(SPOILERS) The reasons for the Archangel's return

SWM wrote:

Keith_w wrote:So exactly why do you think that there would be an issue with launching KEVs from orbit at a speed which would allow the KEV to depart orbit in a way that would not cause an impact with the Safehold? We don't actually know much about TF technology except that it wasn't quite up to Ghana's. We do know that the had gravity compensators for up to 400 Gs, which means that the could accelerate ships carrying humans to that speed, we don't know what speed that they could reach if they didn't have to compensate for gravity, not do we know the size of propulsive device necessary to achieve that speed. We know they had tractor beams and presumably repulsion ones as well. There is so much we don't know about TF tech that it is impossible to say that you can't do this or you can do that. Possibly based on our present level of human knowledge you can't do that (although I think that we could very easily, and I think we do when ever we send something off to a different object in our solar system), but we ain't talking about what WE can or can't do, we are talking about what the TF could or couldn't do.

But we were talking about using gravity assist. If you are using some other method to get escape velocity, you are not using gravity assist. Just as I told you several times already--if you want to get the weapon to escape velocity, you need to use some method other than gravity assist.

As for why I (I can't speak for Joat) don't think the weapon has the means to do get to escape velocity, I answered that all the way back in my first response to you. This style of system would not normally have the means to launch the weapon that fast. It's intended to drop the weapon onto the planet, using the gravity to accelerate it. Such systems don't normally need to boost the weapons as much as you are suggesting. You responded then by suggesting they could just use the planet's own gravity to boost it out. I have shown that gravity assist can't boost the weapon into interplanetary space, and I doubt that the weapon or launcher can do it either.

This style of weapon couldn't do it? You still have not said how you think this style of weapon would work, never mind why it wouldn't do what I suggested. "Dropping" a KEV onto a planet won't work work for reasons I have already mentioned, unless you don't care where it lands, Ghaba-style. As for showing that gravity assist won't work, I am pretty sure that you simply paraphrased the Wikipedia entry and waved your hands, declaring it to be a non-starter.

Keith_w wrote:This style of weapon couldn't do it? You still have not said how you think this style of weapon would work, never mind why it wouldn't do what I suggested. "Dropping" a KEV onto a planet won't work work for reasons I have already mentioned, unless you don't care where it lands, Ghaba-style.

The usual design for a weapon like this is to decelerate the weapon from orbital speed so that it falls into the planet. The deceleration could be done by a launcher in orbit or by rockets on the weapon itself. The weapon may or may not have guidance rockets to assist in final targeting. David has hinted that the weapons on the Rakurai may have guidance systems.

But, in general the purpose of the weapon is to use the gravitational potential energy of the planet to produce the energy released by the impacting weapon. If the gravitational potential energy is the primary source of energy for the impactor, the launcher or rockets only need to provide enough energy to decelerate the weapon from orbit. In that case, it would not have enough energy to boost the weapon out of orbit away from the planet.

It is certainly possible to design an orbital ballistic system with more energy. That would mean that a significant amount of the energy of the impactor would come from the launcher or rocket, in addition to the gravitational potential energy. I have not every said that it is impossible for the OBS to be designed this way. I have only said that I doubt that it is.

As for showing that gravity assist won't work, I am pretty sure that you simply paraphrased the Wikipedia entry and waved your hands, declaring it to be a non-starter.

Actually, I paraphrased the textbooks sitting next to me. And I did not wave my hands. I showed you the equation which demonstrates that the final velocity with respect to the planet is unchanged. You have not disputed that--you just don't seem to believe that this is important.

I have used the term escape velocity up to this point, because that's the term most people are comfortable with. Escape velocity is more complicated than most people realize. It is not a fixed speed--it is dependent on your altitude above the planet. The escape velocity at the Earth's surface is 11.2 km/s. If you launch a rocket at 12 km/s, it will escape the earth's gravity and fly away in interplanetary space. But as the rocket rises, it's velocity slows. At 500,000 km, it's speed with respect to the Earth will be far below 11.2 km/s. In fact, it's relative speed will approach 0.8 km/s as it gets further away from the Earth (12 km/s - 11.2 km/s). But escape velocity depends on the altitude; the rocket is still moving 0.8 km/s faster than escape velocity at that altitude.

