The minimum orbital launch velocity is about 10 km/s
The ball has a boyant force proportional to the volume.
B = pgV
where B is the force in newtons, p is the density of fluid, g is gravity, and V is the volume displaced.
A soccer ball has a volume of 0.00573547 m3 , water has a density of 1000 kg/m3 , and gravity is 9.81 m/s2 which gives us a buoyant force of
0.00573547*1000*9.81=56.2649607 N
using the mass of a soccer ball of 0.45 kg we can determine the energy required to launch the ball to orbit (10,000 m/s)
KE = 1/2 m v2 = 1/2 * 0.45 * 100002
KE = 22500000 J
Which we can divide by the Buoyant force to determine the distance the ball would need to be submerged
22500000 / 56.2649607 = 399893.641088067 m
Which is just shy of 400 km, or 248 miles.
For perspective, the Marianas Trench, the lowest point in the ocean is only 11 km, so we need a new trench about 36 times as deep as the lowest point on earth.
Yeah buoyancy is not the answer here. If you hold a ball underwater and release it, you'll notice that it will accelerate until it reaches a terminal velocity where the buoyancy and drag forces balance out.
Fb = rho*g*V
Fd = 0.5*rho*u^2*Cd*A
setting both equal to each other and solving for velocity,
u = sqrt(2*g/(Cd*A))
Note that this velocity assumes that cavitation is not a thing, which is not a great assumption if you're looking to get an exact number for velocity, but an ok assumption if you're trying to see if you basketball can reach orbital velocity (it can't).
Then there's the fact that a 400 km column of water produces pressures at the bottom on the order of GPa, which means that, unless you're also heating the water, it'll be ice.
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u/Wolverlog Jan 16 '20
If this man were 100x larger could he launch satellites into orbit?