Spring RTS Engine

outer space. What happens? Why don't you get very far? You are essentially trapped on Earth, unless you can find a rocket that can travel at escape velocity away from the Earth.
The escape velocity can be calculated in Newtonian gravity by using energy conservation of an object of mass m in the gravitational field of a planet of mass M in D space dimensions:

The escape velocity for the surface of the Earth is about 11 km/sec. Notice that's only 37 millionths of the speed of light. Under what conditions would the escape velocity from the surface of some planet or star be equal to the speed of light?

For a planet the mass of the Earth, this distance is only about a centimeter. So if the Earth were less than a centimeter in diameter, the escape velocity

For the velocity to equal the speed of light would require such an enormous amount of mas, that neither a star or planet could exist. You're talking of a black hole.

Also there are other effects on escape velocity than simply Newtonian physics. Air resistance? Spacial deformation through gravity? Those are einstein's equations as well as other things.

Where did this come from anyways? a bit random to start talking about it.

Technically you only need an upward velocity of greater than zero to reach space.

Technically you only need an upward velocity of greater than zero to reach space.

Exactly.

According to Wikipedia:

In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a bounded distance from the source.

So with propulsion, you can do what napalm said.
And escaping at a velocity equal to light speed is impossible because of relativity, but im not explaining why because the theories of relativity are making my head burst :)

actully, I just felt like posting while drinking and so i just copied some text out of a page i had open...

I wern't tryingh to make discussion.

I think it was a site on string theroy...

aGorm

link aGorm?

Well how do i know? I had had a few drinks, and I just somehow got there?

aGorm

Ya know, I don't think normal drunk people end up on sites on string theory... but then, how would I know since I've never been drunk
But then, we've known you aren't normal all along aGorm, so whats the surprise?

With a name like aGorm who can blame him...

Hang on, He's talking in 3rd person. What a twat!

Usualy a webbrowser has a history. Although some people delete it...

I will not stand for theses acucastions! I am innocent! It was the other guy! Alantia is a lier! I do not delete my history! <Shifty look>

Zoombie, my history deletes itself!

Exactly! Its all a cover up you see, orginized by the secret internet catell that is whatching our every move!

Okay im done being crazy now.

Also the only gun that can theoreticaly shoot something into space is a rail gun.

depends on where from - the thing that stops a gun from working (mostly) is the air resistance on the way up reduces the velocity of the shell significantly - if you could make an explosive reaction work in a vacuum it might work (a big gun would probably work on the moon for instance, although that has a significantly lower escape velocity). A rail gun isn't really a type of gun at all, there's no explosives, no 'shell' per se and no barrel. (although they're very funky nonetheless)

Zaphod. 1) don't talk relativity, I only got 30% on that module (and light escapes form the sun, dunnit? that's going at the speed of light)
2) I'm not sure that's right. Escape velocity is the velocity which makes something's gravitational potential energy equal to it's kinetic energy (technically escape velocity is anything above that). i.e
1/2*m*V*V = (G*m*M)/r

those small m's cancel:
1/2*V*V=(G*M)/r
V=sqrt([2*G*M]/r)

for earth:
V=sqrt([2*{6.67*10^-11}*{5.97*10^24}]/[6.83*10^6])
V=10,798 m/s

Now alternatively you can do it with propulsion - say you're moving away from the earth at 1 m/s you propulsion has to be slightly more than the gravitational force exerted by the earth (say for 100 km above the earth's surface for a 100kg spacecraft)

(G*m*M)/(r^2)
([6.67*10^-11]*100*[5.97*10^24])/([6.93*10^6]^2)
829 N

In the case of the 11km/s escape velocity you have enough kinetic energy to counteract the earths gravity and move from the surface of the earth ot infinity, this is about 5,829,840,200 J (1.847 lightbulb-years)

In the case of constant propulsion, to get to distance infinity you would have to keep pumping out energy (at a varying rate, and dropping off significantly as you got further from the earth) which would come to a grand total of, you've guessed it: 5,829,840,200 J

I suppose the point is that in both cases you've expended the necessary escape energy

Ok, the mass for a black hole (in a body 1000km in radius):
{3*10^8 (speed of light)}= sqrt([2*{6.67*10^-11}*M]/1000000)
M=[({3*10^8}^2)*1000000]/[2*{6.67*10^-11}]
M=6.75*10^32 Kg

Interesting tidbit; for a big enough black hole, it's density is actually less than water. I'll leave it as an exercise to anyone sadder than me to find out what that distance is.

Atlantai: Air resistance doesn't affect the escape velocity, just your ability to attain it. Space deformations through gravity is what causes you to have to attain escape velocity in the first place

Well, thanks for keeping ym mind working over the holidays.

-Gurkha

5,829,840,200 J (1.847 lightbulb-years)
Scalar->Vector
?
Stupid A-Level physics...i don't have a clue!!!

a lightbulb-year is simply a measure of energy, the amount of energy used by a 100W lightbulb in one year: 100*60*60*24*365.25 = 3,155,760,000 J

Like a lightyear is a measure of length based on how far light can travel in a year.

all four of those units mentioned above (J, M, lightbulb-years and lightyears) are scalars.

ah! thanks! i blame the teachers

Zaphod was correct essentially but you misunderstood and so was I.

The sun and the earth drag space around them as they spin to different extents. These do effect escape velocities and orbits but int he case fo the earth its not noticeable. In the case of the sun you'd ahve been icninerated before you noticed anything. And int eh case of a black hole you'd have the equivilant of a lense with a black spot in the middle, light would bend towards the black hole as it passed around and zoomed off, the closer it got or the steeper the angle the morelikely its bent into the black hole, but ti never reaches because time is frozen at the event horizon. To escape the event horizon you would need an infinite escape velocity.

The Sun also bends light around it as prooven by maths and experiments. And as said, the escape speed is relative to which object your talking about. For example what speed would the earth need to be travelling at to escape the pull of my hand? Pretty fast thats for sure.

Hey im not right or wrong, I was just quoting....

Anyway, talking about bodies that drag space around them is too vague to be of any use mathematically. Meaning you can't really make point with it imo.

Escape velocity is the velocity which makes something's gravitational potential energy equal to it's kinetic energy (technically escape velocity is anything above that).

Hm calculating escape velocity using gravitational potential energy is a way to do it, but that doesn't contradict wikipedia. It's just a different way of describing escape velocity.

When the velocity is higher than escape velocity, the movement curve of the particular object will diverge from origin (earth) to infinity (in a galaxy far far away )
That's the same as saying the kinetic energy should be bigger than the gravitational potential energy from here to infinity.


And lightbulb-years?, since when did gigajoule become obsolete? :)