E-CodeAsteroid deflection by a kinetic impactor, step by step — a TI-89 Titanium program
IMPACT89 is a TI-89 BASIC program for the TI-89 Titanium. Planetary defence, the classic course problem, in the textbook model (coplanar two-body orbits: Earth on a circle at 1 AU, the rock on a 1.2 AU, e=.25 orbit that meets Earth). From the rock's size and density and the impactor's mass, speed, ejecta boost β and lead time.
Five steps: the rock's mass, impact speed and energy in megatons; Earth's capture radius (gravitational focusing); the push Δv=βmU/M; the lever (Kepler's equation back to where the rock was pushed, the new orbit by vis-viva, the delay growing every lap), with the orbits drawn on the graph screen; and the miss in the b-plane, drawn too, or a warning that it still hits.
What it asks for and what it shows
It asks for 6 values at its prompts. In the example below it shows IMPACT · TEXTBOOK MODEL, coplanar two-body orbits, Earth: circle r, push along track; b-plane, STEP 1 OF 5: THE THREAT, STEP 2 OF 5: EARTH'S PULL, b, unpushed: b, STEP 3 OF 5: THE PUSH, impactor 2000 kg, 10 km/s, ejecta boost beta 3, Δv, STEP 4 OF 5: THE LEVER, STEP 5 OF 5: THE MISS, IMPACT · SUMMARY.
Example run
One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Input 1 | 150 |
| Input 2 | 2000 |
| Input 3 | 2000 |
| Input 4 | 10 |
| Input 5 | 3 |
| Input 6 | 12 |
| The screen shows | |
| Text | IMPACT · TEXTBOOK MODEL |
| Text | coplanar two-body orbits |
Earth: circle r= | 1 AU |
| Text | push along track; b-plane |
| Text | STEP 1 OF 5: THE THREAT |
| Text | STEP 2 OF 5: EARTH'S PULL |
b= | R√(1+ve²/v∞²) focusing |
unpushed: b= | 0 → IMPACT |
| Text | STEP 3 OF 5: THE PUSH |
| Text | impactor 2000 kg, 10 km/s |
| Text | ejecta boost beta 3 |
Δv= | beta·m·U/M |
| Text | STEP 4 OF 5: THE LEVER |
| Text | STEP 5 OF 5: THE MISS |
| Text | IMPACT · SUMMARY |
How it's checked
6 test cases, each checked against an independent method. Replayed key by key on a virtual TI-89 Titanium, they make 221 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-89 Titanium calculator and pick “Asteroid deflection by a kinetic impactor, step by step” (IMPACT89).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
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- Kinematics: leave the two unknowns blank
All TI-89 Titanium physics programs · All TI-89 Titanium programs