Solve 2D Asteroid Problem: Step-by-Step Guide

[PolVD]

Homework Statement

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.

Relevant Equations

x = V0x * t
y = V0y * t + 1/2 * g * t^2

Hi everyone! 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!

 

[berkeman]

Homework Statement:: 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.
Relevant Equations:: x = V0x * t
y = V0y * t + 1/2 * g * t^2

Hi everyone! 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!

Welcome to PF.

Are you familiar with Kepler's Laws? Since they are asking about an asteroid (and not a ball thrown on the surface of the planet), I'm guessing they want you to use the equations for orbital motion...

https://pwg.gsfc.nasa.gov/stargaze/Smotion.htm

 

[PolVD]

Welcome to PF.

Are you familiar with Kepler's Laws? Since they are asking about an asteroid (and not a ball thrown on the surface of the planet), I'm guessing they want you to use the equations for orbital motion...

https://pwg.gsfc.nasa.gov/stargaze/Smotion.htm

Actually, I'm not super familiar with physics in general. I'm taking a look at the page you send to me but it is super overwhelming. Are you 100% sure it should go that way? In that case, I would thank a more basic explanation since I have to get the whole formula to get the asteroid position and no a single result. I haven't done any physics in about 10 years. Thanks!

I asked that same question to another forum and this was the thread... But I didn't get any clear answer... That's why I'm here asking too.

 

[pai535]

Hi. I think if you are talking about "asteroids" and "planets", you should start with universal gravitation.

Newton's law of universal gravitation: $$\vec{F} = \frac{GMm}{r^3}\vec{r},$$ where $\vec{r}$ is the position vector (the position of asteroid in this question). $r$ is the distance between the asteroid and planet.

If the gravitational constant is 1, maybe you can define $$G=1,$$ hence $$\vec{F} = \frac{Mm}{r^3}\vec{r}.$$
Then you just need to consider the force components on x and y-axis and use Newton's 2nd law to solve it. (You only need to use the x and y coordinates of forces and acceleration)