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Escape velocity

by jablonsky27
Tags: escape, velocity
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jablonsky27
#1
May25-08, 05:23 AM
P: 74
escape velocity is defined in resnick,halliday,walker as 'the certain minimum initial speed that will cause it to move upward forever, theoretically coming to rest only at infinity. This initial speed is called the escape speed.'

the way escape speed is defined here gives me the impression that it is applicable only to projectiles which are given an initial thrust. during their entire trip after launch, they are not propelled.

if it is really the case then why do we need to worry about escape velocity for rocket launches? what stops a rocket travelling at say 2000km/h vertically upwards from the ground from leaving the earths gravitational field? afterall during its entire flight, it is being propelled upwards constantly.
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dst
#2
May25-08, 05:43 AM
P: 389
Quote Quote by jablonsky27 View Post
escape velocity is defined in resnick,halliday,walker as 'the certain minimum initial speed that will cause it to move upward forever, theoretically coming to rest only at infinity. This initial speed is called the escape speed.'

the way escape speed is defined here gives me the impression that it is applicable only to projectiles which are given an initial thrust. during their entire trip after launch, they are not propelled.

if it is really the case then why do we need to worry about escape velocity for rocket launches? what stops a rocket travelling at say 2000km/h vertically upwards from the ground from leaving the earths gravitational field? afterall during its entire flight, it is being propelled upwards constantly.
Absolutely nothing stops it, provided it can keep a minimum speed that isn't zero.

The "escape velocity" applies only to cases of initial thrust, with no acceleration afterwards - to my knowledge.
jablonsky27
#3
May25-08, 05:53 AM
P: 74
exactly my thoughts dst. but again, if that is really the case then why do we need to worry about the 11km/s figure during rocket launches? those multistage boosters are there just to achieve that speed.

rcgldr
#4
May25-08, 06:21 AM
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Escape velocity

It takes less fuel overall if the acceleration is done quicker. For human spacecraft, the limit is around 3 to 4g's, but for satellites, it can be much higher, although aerodynamic drag limits the maximum amount of efficient acceleration possible.

One way of optimzing fuel usage is to use the centrifugal inertial reaction of the rocket to oppose gravity, instead of using thrust alone to reach high orbital altitudes, the moon, or other planets.
jablonsky27
#5
May25-08, 07:33 AM
P: 74
hi jeff. You are talking about acceleration, i want to know about escape velocity.. I understand that there is a relation between fuel consumption and acceleration but that just tells you how fast or slow you should reach the escape velocity.
My question is why the velocity? Why cant a rocket leave earth at a constant speed(which is less than the escape speed) and continuous thrust and still be able to reach moon?
rcgldr
#6
May25-08, 04:52 PM
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Quote Quote by jablonsky27 View Post
Why cant a rocket leave earth at a constant speed(which is less than the escape speed) and continuous thrust and still be able to reach moon?
It could, but it would require a huge amount of fuel. In the worst case scenario, imagine a rocket just hovering, consuming fuel and not going anywhere.
aerospaceut10
#7
May25-08, 04:58 PM
P: 139
The idea of the escape velocity is that when the thrust is applied, it's supposed to be seen as a....very short impulse. If you delivered all your fuel, theoretically, at one time, and managed to get an impulse to have your spacecraft reach that escape velocity, then that ensures the craft to escape.

However as you can see most spacecraft don't do that currently and it's a bit more drawn out with the thrust. But in most spacecraft maneuvers when they change orbits, planes of orbits and such, they do short impulses for delta V.
jablonsky27
#8
May25-08, 11:19 PM
P: 74
wikipedia says,
Planetary or lunar escape velocity is sometimes misunderstood to be the speed a powered vehicle (such as a rocket) must reach to leave orbit; however, this is not the case, as the quoted number is typically the surface escape velocity, and vehicles never achieve that speed direct from the surface.

In fact a vehicle can leave the Earth's gravity at any speed. At higher altitude, the local escape velocity is lower. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the local escape velocity at that position- at sufficiently high altitude this speed can approach 0 m/s.
so i guess the speed and acceleeartion that the rocket has is for optimisation of fuel consumption.
russ_watters
#9
May26-08, 12:15 AM
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Quote Quote by jablonsky27 View Post
exactly my thoughts dst. but again, if that is really the case then why do we need to worry about the 11km/s figure during rocket launches? those multistage boosters are there just to achieve that speed.

what stops a rocket travelling at say 2000km/h vertically upwards from the ground from leaving the earths gravitational field?
There aren't many practical uses for a rocket that travels at 2,000 km/h. That isn't fast enough to orbit and it would take around 4 years just to reach Mars.

We don't ever need to deal with the 11km/s figure itself, but low earth orbit requires around 8km/s.
pallidin
#10
May26-08, 12:33 AM
P: 2,292
'There aren't many practical uses for a rocket that travels at 2,000 km/h. That isn't fast enough to orbit..."

With due respect, isn't that part of the statement in contradiction to the Wiki article which says
"Planetary or lunar escape velocity is sometimes misunderstood... In fact a vehicle can leave the Earth's gravity at any speed."
jablonsky27
#11
May26-08, 12:58 AM
P: 74
..rocket that travels at 2,000 km/h. That isn't fast enough to orbit..
isnt the orbital speed inversely dependant upon the arbital altitude?

and is there any relation between orbital speed and escape velocity?
pallidin
#12
May26-08, 02:26 AM
P: 2,292
Hello. Escape velocity is a locality term. It has no other meaning.
jablonsky27
#13
May26-08, 02:41 AM
P: 74
what does that mean? 'locality term'?
D H
#14
May26-08, 07:45 AM
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Quote Quote by pallidin View Post
Hello. Escape velocity is a locality term. It has no other meaning.
While escape velocity is indeed a function of distance from the gravitational body, it has a lot of meaning. The escape velocity (a bit of a misnomer; it should be escape speed) at a given altitude is the speed of an object on a parabolic orbit at that altitude. If the object's speed exceeds the escape velocity it is on a hyperbolic trajectory. Smaller speeds mean the object is in an elliptical orbit.

