- #1

- 23

- 0

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter bobthebanana
- Start date

- #1

- 23

- 0

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

- #2

nrqed

Science Advisor

Homework Helper

Gold Member

- 3,764

- 291

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

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 9,970

- 134

[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

- 23

- 0

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

- #5

- 15,393

- 686

- #6

- 23

- 0

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?

- #7

nrqed

Science Advisor

Homework Helper

Gold Member

- 3,764

- 291

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

- 23

- 0

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

- 15,393

- 686

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.

Share:

- Replies
- 29

- Views
- 17K