Express angular position of the Earth as a function of time

Question

Say I have for example the Earth orbiting the Sun (in circular orbit) and I want to express angular position (in radians) as a function of time.

Would I be correct in thinking that $2\pi/t$ does the trick?

Answer 1

The usual representation is

$$\theta = \frac{2 \pi t}{T}$$ where $T$ is the period (one year).

Answer 2

I would think you need to throw in the period. Like $\frac{2\pi\times t}{365 \text{ days}}$ where t is in days.

Answer 3

In circular motion constant angular velocity

$$ \omega = \dfrac{d \theta}{d t} $$

If it is constant, integrate to obtain $\theta = \omega \,t $ for given time less than one period.

For a full rotation around Sun

$$\theta_{max} = \omega \,T $$ where $T$ is for one full time period, 1 year in this case.