Quote Quote by jablonsky27 View Post
Why cant a rocket leave earth at a constant speed(which is less than the escape speed) and continuous thrust and still be able to reach moon?
Theoretically, yes. Practically, no. The amount of fuel required to do so would be enormous.

Quote Quote by jablonsky27 View Post
wikipedia says,
Planetary or lunar escape velocity is sometimes misunderstood to be the speed a powered vehicle (such as a rocket) must reach to leave orbit; however, this is not the case, as the quoted number is typically the surface escape velocity, and vehicles never achieve that speed direct from the surface.

In fact a vehicle can leave the Earth's gravity at any speed. At higher altitude, the local escape velocity is lower. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the local escape velocity at that position- at sufficiently high altitude this speed can approach 0 m/s.
so i guess the speed and acceleeartion that the rocket has is for optimisation of fuel consumption.
The initial work done by mission planners assumes "impulsive burns" -- that is, instantaneous changes in velocity. Say we want to plan a mission to Jupiter with flybys of Venus, Earth, and Earth again for gravity assists, with a final burn to place the vehicle in orbit around Jupiter. (This is what NASA's Galileo mission did; it is called a Venus-Earth-Earth gravity assist trajectory, or VEEGA for short.) Impulsive burns are needed at Earth to escape Earth's gravitational field and place the vehicle on an Earth-Venus trajectory, sometime before each flyby to set the vehicle up for the next phase, and at Jupiter to place the vehicle in orbit. Summing up the magnitudes of the changes in velocity gives the total delta V for the mission. This total delta V is closely aligned with the fuel needed to achieve the mission.

There is a slight problem with working in terms of impulsive burns: Doing so requires infinite thrust (aka infinite impulse). Real vehicles cannot perform impulsive burns. After the initial work, mission planners have to do a reality check because the finite impulse burns used on real vehicles inherently requires more energy to achieve the same change in velocity than does using an impulsive burn.

We use finite impulse burns for two reasons.
  • We can't achieve the infinite thrust needed for impulsive burns.
  • If we could, doing so would kill the passengers or crush the satellite.

The acceleration of a rocket is the rocket's thrust divided by it's mass. The initial acceleration is fairly low because the rocket is loaded with fuel. The acceleration increases as the rocket consumes fuel. This increasing acceleration can become too much for the passengers or cargo to withstand; see the second item on why we don't use impulsive burns. The Shuttle has to throttle down the engines as it burns fuel to keep thrust below three g.
russ_watters
#15
May26-08, 10:17 AM
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Quote Quote by pallidin View Post
'There aren't many practical uses for a rocket that travels at 2,000 km/h. That isn't fast enough to orbit..."

With due respect, isn't that part of the statement in contradiction to the Wiki article which says
"Planetary or lunar escape velocity is sometimes misunderstood... In fact a vehicle can leave the Earth's gravity at any speed."
Quote Quote by jablonsky27
isnt the orbital speed inversely dependant upon the arbital altitude?

and is there any relation between orbital speed and escape velocity?
The critical word in that first sentence was the word practical (which should be obvious from the sentence that follows it).

I don't feel like calculating the actual altitude right now (at the very least, it is well beyond the orbit of the moon), but what use would a satellite orbiting at such a high altitude be?

In fact, you really can't get to the moon (to land safely on it) at 2,000 km/hr, since the moon orbits at 3,600 km/hr. If you flew straight up at 2,000 km/hr, you'd still have to accelerate in order to land on the moon.

So as a practical matter, most of our rockets end up in low earth orbit, at 250-500 km up. Most of the energy involved in an orbit at that altitude is from the speed, so rockets pitch over very soon after they lift off, spending most of their time/fuel trying to reach the necessary speed (~7km/sec).

For a rocket really trying to leave Earth and head for deep space, where is it going? Sure, you could leave earth at a constant 2,000 km/h, but as a practical matter, trips to the inner solar system would take too long and trips to the outer solar system would take generations.

I'm sure NASA scientists/engineers work hard to find the optimal acceleration rate, but the reality is that escape velocity is an energy thing: whether you fly out at a small but constant speed or get shot out of a cannon at escape velocity, the amount of potential energy to be overcome is the same. The difference with flying out at a slow speed is that you also need a constant 1g (whatever 1g is at your altitude) of acceleration force to keep your constant speed.
rewebster
#16
May26-08, 10:50 AM
P: 880
jablonsky27-- just checking if you are confusing 'escape velocity' with 'orbital velocity'?
HallsofIvy
#17
May26-08, 12:32 PM
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Quote Quote by rewebster View Post
jablonsky27-- just checking if you are confusing 'escape velocity' with 'orbital velocity'?
No, he's not. The definition in his original post was clearly for "escape velocity".
HallsofIvy
#18
May26-08, 12:37 PM
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There was a rather silly television program a number of year ago (I forget the name but it starred Andy Griffith, for God's sake!) about a junk dealer who was going to make a fortune by going to the moon to recover material left there by the Apollo missions. One key point was that he was going to do this "cheaply" by accelerating very slowly: they did one demonstration in a car in which they accelerated slowly but long enough to reach speeds that frightened the person being demonstrated to! The program deteriorated from there with mobsters and spies every week.

In addition to other problems with "start slowly" already mentioned, one important reason to reach as fast a speed as you can as quickly as you can is to get through the atmosphere as quickly as possible.


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