## March 17, 2004

### Panspermia Equation

A friend and I were recently discussing the panspermia hypothesis. I mentioned a recent theory to him suggesting that the Earth has most likely "infected" countless other planets with its biological substrate -- the result of massive celestial impacts that have sent Earth's bio-ejecta into the far reaches of space. We concluded that an Earth panspermia infection bubble must exist and that it is steadily growing outward. Assuming that the panspermia hypothesis is valid (and that is a BIG assumption), the next question is: How probable is it that this matter has landed on a planet and successfully transmitted life to it? My friend took this question and came up with a Drake Equation-style formula. I've since made some suggestions. Here's the most recent draft:

Some of the factors below are valued as "odds". That is, they have a value between 0 (impossible) and 1 (certain).

N(i) * f(l) * f(x) * f(e) * f(s) * f(p) * f(q) * f(v) * f(m)

N(i) Number of meteorite impacts or similar events occurring after life develops on earth. The frequency of these events are decreasing over time. This might also include volcanic eruptions, explosions, etc.

f(l) Fraction of those impacts that encounter living matter of the type suitable for panspermic transmission. It's conceivable that any kind of life, no matter how rudimentary, could set off this effect. This fraction might approach 1 as life matures on a planet (ie post "Cambrian Explosion phases"). It might exclude impacts in the polar regions, deserts, etc; early life probably only existed in oceans, and perhaps only in temperate belts.

f(x) Fraction of impacts that eject viable life matter. This is the chance of life surviving the impact and its transmission into space.

f(e) Fraction of that ejecta which escapes the solar system. [For the sake of this discussion we're excluding intra-solar system infection]

T(v) Average duration for the life-substrate on the ejecta to remain a viable panspermic agent. This is a statement of the chance of life (or the life code) surviving the trip.

V(e) Average velocity of ejecta once it has escaped the solar system. The product of T(v) and V(e) is the average distance that ejecta will reach and remain viable. Call this D(v).

N(s) The number of stars within (T(v) * V(e)) of earth.

f(s) The fraction of escaping ejecta that encounters one of these stars. That is, is captured by the gravity of another star and at least enters stellar orbit.

f(p) Fraction of captured ejecta that lands on a planet (or moon).

f(q) Fraction of planets that are susceptible to panspermic infection.

f(v) Fraction of landing ejecta where the life matter is still viable. This is the chance of life surviving the landing.

f(m) Fraction of landing viable life that multiplies into an ecosystem. This is the chance of life thriving in a brand new environment.