General Ignorance

[Nick]

This is my 4,000th post, so I'll pose a question. I have just been watching Sir Patrick Moore's Sky at Night. This brought to mind a question which I'd like answered. Do we have an apropriate boffin in TH?

I am perplexed by space travel. On the face of it I am familiar with the concept of an 'escape velocity' being required in order to leave Earth. OTOH, I recall that a rocket can work in a vacuum. Also, as one moves away from a gravitational force, the force becomes weaker. Therefore, if powered by a rocket, moving away from the centre of gravity, surely one could eventually leave the Earth at any speed?.

Where have I gone wrong?

[Marian]

Maybe thinking too much....

[Nick]

That's why my head hurts!

[seyorni]

It would take a lot more fuel to achieve orbit if you ascended slowly, and the extra weight would require still more fuel. I think the most efficient cost/fuel/weight formula is to achieve escape velocity as quickly as possible.

Of course, I'm no rocket scientist.

[Alan H]

There's a good explanation here. Essentially, the rocket has to go fast enough away from the planet to overcome the gravity that pulls it down: go too slow and you can't escape. The example they give of throwing a ball upwards is good [---][/---] throw it too slowly and (ignoring the effects of friction) it will eventually grind to a halt and fall back to earth. Throw it fast enough (about 7 miles a second or Mach 34!) then it will have the energy to overcome the pull of gravity.

[Nick]

There's a good explanation here. Essentially, the rocket has to go fast enough away from the planet to overcome the gravity that pulls it down: go too slow and you can't escape. The example they give of throwing a ball upwards is good [---][/---] throw it too slowly and (ignoring the effects of friction) it will eventually grind to a halt and fall back to earth. Throw it fast enough (about 7 miles a second or Mach 34!) then it will have the energy to overcome the pull of gravity.

Hmmm..... You might think it a good explanation, but surely it just restates the problem. I understand the 'throwing a ball' analogy, and that makes sense. The difference is that a sky-pointing rocket will have continuing thrust, denied to a projected ball. It is logical that friction and gravity would stop a projectile escaping the earth's gravitational pull if the only force applied was from the start. But what if the thrust continues?

Surely there can be no greater thrust requirement than that necessary to move the rocket away from the earth, at it's point of strongest attraction..... After that, sure it should become easier.....?

Still puzzled.....

[Nick]

Correction:
..... to move the rocket away from the earth at its point of strongest attraction.....

[grammar king]

Supposing that the thrust is greater than the effect of gravity, I suppose you're right. However, perhaps it is that the fuel necessary to do that at any velocity less than the so-called "escape velocity" would weigh too much, and increase the force of thrust required.

[Nick]

Hmmm... I have my doubts. If your hypothesis were true, we wouldn't talk about 'escape velocity' but ' power to weight escape ratio' or some such...... Velocity has nothing to do with weight or fuel consumption. I say this, not because I know the answer and can smirk accordingly, but because I don't.

[tubataxidriver]

Think about it in terms of acceleration. Gravity exerts a force on the rocket which is forever trying to accelerate it towards the centre of the earth. This means that gravity is forever taking a vertical component of speed off the rocket. If the rocket starts slowly, like a car for example, say at 10 metres per second vertical speed, the force of gravity will take 10 metres per second off this speed in every second, so after a little over a second it will be stationary as regards vertical speed, and in subsequent seconds it will begin to accelerate downwards. If the rocket starts with 11,100 m/s vertical component, or gains this due to thrust during its flight, the force of gravity will only chip into this speed very slowly, and by the time it has been reduced to zero vertical component the rocket will have reached a height where gravity has much less effect, and it can enter a stable orbit. Once in orbit , the force of gravity on the rocket causing an acceleration towards the centre of the earth, combined with its horizontal component of speed, will draw the rocket round in a circular track.

[Alan H]

Ah! A good explanation TTD! I was thinking of saying something about gravity being in terms of an acceleration (or rather a deceleration), but hadn't got round to thinking how I was going to say it.

I think many people won't have appreciated that orbiting is really just continually falling towards the earth, but, because of your forward speed, you just continually curve round the earth.

PS I wonder if anyone is going to ask about centrifugal or centripetal forces?

[Nirvanam]

This is my 4,000th post, so I'll pose a question. I have just been watching Sir Patrick Moore's Sky at Night. This brought to mind a question which I'd like answered. Do we have an apropriate boffin in TH?

I am perplexed by space travel. On the face of it I am familiar with the concept of an 'escape velocity' being required in order to leave Earth. OTOH, I recall that a rocket can work in a vacuum. Also, as one moves away from a gravitational force, the force becomes weaker. Therefore, if powered by a rocket, moving away from the centre of gravity, surely one could eventually leave the Earth at any speed?.

Where have I gone wrong?

Lemme attempt to think thru my ignorance on this...lol! OK, we have an object which is inside a bigger object and being kept there by an invisible force of the bigger object. The intensity of this force is a particular level at a particular point (surface) in the bigger object. And this force depends on the mass of the bigger object (is this right, Alan H?, gravitational force of object is directly proportional to mass of object). Now given that any object is made up of particles, the maximum force mustered by that object would be at a point which is closest to most number of particles within that object...in other words maximum point of density..for the Earth it would be the core(?). Since the distance between the surface and the top sphere of the Earth is pretty small compared to the distance between the core and the surface, let's assume that the force is going to be 9.8 m/s2 in the atmosphere as well.

I'd think that as the smaller object gets closer to the end of the bigger object, the acceleration required should start becoming lesser, but the velocity needs to be maintained in order for it to constantly move away from the influence of the bigger object. So, the smaller object can start at a velocity of x kmph accelerate to y kmph and then stay at y kmph without needing to accelerate further. Velocity ensures that there is movement and movement would be required for the object to move out of and away from the bigger object.

Making any sense

[Nick]

Think about it in terms of acceleration. Gravity exerts a force on the rocket which is forever trying to accelerate it towards the centre of the earth. This means that gravity is forever taking a vertical component of speed off the rocket. If the rocket starts slowly, like a car for example, say at 10 metres per second vertical speed, the force of gravity will take 10 metres per second off this speed in every second, so after a little over a second it will be stationary as regards vertical speed, and in subsequent seconds it will begin to accelerate downwards. If the rocket starts with 11,100 m/s vertical component, or gains this due to thrust during its flight, the force of gravity will only chip into this speed very slowly, and by the time it has been reduced to zero vertical component the rocket will have reached a height where gravity has much less effect, and it can enter a stable orbit. Once in orbit , the force of gravity on the rocket causing an acceleration towards the centre of the earth, combined with its horizontal component of speed, will draw the rocket round in a circular track.

Thanks for that explanation, TTD, it sounds almost plausible but I'm still not quite getting the hang of it. D'ya mind if I probe a bit further?

Surely gravity is a constant force? I understand acceleration is expressed as speed per second per second, but I'm still not quite getting it. Suppose I hold a ball in my hand five feet off the ground. The force I need to use to keep it there is (surely) constant. If I then apply some constant extra upward pressure, why is it that the ball won't keep on moving inexorably up, so long as that extra pressure is applied? In your example above, won't the rocket only slow down if no further upward thrust is applied......?

[grammar king]

PS I wonder if anyone is going to ask about centrifugal or centripetal forces?

Hmmm...

[Alan H]

Nick: you now need Newton's laws of motion.

[Paolo]

Thanks for that explanation, TTD, it sounds almost plausible but I'm still not quite getting the hang of it. D'ya mind if I probe a bit further?

Surely gravity is a constant force?

Nope - at least not in intensity since it's mass dependent. Fluctuations in local gravity can even be mapped. In parts of Cornwall, where there is a lot of granite bedrock, the local mass is marginally greater than in sedimentary based London (for example), this means that the force of gravity is marginally higher in Cornwall. Gravity also becomes weaker as you move away from the centre of mass, so as you move away from the Earth the force holding you there constantly decreases. It is possible to still be far enough away from the Earth for gravity be so weak that the acceleration takes years to start dragging things back in, but they are still directly influenced by Earth's gravity (think of geostationary satellites).

I understand acceleration is expressed as speed per second per second, but I'm still not quite getting it. Suppose I hold a ball in my hand five feet off the ground. The force I need to use to keep it there is (surely) constant. If I then apply some constant extra upward pressure, why is it that the ball won't keep on moving inexorably up, so long as that extra pressure is applied? In your example above, won't the rocket only slow down if no further upward thrust is applied......

I thought TTD's explanation was good, but I'll see if I can put it differently. In your example the ball would keep moving up if you kept applying more force than is needed to overcome gravity. Eventually you would indeed leave the Earth's gravitational field - fine in theory, but in practice you would need a source of thrust to keep the ball moving. Of course, that source of thrust would require fuel, which would increase the mass of the ball, meaning you would need to use greater force to overcome gravity, meaning you would need greater thrust, meaning you would need more fuel, meaning you would need greater thrust.... you can see where I'm going with this. Importantly, escape velocity is not relevant or applicable in this example. Escape velocity only applies to an object which receives all of the propulsive energy needed to escape gravity in one go, with no additional thrust - such as when firing a projectile. The escape velocity from Earth is sufficiently high (11.2 km/s) to make it unachievable due to subsequent damage from friction of the object against the Earth's atmosphere.

[Nick]

Bingo! Thanks Paolo! You're explanations have a clarity I envy .

Having said that I think my question wasn't quite as stupid as I feared it might be....

Surely gravity is a constant force?

Nope - at least not in intensity since it's mass dependent.[......]

I meant constant, as opposed to accelerating. (I was vaguely aware that gravity varied from place to place.)

Gravity also becomes weaker as you move away from the centre of mass, so as you move away from the Earth the force holding you there constantly decreases... [...etc]

Yes, I fully understand this. Indeed it was this which was giving rise to my question in the first place.

I thought TTD's explanation was good, but I'll see if I can put it differently. In your example the ball would keep moving up if you kept applying more force than is needed to overcome gravity. Eventually you would indeed leave the Earth's gravitational field - fine in theory,

That's what I thought!

but in practice you would need a source of thrust to keep the ball moving.

Aha! This explains it. I was right about escape velocity being relevant only if all the force were given at once, at outset. I'm happy with that.

Of course, that source of thrust would require fuel, which would increase the mass of the ball, meaning you would need to use greater force to overcome gravity, meaning you would need greater thrust, meaning you would need more fuel, meaning you would need greater thrust.... you can see where I'm going with this. Importantly, escape velocity is not relevant or applicable in this example.

That's what I was thinking...

Escape velocity only applies to an object which receives all of the propulsive energy needed to escape gravity in one go, with no additional thrust - such as when firing a projectile.

Your discussion of energy requirements is beautifully clear and entirely logical. I understood that before, but I hadn't worked out its connection with an escape velocity, only its distinction from.

The escape velocity from Earth is sufficiently high (11.2 km/s) to make it unachievable due to subsequent damage from friction of the object against the Earth's atmosphere.

That's interesting. Presumably the friction decreases as the atmosphere gets thinner, so speed can increase as the rocket goes up. Have I got that right?

[Paolo]

That's interesting. Presumably the friction decreases as the atmosphere gets thinner, so speed can increase as the rocket goes up. Have I got that right?

Yup. Spot on.

I meant constant, as opposed to accelerating. (I was vaguely aware that gravity varied from place to place.)

Well, gravity is actually downward acceleration, hence the 9.81 metres per second per second. So every second the speed increases by 9.81 m/s, at least until a body reaches its terminal velocity - the speed at which friction from air resistance becomes so great that acceleration stops (and it varies according to the shape and mass of the object and it changes depending on the area facing the direction of travel). Effectively the terminal velocity would be the same thing that would prevent a projectile from reaching escape velocity.

[Nirvanam]

A question...where does the Earth end and where does space start? Have physicists defined this clearly?

[Paolo]

A question...where does the Earth end and where does space start? Have physicists defined this clearly?

Theodore von Kármán worked out that space starts at about 100km (not precisely, but close enough to make it worth rounding up to a nice memorable number). This value is partly arbitrary, since the Earth's atmosphere extends further than that, getting thinner all the time, but by the time you get to 100km the atmosphere is so thin it ceases to have much influence and to all intents and purposes you're in a vacuum that is unable to support normal aeronautical flight. It's that practical limitation that really defines space.