Question about escape velocity.

Overblood

So a space shuttle has to go 11km/s to escape the pull of earth's gravity. Is this the escape velocity? But when it orbits the earth isn't it still under the effect of earths gravitational pull?

Overblood

Overblood wrote: »

So a space shuttle has to go 11km/s to escape the pull of earth's gravity. Is this the escape velocity? But when it orbits the earth isn't it still under the effect of earths gravitational pull?

Escape velocity is the speed where the energy the object has due to movement (kenetic energy) is equal to the energy it has due to gravity acting on it (gravitational potential energy). This basically means that the object has to have enough speed to "escape" the pull of gravity. And yes, it's 11km/s. This means that if you give an object an intial speed of 11km/s, and point it staight upwards, it will escape earths gravity without any further propulsion. It's possible to escape the pull of gravity by accelerating upwards faster than gravity pulls you down. You could do this by accelerating upwards with an acceleration greater than 9.8m/s/s (I think this is correct?). This is the way the space shuttle does it. It doesn't start off at 11km/s, but it slowly accelerates to that speed.

Yes, when it's in orbit Earths gravity is still acting upon it. Earths gravity is pulling the Space Shuttle down towards the centre of the Earth, so, it's constantly falling towards Earth. But, it's travelling fast enough forward that the curvature of the Earth means it never actually hits the ground. It's tricky to explain, but, think of it this way: It's falling downwards towards Earth, but, it's going forwards so fast by the time it gets to where it was falling to, the Earths curvature means it actually didn't get any closer.

Perhaps somebody can explain these concepts better than I can, it's late and I'm tired! Hope this helps anyway.

Captain Chaos

I believe it does have to boost it's orbit a little to stay constant becasue it is constantly getting closer to the Earth but seeing as it's only in orbit for a week to 10 days at a time it does not matter much.

The International Space Station has to boost it's own orbit a few times a year and somtimes uses the space shuttle's boosters to boost it when it they are docked together.

I think the shuttle orbits at about 22,000mph or about Mach 27 iirc could be way off.

Also the shuttle uses the Earth's rotation to help reach orbit by having its launch pad as close to the equator as possible in US soil and always heads due East on launch.

Professor_Fink

Overblood wrote: »

So a space shuttle has to go 11km/s to escape the pull of earth's gravity. Is this the escape velocity? But when it orbits the earth isn't it still under the effect of earths gravitational pull?

Escape velocity, as others have pointed out is the velocity you need to be going to escape to infinity if you have no thrust. Space craft never reach this speed. First of all, they almost never need to be able to escape the Earth's gravitational pull. The Shuttle certainly can't do that. Bare in mind that the moon is gravitationally bound to the Earth, so even going there requires much less energy. Even so, space craft use engines to provide continuous thrust which is enough to overcome the downward pull of the earths gravity. The speed at which they go up is largely irrelevant, as long as the go up, rather than down. This is satisfied as long as the upward force generated by the engines is greater than m*g.

Overblood

-JammyDodger- wrote: »

Earths gravity is pulling the Space Shuttle down towards the centre of the Earth, so, it's constantly falling towards Earth. But, it's travelling fast enough forward that the curvature of the Earth means it never actually hits the ground. It's tricky to explain, but, think of it this way: It's falling downwards towards Earth, but, it's going forwards so fast by the time it gets to where it was falling to, the Earths curvature means it actually didn't get any closer.

Perhaps somebody can explain these concepts better than I can, it's late and I'm tired! Hope this helps anyway.

I know how orbits work! It's just escape velocity I was asking about.

So if the space shuttle travelled upwards at 11km/HOUR, would it still make it to space?

Overblood

Overblood wrote: »

So if the space shuttle travelled upwards at 11km/HOUR, would it still make it to space?

If there was no atmosphere, and you launched the Space Shuttle with a speed of 11.2 km/s, it would make it to "infinity" (i.e. out of Earths gravitational attraction) without any further propulsion. So it just needs that initial speed. But this isn't how anything gets into space, as it's impossible to give anything an intial speed of 11.2 km/s.

Professor_Fink

-JammyDodger- wrote: »

But this isn't how anything gets into space, as it's impossible to give anything an intial speed of 11.2 km/h.

Actually, last I heard they had managed 10km/s with an experimental rail gun.

