Could a large planet spin fast enough to weaken its gravity a noticeable amount, without falling apart?
The apparent gravity you feel from a planet is due to the amount of matter the planet is made of and the distance you are from the center of the planet. The more matter, the greater the gravity, and the closer you are to the planets surface, the greater the gravity.
Lets find a local planet and put our Friend A on it’s surface. The gravity he feels is easy to calculate. What matters is how dense the planet is, and what the distance from him to the center of the planet is. If the planet is denser (lead), it’s made of more stuff and has a higher gravity. Less dense (like marshmallows) will result in lower gravity.
If we dig a tunnel down into the planet and put our friend B in it, she will feel less gravity for two reasons. First, there’s less stuff between her and the center of the planet because some of the planet is now over her head. Second, that part of the planet will pull up on her, and will reduce the gravity she feels a little bit as well.
If you are at the center of the planet, you will feel no gravity. The mass of the planet is pulling you in all directions at the same time with the same force, so it all cancels out. I have to give a shout out to the movie Total Recall (the newest one, not the one with Arnie and “get your ass to Mars”). They show that the Fall experiences zero-gravity as it passes through the core of the Earth. A nice piece of scientific accuracy in a movie.
If we start spinning the planet, both A and B will also feel another force - a centripetal force that tried to toss them away from the center of spin. It’s the same force that you feel on a carousel or in a car making a quick turn. This force, because it is in the direction opposite the planet’s gravity, will result in both A and B feeling slightly less gravity. The planet’s gravity is still there, but it’s being partly counteracted by another force.
The faster you spin the planet, the less gravity A and B will feel.
And yes, you need to be careful. If you spin the planet too fast, it will fling itself apart. You’d have to spin the Earth about 100 times faster to fling people off the equator. Any faster than that and you’d start to throw off pieces of the planet itself.
The Earth has a bulge around the equator as a result of it’s spin. It’s not much, but it’s there. That means you’ll weigh less at the equator than at the poles - because you’re further from the center at the equator, and the centripetal force if higher at the equator than at the poles.
This centripetal force is also partly why most US space launches take place in Florida and are launched towards the east (the direction the Earth spins). It’s closer to the equator than the rest of the nation, and that gives the rockets a bit of a boost. Not much, but rockets are hard enough as it is. Any little bit helps.
For more information, this video is pretty good. Warning - it shows math!
So, yes, it is possible for a large planet spin fast enough to weaken its gravity a noticeable amount. Our own Earth does. I’m not sure how noticeable 0.34% is, but it can be easily measured.