So a more complete way of analyzing it is by examining the mechanical energy E of the rocket (or KEW, in this case). The mechanical energy is the sum of the kinetic energy K(with respect to the planet) and the gravitational potential energy U (with respect to the planet). E = K + U.

The kinetic energy is the familiar K = 1/2 mv^2. The gravitational potential energy is U = -GMm/r. Notice that the gravitational potential energy is negative! The full equation then becomes E = (1/2 mv^2) - (GMm/r).

This equation is critically important. This total mechanical energy is a constant, unless energy is added or subtracted to the system by some other source. In other words, you could change the total mechanical energy if you used a rocket, or a launcher, or some other method of transferring energy to the KEW. But if you don't use transfer energy to or from the KEW, the total mechanical energy stays the same.

Notice that the gravitational potential energy is dependent on r, the distance from the planet. Imagine a KEW in an elliptical orbit, or falling toward the planet. As the KEW gets closer to the planet, the gravitational potential energy decreases (becoming more negative). Since E is a constant, the potential energy U is transferred to K. K increases, which means it moves faster. Similarly, as the KEW moves away from the planet, the kinetic energy K is transferred to the potential energy U. An object which is in free-fall (whether rising, falling, in orbit or not) transfers energy between K and U as the altitude changes. An object in an elliptical orbit goes through a cycle, with maximum K at perigee (or periapse), and minimum K at apogee (or apoapse). But the energy E stays the same the entire time.

If the total energy E is negative, then the object is in orbit. (If the orbit intersects the planet, we would call it falling.) An astronomer would say that the object is bound. If the total energy E is positive, it is not in orbit--it will escape the planet (assuming it doesn't hit something). It is unbound. In common speech, the object has escape velocity. If the total energy is exactly E, then it has barely enough energy to escape the planet. In technical terms, the speed of the object would approach zero as the object approaches infinite distance.

Let me emphasize once again that this equation applies whether you are in orbit or not. In particular, it will still apply even when you are using a gravity assist. If the total mechanical energy E with respect to the planet is less than zero, it is trapped in orbit. You would need some other source of energy to get the object out of orbit. That energy might be rockets, or electromagnetic launcher, or solar sails, or manipulating the planet's magnetic field, or whatever. But if you do that, it is that energy source which is getting the object out of orbit, not gravity assist.

SWM wrote:..snip..
Let me emphasize once again that this equation applies whether you are in orbit or not. In particular, it will still apply even when you are using a gravity assist. If the total mechanical energy E with respect to the planet is less than zero, it is trapped in orbit. You would need some other source of energy to get the object out of orbit. That energy might be rockets, or electromagnetic launcher, or solar sails, or manipulating the planet's magnetic field, or whatever. But if you do that, it is that energy source which is getting the object out of orbit, not gravity assist.

To simplify things we can use an old physics experiments used in schools: Imagine a marble in a rice-bowl. Now make the marble move fast enough so it leaves the rice-bowl without touching the marble or moving the rice-bowl. You are allowed to drop the marble into the bowl along any point ON the edge of the bowl.

You'll quickly notice it's impossible to have the marble leave the bowl. If you on the other hand drop the marble from a height onto the inner edge the bowl the marble will due to it's increased speed leave the bowl.

There is a reason we refer to a planets gravity as a well, when you are in an energy equilibrium within it (ie. stable orbit or on the surface) you need energy to get out of it.

SWM wrote:

Keith_w wrote:This style of weapon couldn't do it? You still have not said how you think this style of weapon would work, never mind why it wouldn't do what I suggested. "Dropping" a KEV onto a planet won't work work for reasons I have already mentioned, unless you don't care where it lands, Ghaba-style.

The usual design for a weapon like this is to decelerate the weapon from orbital speed so that it falls into the planet. The deceleration could be done by a launcher in orbit or by rockets on the weapon itself. The weapon may or may not have guidance rockets to assist in final targeting. David has hinted that the weapons on the Rakurai may have guidance systems.

But, in general the purpose of the weapon is to use the gravitational potential energy of the planet to produce the energy released by the impacting weapon. If the gravitational potential energy is the primary source of energy for the impactor, the launcher or rockets only need to provide enough energy to decelerate the weapon from orbit. In that case, it would not have enough energy to boost the weapon out of orbit away from the planet.

