A planet follows an elliptical path described by $x^2+y^2=1$. A comet follows the parabolic path $y=x^2-1$. Where might the comet intersect the orbiting planet?

The comet might intersect the planet's orbit at the points $◻$.
(Type ordered pairs. Use commas to separate answers.)

Step 1 ：To find the intersection points, we need to solve the system of equations given by the planet's orbit and the comet's path.

Step 2 ：We can substitute the expression for $y$ from the comet's equation into the planet's equation and solve for $x$.

Step 3 ：Solving the equation $x^2+(x^2-1{)}^2=1$ gives us the $x$ values of -1, 0, and 1.

Step 4 ：Using these $x$ values, we can find the corresponding $y$ values from the comet's equation $y=x^2-1$, which are 0, -1, and 0 respectively.

Step 5 ：The intersection points are $(-1,0)$, $(0,-1)$, and $(1,0)$.

Step 6 ：The comet might intersect the planet's orbit at the points $\boxed{{\displaystyle (-1,0),(0,-1),(1,0)}}$.