How long does the probe take to fall from 2.00 × 10³ km above the surface, starting from rest, to the centre of Vulcan, if Vulcan is the same density all the way through and we ignore air? And how many Vulcans per second is that?
(you can drag the dotted numbers and click the wavy words to change them)
t = 1.36 × 10³ sso5.15 × 10⁶ Vulcans/s✓ same as the formula
(space bar = drop, arrow keys = step through it)
The probe is above the surface.
| Euler | Exact | diff. | |
|---|---|---|---|
| time to surface, t₁ | 671 s | 671 s | -0.000601 % |
| surface to centre, t₂ | 687 s | 687 s | 0.00120 % |
| total time | 1.36 × 10³ s | 1.36 × 10³ s | 0.000312 % |
| speed at surface | 6.51 × 10³ m/s | 6.51 × 10³ m/s | -0.000850 % |
| speed at centre | 1.16 × 10⁴ m/s | — | — |
| rate (Vulcans/s) | 5.15 × 10⁶ | 5.15 × 10⁶ | -0.000312 % |
Toward the centre is positive. The shaded part is when it's inside the planet. Hover over a graph to see where the probe was at that time, or click to move it there.
Top speed is right at the centre, since g is 0 there and it stops speeding up.
Biggest at the surface, then goes down to 0 at the centre.
Outside the planet both models give the same GM/r² curve. They only split up inside.
Same drop, both models. Drag is on its own graph because it makes the fall take way longer, and the other lines got squished when they were together.
All the physics code is in src/lib/physics.ts.