**Background:**

Most sporting events (and non-sporting events) are affected by the pull of gravity. However, the pull of gravity can actually vary a tiny bit due to both 1) location on Earth and 2) the positions of various nearby planets, moons, and stars*.

*[*] Usually just one star.*

**The Issue:**

Currently, **no** sport adjusts world records for differences in gravitational pull!

Fortunately, this is easy to fix. Unlike more immediately obvious sources of advantage (e.g. wind, air temperature, weather conditions), the position of celestial bodies is easily determined and not subject to dispute.

Additionally, since it affects all participants equally (since they are in close geographical proximity), normalizing for remote gravitational effects won’t affect who wins a specific competition—all competitors will get the same “gravitational factor” adjustment.

**Proposal:**

For sports that are heavily affected by the influence of gravity, we can normalize the distances / times by gravitational pull (Figure 1).

The most obviously-affected sports involve jumping (e.g. high jump, long jump, pole vault) or thrown objects (e.g. discus toss, javelin throw, shot put). In these events, *less gravity* means *more distance/height*.

**Case Study:**

Let’s consider the simplified case in which we tally up the gravitational effects of some of the main offenders: specifically, the Earth, Sun, Moon, Jupiter, and Saturn (Mercury, Venus, and Mars don’t make the cut: sorry).

For non-planetary-scale objects, we can implement Wikipedia’s gravitational attraction formula as a function called “`calc_accel`

” (calculate acceleration due to gravity), as follows:

`G = 6.674e-11 # Universal Gravitational Constant (units: m³/(kg*s²)`

`calc_accel = function(mass_kg, dist_m) {G * mass_kg / (dist_m**2) }`

*(This code is in the “R” programming language.)*

*Let’s plug in Wikipedia’s mass and distance numbers, hopefully without making any mistakes:*

`sun = calc_accel(mass_kg=1.989e30, dist_m=1.47e11) # `

`0.0061430820`

`jupiter = calc_accel(mass_kg=1.898e27, dist_m=9.68e11) # `

*0.0000001352*

`saturn = calc_accel(mass_kg=5.683e26, dist_m=1.7e12) # `

*0.0000000131*

`earth = calc_accel(mass_kg=5.9722e24, dist_m=6371000) # `

*9.8198608850*

`moon = calc_accel(mass_kg=7.348e22, dist_m=3.63e8) # `

*0.0000372171*

*(Note the callous disregard for proper significant figures. Also note that only the sun is really doing any work—“pulling its own weight,” if you will.) See simplified force diagram in Figure 2.*

It seems like the worst situation for an athlete would be when all the planets are pulling them in the same direction as the Earth (Figure 3), so initially we might think:

`maybe_worst = (earth + moon + sun + jupiter + saturn) # ➜ 9.82604 m/s²`

And the best configuration would be if everything is pulling the athlete *away* from the Earth:

`maybe_best = (earth - moon - sun - jupiter - saturn) # ➜ 9.81368 m/s²`

That’s actually a big difference! Does that mean that it’s (9.81368/9.82604), or 99.8742% as much work to lift something on the worst day than the best day?

Unfortunately, probably not: I didn’t consider that the Earth is **in orbit** around the Sun, so

**we probably shouldn’t count the Sun there.**(After all, someone in Earth orbit can float around in “zero G” even though they’re experiencing ~90% of Earth’s gravity).

**Fixed (?) Version:**

Excluding the Sun from those calculations gives:

`worst = (earth + moon + jupiter + saturn) # ➜ 9.819898 m/s²`

`best = (earth - moon - jupiter - saturn) # ➜ 9.819824 m/s²`

`# (best / worst) is 0.9999924`

So if it’s 99.99924% as much work to lift something on the best day vs. the worst day, maybe that could add up over the course of a marathon. Let’s assume, without doing any research at all, that **half** of a runner’s effort is counteracting gravity and half is overcoming air resistance.

Then, for the gravity half, we end up with (1-9.819824/9.819898)**/2** effort that can be saved, or 0.000003767859911 per 1 unit of running.

For a 2-hour marathon, a run would be this much longer during the worst configuration of planets:

`(0.000003767859911 * 120 minutes) = `

**0.0271 seconds**

About 3 hundredths of a second! Maybe not totally worth adjusting for, sadly.

**Conclusion:**

Maybe we’d be better off in the future by normalizing for:

- Local gravitational differences (see https://en.wikipedia.org/wiki/Gravity_of_Earth ) .
- The effect of the rotation of the Earth.

**PROS: **Opens the door for exciting new ways of nit-picking world records in sports.

**CONS: **Sadly, it appears to be a negligible effect.

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