Consider a star located at the origin of a coordinate system. A planet orbiting the star has polar coordinates ($r, θ$) where $r$ is a constant. What is the shape of the orbit? If $\frac{dθ}{dt} = ω$ where $ω$ is constant, write down an expression for the speed of the planet in terms of $r $ and $ω$.
I believe the shape of the orbit is a circle since $r$ is constant.
I am unsure about the second part. I first thought that this since this a circle, we can write $ω = \frac{dθ}{dt} = \frac{2\pi}{\frac{2\pi r}{v}} = \frac{v}{r}$, so $v = ωr$.
My other thought was that since $r$ is a constant, and the force of gravity always points towards centre of coordinate system, that it must be a central force. Is this a valid method of solving ?