How to make a planet with differential gravity and constant daylight

I am hoping to create a planet with a greater rotational speed, making it oblong, thus causing differential gravitaion from the equator to the poles. I am hoping for the gravitarion to be lighter than the moon (possibly just heavy enough to prevent a person from jumping off the planet [the tangential speed would factor into this]) at the equator, and heavier than Earth's gravity (possibly by a lot) at the poles. I am hoping the difference can be relatively substantial, but I'm not sure how that would work, exactly. If the shape of a planet based on the various factors of rotational speed, mass/gravity, etc. can be obtained (a graph, like y = x^2), that would be most helpful.

I am also hoping to have the planet be "always day", such that there is always a relatively large amount of light impacting the entire surface. I considered having just the rotational speed account for this, but that wouldn't work with the necessary mass of the planet. The rotational speed could help factor into it, though. It was suggested to me that the atmosphere be denser, thus refracting the light from the star, which could possibly allow a person to see the sunrise and sunset at the same time (nifty). Plus, with the change in density, there would be a change in pressure, thus creating differences in planetary chemistry that would be interesting to explore. And as buoyancy is determined by density (I believe), it could result in certain elements floating a ways up in the atmosphere (a literal layer of water floating in the air sounds intriguing). As a last resort, multiple stars can be used. I'm hoping to simply "manipulate" the light, but a multi-star system could work if it would be the best possible option.

After the proposed rotational speed, mass, etc. has been presented, any additional effects they would cause on the planet would be very interesting, and greatly appreciated.

posted over 7 years ago

Iter‭

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