# Escape velocity

## Main Question or Discussion Point

Hi all,
(i hope this hasn't been done lately)
But is it true that you can escape from the earth at any speed - provided you have enough fuel etc.?

And that 25 000 mph is the speed you have to "throw" a Saturn V rocket up at so that it doesn't fall back down?

thanks
david (aka fluxion)

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marcus
Gold Member
Dearly Missed
hello fluxion

escape velocity is about getting free from the gravitational influence of something

you simplify it by imagining the earth (or whatever body) alone in the universe, so there's no competition

then if you go always less than escape velocity then you never escape because no matter how far you get to
when you turn off the engine and stop you will start falling back to earth----or if you have some sideways motion you will go into orbit around earth.

so if you don't achieve escape velocity at SOME distance, you will always be tied to the earth in some way---falling back or orbiting.

============

if you want to escape from earth, but do it very slowly like going only 1 kilometer per hour, then you can use a lot of fuel and do it:
you can rise very slowly and keep on rising until you are so far away that
*escape velocity itself is only 1 kilometer an hour*!

Escape velocity declines with distance. so by taking a long time and using a lot of fuel you can achieve a slow escape velocity, but very far away.

but you still achieve escape velocity! If you want to ultimately escape earth then it is inevitable that eventually you do achieve escape velocity (even if by that time it is a very small velocity)
============

Use Google to calculate escape from earth surface----which is "radius of earth" from the center

Put this in the box, and press "search"

sqrt (2*G*mass of earth/radius of earth)

If you type that in the Google window and press search, then Google calculator will give you back

sqrt((2 * G * mass of Earth) / radius of Earth) = 11 180.7201 m / s

which is 11 kilometers a second

If you want to know the escape velocity at a distance of 300 astronomical units, say, then put this in

sqrt (2*G*mass of earth/(300 astronomical unit))

then Google calculator will give you back
sqrt((2 * G * mass of Earth) / (300 Astronomical Unit)) = 4.214945 m / s

that means that if you are already 300 AU from earth center (in an otherwise empty universe) then escape velocity for you is only 4.2 meters per second. Lucky you, a comparatively slow speed that will not be hard to achieve. Even a bicycle can go 4 meters a second.

Last edited:
Thank you Marcus, that clears it up for me nicely
(and sorry about misplacing that question - my first post)
flux

hi marcus. since fluxion mentioned about escape velocity, does that mean the reason for light unable to escape the blackhole is because the black hole's escape velocity is that of the speed of light? thus the EV increases as the sun turns from a white dwarf to a neutron star and lastly a blackhole?

hi marcus. since fluxion mentioned about escape velocity, does that mean the reason for light unable to escape the blackhole is because the black hole's escape velocity is that of the speed of light? thus the EV increases as the sun turns from a white dwarf to a neutron star and lastly a blackhole?
That is what I thought, but seeing as marcus said you can escape at any velocity if you have enough "fuel", there must be something else?

Is it just that infinite energy is required to escape a black hole?

Is it just that infinite energy is required to escape a black hole?
you can say so. as the mass of the gravitational body of an object (blackhole) approaches infinity, and/or an objects proximity to the body approaches zero the escape velocity approaches c, the speed of light. however, for black hole theory to be valid the escape velocity must exceed the speed of light as the mass approaches infinity and/or the distance approaches zero.