What would happen if the Earth rotated at the rate required to achieve orbit at its radius? I.e ~7k m/s instead of ~460 m/s

Question

To achieve a circular orbit, you need to have a velocity of $$v = \sqrt{Gm/r}$$ which is about 7 km/s at the Earth’s radius, but the Earth’s rotational speed is only about 460 m/s (by taking the circumference and dividing by $24*60*60$).

What would happen if the Earth was rotating at the 7 km/s speed? What would jumping be like? Would air travel use orbital mechanics? Would the planet even stay together?

I’m less interested in the effects of a sudden change to that rotational velocity (like your face would melt off because the air would burn as the rotation accelerated), and I’m more interested in what moving around would be like on the planets surface. Instead of speeding up the Earth, a decrease in G to make the speeds match up would be an alternative scenario.

Answer 1

Weight loss at the equator due centrifugal acceleration is ~0.3% compared to the geographic poles.

Scaling this up with your numbers ~7Km/s tangential velocity will result in a maximum weight loss due to centrifugal of ~87% at the equator compared to the poles. Intermediate values can be computed depending on the Earth's circumference at your latitude home position. Also at that spin tangential velocity, the Earth will do a full spin rotation in ~1h 36min (radius of Earth $6.37X10^6 m$). A human weighting at the North pole 75kg would weight ~9.8 Kg at the equator. That is about 1/8th (1.24 $m/s^2$) of the Earth's normal gravity acceleration of 9.8 $m/s^2$.

I'm not sure with that kind of spin angular acceleration the Earth could keep its spherical shape. In the case the Earth deforms heavily then the poles would be much closer to the center of mass therefore the gravitational acceleration would be greater than 9.8 $m/s^2$ at the poles and weight loss at the equator would be less as previous calculated. Everything needs to be recalculated then, taking into account the new shape of the Earth.

Making the Earth a true oval, egg shaped, would have dramatic effects when travelling from one place to other. Your muscles and body would need constantly to adapt to the new net gravity. I don't think that planet could sustain life under these conditions.