It is certainly possible to design an orbital ballistic system with more energy. That would mean that a significant amount of the energy of the impactor would come from the launcher or rocket, in addition to the gravitational potential energy. I have not every said that it is impossible for the OBS to be designed this way. I have only said that I doubt that it is.

As for showing that gravity assist won't work, I am pretty sure that you simply paraphrased the Wikipedia entry and waved your hands, declaring it to be a non-starter.

Actually, I paraphrased the textbooks sitting next to me. And I did not wave my hands. I showed you the equation which demonstrates that the final velocity with respect to the planet is unchanged. You have not disputed that--you just don't seem to believe that this is important.

I have used the term escape velocity up to this point, because that's the term most people are comfortable with. Escape velocity is more complicated than most people realize. It is not a fixed speed--it is dependent on your altitude above the planet. The escape velocity at the Earth's surface is 11.2 km/s. If you launch a rocket at 12 km/s, it will escape the earth's gravity and fly away in interplanetary space. But as the rocket rises, it's velocity slows. At 500,000 km, it's speed with respect to the Earth will be far below 11.2 km/s. In fact, it's relative speed will approach 0.8 km/s as it gets further away from the Earth (12 km/s - 11.2 km/s). But escape velocity depends on the altitude; the rocket is still moving 0.8 km/s faster than escape velocity at that altitude.

So a more complete way of analyzing it is by examining the mechanical energy E of the rocket (or KEW, in this case). The mechanical energy is the sum of the kinetic energy K(with respect to the planet) and the gravitational potential energy U (with respect to the planet). E = K + U.

The kinetic energy is the familiar K = 1/2 mv^2. The gravitational potential energy is U = -GMm/r. Notice that the gravitational potential energy is negative! The full equation then becomes E = (1/2 mv^2) - (GMm/r).

This equation is critically important. This total mechanical energy is a constant, unless energy is added or subtracted to the system by some other source. In other words, you could change the total mechanical energy if you used a rocket, or a launcher, or some other method of transferring energy to the KEW. But if you don't use transfer energy to or from the KEW, the total mechanical energy stays the same.

Notice that the gravitational potential energy is dependent on r, the distance from the planet. Imagine a KEW in an elliptical orbit, or falling toward the planet. As the KEW gets closer to the planet, the gravitational potential energy decreases (becoming more negative). Since E is a constant, the potential energy U is transferred to K. K increases, which means it moves faster. Similarly, as the KEW moves away from the planet, the kinetic energy K is transferred to the potential energy U. An object which is in free-fall (whether rising, falling, in orbit or not) transfers energy between K and U as the altitude changes. An object in an elliptical orbit goes through a cycle, with maximum K at perigee (or periapse), and minimum K at apogee (or apoapse). But the energy E stays the same the entire time.

If the total energy E is negative, then the object is in orbit. (If the orbit intersects the planet, we would call it falling.) An astronomer would say that the object is bound. If the total energy E is positive, it is not in orbit--it will escape the planet (assuming it doesn't hit something). It is unbound. In common speech, the object has escape velocity. If the total energy is exactly E, then it has barely enough energy to escape the planet. In technical terms, the speed of the object would approach zero as the object approaches infinite distance.

Let me emphasize once again that this equation applies whether you are in orbit or not. In particular, it will still apply even when you are using a gravity assist. If the total mechanical energy E with respect to the planet is less than zero, it is trapped in orbit. You would need some other source of energy to get the object out of orbit. That energy might be rockets, or electromagnetic launcher, or solar sails, or manipulating the planet's magnetic field, or whatever. But if you do that, it is that energy source which is getting the object out of orbit, not gravity assist.

Not to belabour the point, but I really didn't start out suggesting that you could use gravity assist to depart Safeholdian orbit, I suggested that as a way of overcoming the "you cant break out of orbit" suggestion.
I suggested that it could be used to increase the velocity relative to the local stellar object, until you(?) complained that that wouldn't work either, which it will. I don't actually care that it doesn't increase its velocity relative to the object from which it is using for the gravity assist, I only care if it is increasing its velocity relative to everything else in that solar system, which it will.

This is the simplified explanation from Wikipedia:
A "stationary" observer sees a planet moving left at speed U and a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction (to the left). Since the planet is moving left at speed U, the total velocity of the spaceship relative to the observer will be the velocity of the moving planet plus the velocity of the spaceship with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.
http://en.wikipedia.org/wiki/Gravity_assist

There is an image there which might give you a clearer understanding of my point, especially if you consider the planet to be Safehold.

