula?

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- #1

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given the major axis length, minor axis length, at the given angle THETA. what's the formula?

- #2

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given the major axis length, minor axis length, at the given angle THETA. what's the formula?

[tex] r(\theta) = r_{max} \frac{1-e}{1+ e cos \theta} [/tex]

with r_max = aphelion = a(1+e). Here my angle is chosen to be zero at perihelion (you can check that when theta=0, we recover a(1-e) = perihelion and when theta= 180 degrees, we get the aphelion).

Patrick

- #3

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[tex](\frac{x}{a})^{2}+(\frac{y}{b})^{2}=1[/tex]

Now, just make a standard polar coordinate change of (x,y) and gain an equation for the radius r!

- #4

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wikipedia says it's (1 - e^2) as opposed to (1 - e) in that equation nrqed. Who's right?

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- #6

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what is the formula? I'm not sure how to convert to polar coordinates

x = rcos(theta)

y = rsin(theta)

and plug those values into that equation and solve for "r"? or am i doing something wrongly?

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Oh.. yes. Good catch. Sorry, for some reason I was thinking about it as an astronomy question when I posted, not as a math question, so I though it as asking the distance from one focus (eg the Sun). This is clear in my answer since I specified that the distances at zero and 180 degrees are the perihelion and aphelion. Sorry!

- #8

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so from center... is it:

(ab)/((b^2cos^2t+a^2sin^2t)^(3/2))

or

(ab)/((b^2cos^2t+a^2sin^2t)^(1/2))?

(ab)/((b^2cos^2t+a^2sin^2t)^(3/2))

or

(ab)/((b^2cos^2t+a^2sin^2t)^(1/2))?

- #9

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so from center... is it:

(ab)/((b^2cos^2t+a^2sin^2t)^(3/2))

or

(ab)/((b^2cos^2t+a^2sin^2t)^(1/2))?

Obviously not the first one, as the units are wrong (they are 1/length).

Not so obviously, the second one is wrong too. Don't just guess an answer.

Show your work so we can show where you went astray.

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