Calc III Lab #5: Crashing into the Sun

The simplest scenario to imagine is that an object starts at some position (x,y) and is initially at rest. The force of gravity then accelerates the particle according to Newton's Second Law of Motion.

Use DsTool to compute a trajectory beginning at the point (x,y)=(0,4) when that point has initial velocity (vx, vy)=(0, 0). The initial conditions for the trajectory are visible in the Selected Point Panel. What is the fate of the trajectory? Change the initial condition from (x,y)=(0,4) to some other point and compute the trajectory starting from the new point.

Question #1:

• Describe the shape of a trajectory starting at (x,y) with velocity (vx, vy)=(0,0).
• Does this shape agree with your expectations?
• Can you tell how the trajectory is parametrized by time by looking at its shape?
• While DsTool is computing the trajectory, can you see the particle "moving" in time?

Go To

• Next page: Periodic orbits
• Outline page: Outline
• DsTool page: DsTool help page