Riddle me this

Any of you guys know how much planetary spin rate and a slightly lower air pressure than earths, could offset gravity? And say you had a planet 4x the size of earth, would the gravity also be 4x stronger, or does a lot of that depend on the size of ita molten iron core?

And just how much of a greater gravity do you think humans could realistic survive in? 1.5ish? Surely 2x would be too high for long term

Or is earths gravity even ideal for human habitation? What if it was .75% ?

Pun wrote:Any of you guys know how much planetary spin rate and a slightly lower air pressure than earths, could offset gravity? And say you had a planet 4x the size of earth, would the gravity also be 4x stronger, or does a lot of that depend on the size of ita molten iron core?

I don't know the answer to most of your queries (they lie far beyond the scope of my studies), however I can answer one question. Surface gravity (the gravity that one feels at the surface of the planet) can be calculated by the following:

g=(4/3)∏Gρr

Where:
g=gravity
4∏/3 = volume of planet
ρ=density of planet (m/v)
r=radius of planet (distance from center to point of observation, be it the surface or above the surface)
G=gravitational constant=6.67384x10^-11 N(m/kg)^2

So if you run this calculation for a planet with the same mass as the earth, but 4x the radius, you would end up with a very weak gravitational field (the same field you would encounter if you were orbiting the earth at a height of 4x earths radius).

Bryant wrote:

Pun wrote:Any of you guys know how much planetary spin rate and a slightly lower air pressure than earths, could offset gravity? And say you had a planet 4x the size of earth, would the gravity also be 4x stronger, or does a lot of that depend on the size of ita molten iron core?

I don't know the answer to most of your queries (they lie far beyond the scope of my studies), however I can answer one question. Surface gravity (the gravity that one feels at the surface of the planet) can be calculated by the following:

g=(4/3)πGρr

Where:
g=gravity
4π/3 = volume of planet
ρ=density of planet (m/v)
r=radius of planet (distance from center to point of observation, be it the surface or above the surface)
G=gravitational constant=6.67384x10^-11 N(m/kg)^2

So if you run this calculation for a planet with the same mass as the earth, but 4x the radius, you would end up with a very weak gravitational field (the same field you would encounter if you were orbiting the earth at a height of 4x earths radius).

Disregard that, I wasn't thinking clearly (as the math will show). 4x the radius of the earth with the same density would yield a gravitational field 4x that of the earth. Like I said, I'm not a physicist!

We can easily calculate this:

g=(4π/3)(6.67384x10^-11 N(m2/kg2))(5515 kg/m3))(4x6356800 m)=39.202 m/s2
gravity=(volume of sphere)(gravitational constant)(density of earth)(4xradius of earth)

39.2/9.8=4