Can someone provide a parametric equation for the earth's orbit around the sun?

Question

Well maybe it's impossible to do. I was thinking something something like:
x = a cos(t)
y = b sin(t)

where t is something like
t = (day * 2 * pi) / (year)

That equation with the right numbers filled in would give me the path but it wouldn't be accurate to the day because the orbit speeds up the closer it gets to the earth.

I'm attempting to write a computer simulation so having a parametric equation would help.

Answer 1

At least with respect to the angle (called true anomaly)

Measured from perigee around the ellipse out to apogee and back, the trajectory equation is:

r = a(1-e^2)/[1 + e cos (nu)]
where
a is the semi-major axis
e is the eccentricity
and nu is the angle of the radius vector measured counter-clockwise from perigee

To put this in relation to time, you need the angular velocity (the rate that nu changes). Unfortunately, the angular velocity changes constantly, but at any given time, it's equal to:

h/r^2
where
r is the magnitude of the radius
h is the specific angular momentum per unit mass

h = sqrt[mu*a(1-e^2)]
where
a is the semi-major axis
e is the eccentricity
mu is heliocentric gravitational constant (universal gravitational constant * mass of Sun)

Answer 2

Check out this page for how to calculate Earth's position using orbital elements:
http://ssd.jpl.nasa.gov/?planet_pos

The orbital elements for the Earth-Moon barycenter for J2000 are:

a:1.00000261 AU
e : 0.01671123
I: -0.00001531°
L: 100.46457166°
long.peri. 102.93768193°
long.node. 0.0°

Answer 3

Visually, Sun revolves around the Earth. Scientifically, Earth revolves around sun.

Answer 4

I am not sure what you mean by that. Usually an orbit is specified by the orbital elements, not an equation.