Can anyone help me with the following mechanics question:
Information:
A Planet moves under the gravitational influence of a massive star, so that (ignoring the centre of mass) its motion is restricted to a plane, and its position vector and velocity vector have the form
$r = r$ $\Biggl(cos\theta,sin\theta,0 \Biggr)$, $\dot{r} = \dot{r} \Biggl(cos\theta,sin\theta,0 \Biggr) + r \dot{\theta}\Biggl(-sin\theta,cos\theta,0 \Biggr)$.(All column vectors)
respectively where $r$ is the radial distance and $\theta$ is the polar angle.
If $r(0) = (1,8,0)$ (Column vector) and $\frac{dr}{dt} = (4,2,0)$ (Column vector) are the initial position and velocity of the planet, calculate $r(0), \frac {dr}{dt}(0), \theta (0)$ and $\frac{d\theta}{dt}(0)$.
All help will be appreciated.
Thanks,
Euden