Graphing the orbit of the earth

[calypso]

Hi I am trying to graph the position of the earth everyday for a year, moving counter clockwise and starting at (1,0) where the units are in AU.
I have to find the x co ordinates of the earth using a cosine graph where the y value is the x position of the earth and the x value is the day in the year.
I have tried graphing this, but I cant seem to get the B (period) value in the equation right, as there should only be a frequency of 1 over a period of 365 days, but when i graph it there is a frequency of eight.

So at day 0 (x value), the y value (x co ordinate of the earth) should be one, at day 91.25 it should be 0, at day 182.5 it should be -1, at day 273.75 it should be 0 and at day 365 it should be 1.

However, I wasnt able to graph this properly and am really confused! Any help would be appreciated,

Thanks, Calypso

 

[HallsofIvy]

Probably, the simplest thing to do is use "parametric equations". x= A cos(t), y= B sin(t), with t going from 0 to \(\displaystyle 2\pi\), will give (x, y) values around an ellipse with center at (0, 0), one axis along the x-axis, from (-A, 0) to (A, 0), the other along y-axis, from (0, -B) to (0, B). If you want "d" to be days, from 0 to 365, then you want \(\displaystyle x= A cos\left(\frac{365}{2\pi}t\right)\), \(\displaystyle y= B sin\left(\frac{365}{2\pi}t\right)\).

 

[Ishuda]

...\(\displaystyle x= A cos\left(\frac{365}{2\pi}t\right)\), \(\displaystyle y= B sin\left(\frac{365}{2\pi}t\right)\).

HallsofIvy,

I know that imitation is the sincerest form of flattery but please, just because I am always making typo's, don't feel that you have to do so. Isn't it
\(\displaystyle x = A cos\left(\frac{2\pi}{365}t\right)\), \(\displaystyle y= B sin\left(\frac{2\pi}{365}t\right)\)
if we want t to be in days? Or have I gone and misunderstood AGAIN!

 

[HallsofIvy]

Perhaps I should stop standing on my head so much!

Yes, it should be \(\displaystyle x= A cos(\frac{2\pi}{365}t)\), \(\displaystyle y= B sin(\frac{2\pi}{365}t)\).

 

[Deleted member 4993]

[SIZE=+2]"

[/SIZE]OU are old, Father William," the young man said,
"And your hair has become very white;
And yet you incessantly stand on your head-
- Do you think, at your age, it is right?"

- Lewis Carroll
Read more at http://www.poetry-archive.com/c/father_william.html#O17CKslLEcBY7p83.99

 

[calypso]

Probably, the simplest thing to do is use "parametric equations". x= A cos(t), y= B sin(t), with t going from 0 to \(\displaystyle 2\pi\), will give (x, y) values around an ellipse with center at (0, 0), one axis along the x-axis, from (-A, 0) to (A, 0), the other along y-axis, from (0, -B) to (0, B). If you want "d" to be days, from 0 to 365, then you want \(\displaystyle x= A cos\left(\frac{365}{2\pi}t\right)\), \(\displaystyle y= B sin\left(\frac{365}{2\pi}t\right)\).

Thanks I think I've got it!

 

[HallsofIvy]

[SIZE=+2]"

[/SIZE]OU are old, Father William," the young man said,
"And your hair has become very white;
And yet you incessantly stand on your head-
- Do you think, at your age, it is right?"

- Lewis Carroll
Read more at http://www.poetry-archive.com/c/father_william.html#O17CKslLEcBY7p83.99

I thought of that as I was typing my response!

Of course, what is really appropriate is the second stanza:

"In my youth," Father William replied to his son,
"I feared it might injure the brain;
But now that I'm perfectly sure I have none,
Why, I do it again and again."