If Ve1 and Ve2 are the velocities of a stone of mass 100 grams and ball weighing 200 grams which are projected up.
If they escape into outer space what is the ratio of their escape velocities?
First of all there are 4 escape velocities, one to just get into earth's orbit (it's around 7.9 km/s)
the second to get out of earth's gravitational field (11.2 km/s) (because floating around earth can be a bit boring ) the third to escape the sun system (42.1 km/s) and last but not least to get out of our galaxy, the milky way (320 km/s).
while the mass of the bodies sent into space makes no difference in these velocities (e.g. the velocity needed is the same for a 1g or a 1000 tons rock) it does make a difference in energy needed to accelerate a body to this speed of course (that's why it still matters how heavy e.g. a rocket sent into space is). But their escape velocities stay the same!
(p.s. the only mass that matters in the calculation of escape velocities, are the masses of the celestial bodies whose gravitational force one has to escape, that's why VE3 is much higher than VE2 (since ME3 is the mass of the Sun while ME2 is the mass of our small planet Earth )
P.p.s. the real values for these velocities VEopt. are a lot smaller if you make use of the rotation force of let's say earth or the sun! VE4opt then reduces from 320 to "only" 100 km/s making our escape from the milky way at least in far future a bit more probable )
Oh this was a test ? then I'm sorry to have spoiled it (I have an unfair advantage ) I thought you didn't know it yourself and wanted someone to explain anyhow, a great question to ask your friends It's as good as: would you rather spend a day on Venus eating nothing but bread and water or a year eating everything you want
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