This applet simulates the motion of a celestial body under the gravitational attraction of another (much bigger) depitched as a large Yellow dot (imagine the Sun) and aproximatively motionless. As a first approximation the motion is considered as uniformly accelerated during a time interval : this is accurate only in the limit where , i.e. when the time interval is sufficiently small.
You can set

the initial position of the moving body,

the initial velocity of the moving body,

the time interval .

To perform the simulation click on Initialise in order to put the body in its initial position and then click on Start evolution.
To end the simulation click on Stop evolution, while to cancel the traced orbit click on Clear trace.

Perform various simulations in order to find a balance between the goodness of the approximation and its speed of execution. Then construct the conic passing through five points well spaced along the orbit. Confirm that the orbits you find are conics: ellipses, hyperbolas or, if you are very lucky, parabolas or circles.