100 mile diameter sphere of solid lead.. what would be the surface gravity?

Discussion in 'Techforge' started by Midnight Funeral, May 20, 2007.

  1. Midnight Funeral

    Midnight Funeral CĂșchulainn

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    Anyone any idea on this one? I have no idea what kinda calculations are needed here.
  2. Dan Leach

    Dan Leach Climbing Staff Member Moderator

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    I dont know the mass/gravity equation. But going on other small bodies in the solar system i'd say it would be very small indeed. The escape velocity would be probably just a few mph. You would certainly be able to jump off it, or if you judge it right, jump into orbit
  3. Fox Mulder

    Fox Mulder Fresh Meat

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    g = GM/R^2 (G Newton's gravitational constant)

    Newtonian gravity is more than accurate enough for this small mass.

    g~9.8 for Earth (m/s^2)

    ~0.25 I get for this sphere of lead, about 1/40th of Earth's

    density of lead is 11340 kg/m^3, use this to find the sphere's mass.

    Earth velocity I think (trying to use google's calculator) works out about 200m/s, Earth's is about 11,000m/s.
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  4. Fox Mulder

    Fox Mulder Fresh Meat

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    You must have strong legs :bergman:
  5. Midnight Funeral

    Midnight Funeral CĂșchulainn

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    Well I found a calculator that would do this for me. http://www.ericjamesstone.com/weird_stuff/gravitator.htm You plug in the radius and density and it spits out the surface acceleration, and what that is as a fraction (or multiple) of earth's gravity. Sorry to bother yall.

    I got the density figure from here. Turns out it'd be 0.25 m/s squared (a little under 1 fps squared). You probably couldn't generate escape velocity by jumping, but you'd jump pretty high.

    Made of Osmium, the densest element known, things would fall at 0.51 m/s squared. (1.67' squared)

    Also while playing around with the calculator it I discovered an interesting fact: The moon if made of uranium would have almost the same gravity as earth. (0.94 G).

    If you had a world made of solid aluminum on the other hand, it could be 26,000 km in diameter (16,155 miles) - for a surface gravity of 1G, identical to earth, while being a little more than twice earth's diameter.

    A planet made completely of ice would be 76,000 km in diameter (47,224 miles) for a gravity of 1G at the surface. This is a little bigger than Uranus.

    If made of Lithium, the least dense room temp solid element, a 1G planet would be 131,000 km (81,399 miles) in diameter - about the size of Jupiter!
  6. Spider

    Spider Splat

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    If you assume constant density, then it's pretty easy to work out. Just calculate the total mass and plug the numbers into Newton's Law of Gravitation.

    The trouble is, the density isn't going to be constant. Off the top of my head, I have no idea how much it would vary by, either. :shrug: