2D asteroid problem

[PVega]

I don't know how to solve the next problem, and if anyone could explain to me step by step how it is solved I would thank you a lot. I know it's not hard, but I'm not seeing how to do it. Thank you in advance!

An asteroid passes next to a planet with mass m, and position (0, 0). The asteroid has an initial velocity (Vx, Vy) and a starting position (Px, Py). Considering that gravitational constant is 1, and ignoring the size of both objects, get the formula to calculate the asteroid position in the future.

 

[Romsek]

If you are going to assume that some gravitational interaction is going to occur between the planet and the asteroid, which it would, then you can't ignore the mass of the asteroid.

Are you sure you're not given that?

 

[PVega]

I have the mass of the planet, but not the mass of the asteroid. Which is ignored is the size of both.

 

[Dr.Peterson]

I don't think the asteroid's mass is needed; of course, this is vastly oversimplified, with no sun to consider.

What topics have you recently learned that this would be intended to exercise?

Can you use Newton's Laws to write a vector differential equation?