Sphere of Osmium

Not your personal homework solver.

what is 1G?

>>7683381
1000$

>>7683378
Not homework, just curious!

File: battle_ship_board_game_progress.jpg (321KB, 1600x1066px) Image search: [Google]

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>>7683381

>>7683369
mass of earth: 5.972 × 10^24 kg
density of osmium: 22.59g/cm^3
volume of osmium with equivalent earth mass: (2.64365 * 10^26)cm^3
a sphere with this volume has a radius of 3981.4km, 62.42% the radius of the Earth

>>7683409
this is assuming you mean 1g, as in earth gravity acceleration, not the universal gravitational constant

and this isn't surface gravity, left as an exercise to the reader

>>7683409
>mass of earth: 5.972 × 10^24 kg
>density of osmium: 22.59g/cm^3
>volume of osmium with equivalent earth mass: (2.64365 * 10^26)cm^3
>a sphere with this volume has a radius of 3981.4km, 62.42% the radius of the Earth

F_grav ~ γ * M * m / r2, so, not quite the right answer.

>>7683369
g = 9.81m/s^2 = G [ 22590kg/m^3 (4/3πr^3) ] / r^2 = G * 22590kg/m^3 * (4/3πr)

http://www.wolframalpha.com/input/?i=g+%2F+%5BG+*+22590kg%2Fm%5E3+*+%284%2F3+*%CF%80%29%5D+&a=UnitClash_*g.*StandardAccelerationOfGravity--&a=UnitClash_*G.*GravitationalConstant.dflt--

r = 1553 km = ~~ ( 0.24 ) × polar radius of Earth (~~ 6357 km ) = ~~ 1.3 × Pluto equatorial radius ( 1.151×10^6 m )

>>7683369
radius of 499.3km

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>>7683449
that is too small

r=3g/(4π*G*rho)

G=6.67428e-11 m^3/(kg*s^2)
g=9.80665 m/s^2
rho_Os=2.259e4 kg/m^3

r=1.552785307e06 m

Is the assumption of constant density justified?
Is there enough Osmium in the known universe?

>>7683527

Also don't forget to take into accout the fact even a sphere made entirely of one material would become denser as you get towards the core.

>>7683369
Assume uniform density,
9.8 N/kg = G* ((4/3)pi*rho*(r^3)/r^2 = G*Rho*pi*r *1.3333
And that's it.

>>7683381
9,81m/s2

>>7683369
>not being able to calculate this

Is this a joke are you guys not able to solve this problem?

>>7683381
Earth's gravity. Or 9.81m^-2

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>>7683369
I could not help but notice your png was not optimized anon.
I have optimized your png.
Your png is now optimized.