Earth-like planet which is smaller but has the same gravity
If there were a planet similar to earth where the lines of latitude and longitude were half as far apart (about 35 miles instead of about 70), but the planet's density were increased to compensate for lost gravitational force, how similar to earth could it really be?
Would it be possible for weather and seasons be essentially the same or would they have to be altered? Would the horizon be visibly different to the naked eye? Could air pressure be essentially the same at the same measurements from sea level? Would there be any other significant, unavoidable changes to that world?
The goal is to try and keep the planet as earth like as possible while shortening the distance between equatorial lines (bringing the arctic circle closer to the equator, so it would take only half the time to walk between them)
As a bonus question, what would that planet's radii be? I was thinking 0.5 but my mental math for 3d space isn't too great.
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