What is the trajectory of a cannonball fired from the equator in space?

[FermatPell]

Homework Statement

Imagine that you are an observer in space (so you are in an inertial system), when the cannon (located on the equator) fires a cannonball in north direction. What does the trajectory of the cannonball look like from your perspective? Is it a straight line (that would mean that the cannonball is not affected by Earth's rotation) or something like a spiral?

Homework Equations

The Attempt at a Solution

I think that, since the only real force acting on the body is the gravitational force, the trajectory is like a spiral. I also know that no Coriolis force exists in my inertial frame of reference. Am I right?

 

[zorro]

I think that, since the only real force acting on the body is the gravitational force, the trajectory is like a spiral. I also know that no Coriolis force exists in my inertial frame of reference. Am I right?

The question is not so clear for me. This is what I think-
If you consider the Earth to be an inertial frame of reference, then the trajectory of the ball would be a straight line.
If you consider the Earth to be a non-inertial frame of reference (take its rotation in account), then the trajectory of the ball would be similar to a spiral.

In both the above cases, you are in an inertial frame of reference, so there will not be any Coriolis force.

 

[willem2]

If you don't shoot the cannonball faster than escape velocity, the orbit will be an ellipse. Look up two-body problem. Of course the ellipse will intersect the surface of the Earth again at some point.