MadSci Network: Astronomy

Re: How high would a bullet go if fired from Io directly at Jupiter?

Date: Fri Jan 19 11:57:41 2001
Posted By: Adams Douglas, Senior Developer
Area of science: Astronomy
ID: 979016487.As

Good question, Rick. But, wow, that's some rifle you've got there. Most rifles have muzzle velocities in the 2500 ft/sec range. I think a 22-250 Remington is 3750, but I digress.

The escape velocity for a body is

                vesc = sqrt(2GM/R)

where M is the mass of the object (Io's mass is 8.93*10^22 kg), R is its radius (Io is 1815 km) and G is the universal gravitational constant (6.67*10^-11 Nm^2/kg^2). I'll let you do the math.

If an object moved fast enough to escape Io's gravity, it still might not move fast enough to escape Jupiter's gravity, in which case it would go into orbit around Jupiter depending on where you pointed it. Aiming directly at Jupiter would not be the best way to insure it hit Jupiter, because it would still also have Io's orbital velocity as a component of its motion.

What do you think the best direction to fire your bullet would be to get it to fall straight in to Jupiter?

Best wishes,
-Adams Douglas

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