I'm trying to simulate the motion of an object near a force field, given an initial velocity $v_0$.

I couldn't find anything that fits what I'm trying to achieve.

I have a point of mass $m_1$ in the origin of the Cartesian plane (0.0, 0.0) (blue in the image).

The coordinate system is the Cartesian one.

The position of $M_1$ shouldn't change.

I figured out this:

  • The attraction force between the blue body and the red body is F defined like this: $F =G{m_0m_1}/{r^2}$ by Newton's theory.
  • The resulting position of the red body should be the sum of $v_0$ and a vector representing the component of the motion directed towards the center.

But I didn't get further than that. How could I calculate the position of the body at time t?

enter image description here

  • $\begingroup$ Are you saying assume the position of $M_1$ is fixed? $\endgroup$ – Bob D Feb 5 '20 at 14:06
  • $\begingroup$ try to pick one coordinate system: either Cartesian $(x, y)$ or Radial $(r,\theta)$. Plot your FBD and write all motion equations in terms of just one coordinate system. you will get your answer. $\endgroup$ – Vikash Kumar Feb 5 '20 at 14:59
  • $\begingroup$ @bob d yes sorry I've fixed the question $\endgroup$ – Fabrizio Feb 5 '20 at 16:30
  • $\begingroup$ @Vikash Kumar what do you mean with fbd? $\endgroup$ – Fabrizio Feb 5 '20 at 16:32
  • $\begingroup$ Does this answer your question? How to predict the location of a planet at a given time? $\endgroup$ – Bill N Feb 5 '20 at 17:59

For the body with mass $m_0$, split the velocity and acceleration vectors into its perpendicular components. Let the body be at position $(a,b)$ initially. The displacement due to the initial velocity will be $s=vt$. Do the same for the acceleration using the formula $s=\frac 12at^2$. Add them together for the x-components and y-components and you arrive at your answer.


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