Spear

-JammyDodger- wrote: »

If there was no atmosphere, and you launched the Space Shuttle with a speed of 11.2 km/h, it would make it to "infinity" (i.e. out of Earths gravitational attraction) without any further propulsion. So it just needs that initial speed. But this isn't how anything gets into space, as it's impossible to give anything an intial speed of 11.2 km/h.

He said hour not second.

Professor_Fink

Professor_Fink wrote: »

Actually, last I heard they had managed 10km/s with an experimental rail gun.

That's mad. I've read about one that can propell projectiles to 6km/s alright. I'd imagine it would me next to impossible to propell anything bigger than a bullet to that speed so quickly though?

Spear wrote: »

He said hour not second.

Oops, my mistake - wasn't really thinking! I'll change it now.

Overblood

So if the space shuttle travelled upwards at 11km/H-O-U-R, would it still make it to orbit?

Professor_Fink

Overblood wrote: »

So if the space shuttle travelled upwards at 11km/H-O-U-R, would it still make it to orbit?

As long as the engines kept going, then yes, although it would take an age and be aerodynamically unstable.

Overblood

Professor_Fink wrote: »

As long as the engines kept going, then yes, although it would take an age and be aerodynamically unstable.

So as long as the aerodynamics are OK and you have enough fuel, escape velocity can be ignored?

Professor_Fink

-JammyDodger- wrote: »

I'd imagine it would me next to impossible to propell anything bigger than a bullet to that speed so quickly though?

Well, I believe there has been success (although not quite that fast) for upto a couple of hundred kilos.

Overblood

Overblood wrote: »

So as long as the aerodynamics are OK and you have enough fuel, escape velocity can be ignored?

The idea of escape velocity doesn't concern itself with fuel. It's the initial speed which you would have to give an object for it to escape the gravitational attraction of a body without any further propulsion. On Earth it's 11200m/s. If you're using propulsion it becomes irrelevant. As Profressor Fink has already said, if you use propulsion, the rocket engines must produce a thrust that is greater than the weight of the rocket.

Professor_Fink wrote: »

Well, I believe there has been success (although not quite that fast) for upto a couple of hundred kilos.

Thats interesting. I wonder will it ever become a feasible method for getting satellites into orbit? I suppose such acceleration would damage onboard components though.

Professor_Fink

-JammyDodger- wrote: »

Thats interesting. I wonder will it ever become a feasible method for getting satellites into orbit? I suppose such acceleration would damage onboard components though.

That's the idea. I have some photos of one experimental system I took at Florida Tech, but unfortunately they're on a different continent. I'll post them once I get back later next week.

EDIT: Actually, I had one on Flickr: http://static.flickr.com/2243/2203118066_689279ab91.jpg

Svenolsen

Very slightly off topic I know.

But.....

You can escape from the gravitational field of the earth by WALKING !!!

If you build a ladder high enough you can climb up the ladder at a leisurely pace until you reach the end of the ladder.Even if the ladder is a million miles high !

Think about it !!!

If Materials Science can make a cable strong enough in the future to reach Geosynchronous Orbit we will be able to get into a "Space Elevator" and ride up to a Geosynchronous Space Station just like we do in a building.

See:
http://en.wikipedia.org/wiki/Space_elevator

Arthur C. Clarke's novel "The Fountains of Paradise" was about such an elevator:

http://en.wikipedia.org/wiki/The_Fountains_of_Paradise

.

Professor_Fink

Svenolsen wrote: »

You can escape from the gravitational field of the earth by WALKING !!!

If you build a ladder high enough you can climb up the ladder at a leisurely pace until you reach the end of the ladder.Even if the ladder is a million miles high !

Actually, you can't. The gravitational field extends to infinity.

Svenolsen

Professor_Fink wrote: »

Actually, you can't. The gravitational field extends to infinity.

Ok Ok. That's nit-picking.

You know what I meant!

Not much left of the Earth's gravitational field at the distance of the Andromeda Galaxy!

.

Svenolsen

Correcting myself.

At a certain distance above the Earth's surface WALKING PACE EXCEEDS THE ESCAPE VELOCITY AT THAT POINT.

So I was right first time Professor Fink.

There!

Professor_Fink

Svenolsen wrote: »

Correcting myself.

At a certain distance above the Earth's surface WALKING PACE EXCEEDS THE ESCAPE VELOCITY AT THAT POINT.

