I suggest you get a relay that is rated for about 10 or 20 amps AC. Motors are inductive loads and a bigger relay will be better.
An Arduino cannot provide enough current on its I/O pins to power a coil in an electromechanical relay. Either use s solid-state relay or use the Arduino to trigger a transistor that switches the current in the relay coil.
You could use a solar panel to charge a battery that powers the Arduino but I suspect it would be more trouble than it is worth considering that you already have AC power for the motor. i suspect you will need a much bigger solar panel than what you have in mind.
...R