If an otherwise too massive planet rotates fast enough, would the equatorial region become habitable?

Question

Ok, So I'm writing with an eye toward pondering the constraints of terraforming, which are more numerous than most people think, which creates a plethora of fun quirks and constraints for story purposes. However, some of the physics behind our world's operation is more difficult to get details on, and as I don't possess a physics degree, I'm often scratching for input.

Some of my questions were answered handily in the mathematics presented in this question, but I have questions of what a slightly less extreme example than Sheraff was asking about might pose.

So my first question is as follows: If humanity found a promising world that was in the Goldilocks zone, but that stood to be a little on the heavy side compared to Earth (Let's say 10% heavier for the sake of round numbers, but we can adjust for speculative purposes), could a faster rotation make such a world's equatorial region habitable from a gravity standpoint, even if its polar regions remained too heavy to safely colonize?

• The specific acceleration due to gravity or mass of the planet isn't relevant to the question. Assume it's high enough that living on the poles wouldn't be possible.

Answer 1

Yes.

Although a fast rotating planet also generates a much more strong coriolis wind, and living on a planet where the wind speed is close to the sound speed, that might not be fun.

This effect we are actually using also on the Earth for space launches. The equator is rotating with about 1.5 mach, and to reach orbit, we need about 25 mach. Thus, launching rockets from close to the Equator, in the direction of the Earth rotation, spares some percent of fuel.

But: Some G is not a big problem in colonization. The largest problem of the colonization that there is nothing what we could colonize. Second largest problem is that we still must pay astronomic sums to even leave the Earth orbit, and we have absolutely nothing to reach the closest star.

Answer 2

Centrifugal acceleration $a_c$ in terms of radius $r$, angular velocity $\omega$

$a_c = r \omega^2$

On Earth at the Equator, this works out to roughly $-0.003 g$ where $g$ is acceleration due to gravity on Earth.

So if your planet is roughly Earth-sized, you can roughly estimate the influence of rotation on acceleration by dividing the length of Earth's day by the length of your planet's day, squaring the ratio, and multiplying by $-0.003 g$.

To reduce Earth's felt gravity at the equator by 10% you'd have to reduce the length of the day to just 4 hours, which I think is implausible for planet formation and is not compatible with having a 1 bar atmosphere that doesn't sandblast everything with tornado-force winds all the time. So no: while physics permits reducing felt gravity by increasing rotation, the effect of faster rotation would not sufficiently reduce felt gravity over the domain compatible with habitability.

Fortunately, 10% of a gravity more or less is not likely to be a big medical problem for your colonists anyway.