So I was right first time Professor Fink.

There!

Well, if we're getting pedantic, how about this: Humans walk at about 5km/h. Since the Earth's mass is 6*10^24 kg. So using 1/2 m v_escape^2 = G m_Earth m/r we get r = 2 G m_Earth/v_escape^2. So the distance from the centre of the earth you need to be at for the escape velocity to be walking speed is approximately 4.1*10^14 m or 4.1*10^11 km. Since the radius of the Earth is only 6400km, so it would take you 9.43 million years. Since the longest anyone is known to have lived is 122 years, I think we can say definitively that you can not escape the Earth's gravitational field by walking.

Professor_Fink

Professor_Fink wrote: »

That's the idea. I have some photos of one experimental system I took at Florida Tech, but unfortunately they're on a different continent. I'll post them once I get back later next week.

EDIT: Actually, I had one on Flickr: http://static.flickr.com/2243/2203118066_689279ab91.jpg

Thanks for the link. They're very interesting, just had a quick read on wikipedia about them. It says that a speed of 20km/s was achieved, albeit it with a small mass. I wonder is that the fastest projectile speed ever achieve? Or are there methods of gaining faster speeds?

Professor_Fink

-JammyDodger- wrote: »

Thanks for the link. They're very interesting, just had a quick read on wikipedia about them. It says that a speed of 20km/s was achieved, albeit it with a small mass. I wonder is that the fastest projectile speed ever achieve? Or are there methods of gaining faster speeds?

Well, the smaller you go, the easier we can acelerate things. Particle colliders accelerate electrons and protons to very close to the speed of light. I know thats obvious, but it makes it hard where to draw the line.

Capt'n Midnight

you need about twice the energy of robital velocity to get to escape velocity

88 minutes is a low earth orbit time call it an hour and a half
the earth is 40,000 Km / 24,000miles around so you need to do about 18,000 mph
actually it's only 17,000mph at the equator because the earth does 24,000 miles in 24 hours

look up gravity drag and air resistance means you need a good bit more than 17 or 18,000 to get to orbit

problem with a chemical rocket is that all the energy comes from the fuel which has to be carried with you too , using a ground based energy source would be a better idea

other ways to get to orbit
space elevators
http://www.slingatron.com/ http://www.defensetech.org/archives/002387.html

Professor_Fink

Capt'n Midnight wrote: »

you need about twice the energy of robital velocity to get to escape velocity

88 minutes is a low earth orbit time call it an hour and a half
the earth is 40,000 Km / 24,000miles around so you need to do about 18,000 mph
actually it's only 17,000mph at the equator because the earth does 24,000 miles in 24 hours

I'm afraid your a little off. To start with, kinetic energy is quadratic in velocity, so you would need a quater the kinetic energy. Secondly, the direction of motion in orbit is orthogonal to the direction of motion for minimum escape energy, so there is no way to directly convert this energy into velocity for moving away from the planet. The thing to do is to continuously accelerate so that the orbit grows. But this approach has nothing to do with escape velocity.

Capt'n Midnight

http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed14.htm
"I mentioned earlier, notice that the orbital period and the escape velocity vary by a square root of two if you are at a particular position."

if the velocities vary by root(2) then the kinetic energy varies by 2


Yes you can continuously increase your orbit, but only after you reach orbital velocity.
at present you need chemical rockets to get to orbit , then you can switch on the ion-drive for the trip to the moon.


orbits are tangential, but which ever way you work it out a large component of the vector is away from the planet.

Professor_Fink

Capt'n Midnight wrote: »

http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed14.htm
"I mentioned earlier, notice that the orbital period and the escape velocity vary by a square root of two if you are at a particular position."

if the velocities vary by root(2) then the kinetic energy varies by 2

Well, the velocity you mention was 18000km/h, while the escape velocity from the Earth's surface is 11km/s which is approximately 40000km/h, roughly a factor of two more (nor sqrt(2)). Now since you were refering to low earth orbit, I assumed you were talking about a couple of hundred km up. In this case the gravity would be about the same as on the surface, so it should be a factor of 4 in the difference in energies.

