You'll need to AddForce to the Rigidbody.

rigidbody.AddForce(transform.forward * 20); // tune '20' to control the velocity

Note that if you add this to Update(), it will accelerate (as the force is applied every frame).

Also, you've said it's taking the rotation of the player - that won't necessarily mean the object is heading towards them, it's just matching the rotation, so it will move parallel.

The object that spawns the Sphere object will need to Transform.LookAt the player position

use:

transform.LookAt(Insert Player Position Here)

to look at your player, and:

rigidbody.AddRelativeForce(0, 0, 1); // Or whatever speed you want

to move forward

you can use Vector3.forward of your shooter object.