Svenolsen

Professor_Fink wrote: »

Well, if we're getting pedantic, how about this: Humans walk at about 5km/h. Since the Earth's mass is 6*10^24 kg. So using 1/2 m v_escape^2 = G m_Earth m/r we get r = 2 G m_Earth/v_escape^2. So the distance from the centre of the earth you need to be at for the escape velocity to be walking speed is approximately 4.1*10^14 m or 4.1*10^11 km. Since the radius of the Earth is only 6400km, so it would take you 9.43 million years. Since the longest anyone is known to have lived is 122 years, I think we can say definitively that you can not escape the Earth's gravitational field by walking.

You are very pessimistic about our future longevity Professor Fink.

In the future we will all live to be more than 9.43 million years old and we will be able to walk to the ends of eternity.

I never once implied that a human being could stroll out of the gravitation well of the earth in the "Three Score and Ten" or so years that our miserably temporary bodies last.

A robot which does not die could do it though!

.

Professor_Fink

Svenolsen wrote: »

I never once implied that a human being could stroll out of the gravitation well of the earth in the "Three Score and Ten" or so years that our miserably temporary bodies last.

The proposition that the Earth's gravitational field can be escaped by walking used the word "you" to describe the person doing the walking, which I assumed referred to either one of us, or a person in general. Neither case fits your answer. I do however think we have gone way off topic at this stage, so lets try to get back to the topic.

Capt'n Midnight

Professor_Fink wrote: »

Well, the velocity you mention was 18000km/h, while the escape velocity from the Earth's surface is 11km/s which is approximately 40000km/h, roughly a factor of two more (nor sqrt(2)). Now since you were refering to low earth orbit, I assumed you were talking about a couple of hundred km up. In this case the gravity would be about the same as on the surface, so it should be a factor of 4 in the difference in energies.

My cunning plan succeded :pac:
I used mph instead of kmph because the numbers are easier, though strictly speaking Knots would have been better as there are 24,000 of them around the equator.

http://en.wikipedia.org/wiki/Orbital_mechanics

The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M is

V=sqrt(GM/r)

so starting at the surface (or LEO to a first apporximation) of the earth then V squared for an orbit is GM/r
to escape the earth V squared is 2GM/r , twice the energy.

since NASA and co. park space craft in orbit from time to time before heading earth there can't be too much energy lost compare to a direct assent.


why use a rocket ?
http://en.wikipedia.org/wiki/Non-rocket_spacelaunch



Also the shuttle isn't built to leave the earth max altitude is 1,000Km so no point in going 11Km/s

Capt'n Midnight

http://en.wikipedia.org/wiki/Ram_accelerator

Thus if propellant mixtures having a sound speed of 1000 m/s (e.g. fuel-rich H2-O2 mixtures) are used, muzzle velocities in excess of 8000 m/s are possible.

http://en.wikipedia.org/wiki/Light_gas_gun

Velocities ranging from 1 km/s up to 7 km/s can be achieved.

circular orbit: 6.9 to 7.8 km/s

Single stage to orbit type speeds :eek:

Professor_Fink

Unfortunately the acceleration from "space guns" is usually enough to turn humans into mush, so they won't be useful for manned space flight.

Svenolsen

Professor_Fink wrote: »

The proposition that the Earth's gravitational field can be escaped by walking used the word "you" to describe the person doing the walking, which I assumed referred to either one of us, or a person in general. Neither case fits your answer. I do however think we have gone way off topic at this stage, so lets try to get back to the topic.

What I meant was that "initial velocity" is irrelevant provided energy is being continuously supplied.

Originally I had this sentence in mind:

"A snail can crawl out of the earth's gravity well at it's own pace,provided it can live long enough."

(I changed it to "humanise" it, clumsily I know.):

Hope that clears up my point.

.

Capt'n Midnight

Professor_Fink wrote: »

Unfortunately the acceleration from "space guns" is usually enough to turn humans into mush, so they won't be useful for manned space flight.

LOL
and a very thin layer of mush at that


most of the stuff to be sent into orbit is freight/fuel so still it would be handy if you could send up fuel as ice or if all else fails you could use zinc or something to fuel an ion drive when you meet it later in orbit.

space elevators are freight only too as it would take bloody ages to get into orbit as well as a leisurely passage through the radiation belts

mickeydevine

I always assumed a shuttle stayed in orbit using centrifugal force. Why cant this stuff be simpler aaaaaaaarrrrrggggggghhhhh.