PS, there is a list in the article of many of the interplanetary probes which have used gravity assist, the last mentioned is the one I like the best:

"The Rosetta probe, launched in March 2004, used four gravity assist manoeuvres (including one just 250 km from the surface of Mars) to accelerate throughout the inner Solar System - enabling it to match the velocity of the 67P/Churyumov–Gerasimenko comet at their rendezvous point in August 2014."

Notice it got to within 250Km of the surface of Mars.

Joat42 wrote:

SWM wrote:..snip..
Let me emphasize once again that this equation applies whether you are in orbit or not. In particular, it will still apply even when you are using a gravity assist. If the total mechanical energy E with respect to the planet is less than zero, it is trapped in orbit. You would need some other source of energy to get the object out of orbit. That energy might be rockets, or electromagnetic launcher, or solar sails, or manipulating the planet's magnetic field, or whatever. But if you do that, it is that energy source which is getting the object out of orbit, not gravity assist.

To simplify things we can use an old physics experiments used in schools: Imagine a marble in a rice-bowl. Now make the marble move fast enough so it leaves the rice-bowl without touching the marble or moving the rice-bowl. You are allowed to drop the marble into the bowl along any point ON the edge of the bowl.

You'll quickly notice it's impossible to have the marble leave the bowl. If you on the other hand drop the marble from a height onto the inner edge the bowl the marble will due to it's increased speed leave the bowl.

There is a reason we refer to a planets gravity as a well, when you are in an energy equilibrium within it (ie. stable orbit or on the surface) you need energy to get out of it.

That's a really clever experiment Joat, what does it have to do with a KEV that is powered either externally or by some form of thruster so that it can a) be launched from an orbital platform and b) slowed so that its orbit decreases until it impacts Safehold? There's a reason for retro-rockets.

Keith_w wrote:Not to belabour the point, but I really didn't start out suggesting that you could use gravity assist to depart Safeholdian orbit, I suggested that as a way of overcoming the "you cant break out of orbit" suggestion.

Um, what exactly is the differenct from "depart Safeholdian orbit" and "break out of orbit"?

I suggested that it could be used to increase the velocity relative to the local stellar object, until you(?) complained that that wouldn't work either, which it will. I don't actually care that it doesn't increase its velocity relative to the object from which it is using for the gravity assist, I only care if it is increasing its velocity relative to everything else in that solar system, which it will.

This is the simplified explanation from Wikipedia:
A "stationary" observer sees a planet moving left at speed U and a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction (to the left). Since the planet is moving left at speed U, the total velocity of the spaceship relative to the observer will be the velocity of the moving planet plus the velocity of the spaceship with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.
http://en.wikipedia.org/wiki/Gravity_assist

There is an image there which might give you a clearer understanding of my point, especially if you consider the planet to be Safehold.

PS, there is a list in the article of many of the interplanetary probes which have used gravity assist, the last mentioned is the one I like the best:

"The Rosetta probe, launched in March 2004, used four gravity assist manoeuvres (including one just 250 km from the surface of Mars) to accelerate throughout the inner Solar System - enabling it to match the velocity of the 67P/Churyumov–Gerasimenko comet at their rendezvous point in August 2014."

Notice it got to within 250Km of the surface of Mars.

I am fully aware of the list of interplanetary probes that used gravity assist. I know several of the project scientists who worked on those probes. Notice that none of those probes used gravity assist to escape the Earth's orbit. They all used gravity assist on other planets, and they always approached that planet with a speed greater than escape velocity.

Let me show you why the velocity of the object relative to the planet matters. Imagine a satellite in orbit around the Earth with an orbital speed of 5 km/s (well below escape velocity). Sometimes it is moving in the direction opposite to the Earth's motion, sometimes it is moving in the same direction as the Earth's motion. The orbital velocity of the Earth around the Sun is 30 km/s. What is the velocity of the satellite relative to the Sun? When it is moving opposite to the Earth's motion, the velocity relative to the Sun is 25 km/s. When it is moving in the other direction, it is moving 35 km/s. The velocity of the satellite relative to the sun oscillates between 25 km/s and 35 km/s. The act of swinging around the backside of the Earth increases the velocity of the satellite with respect to the Sun--this is exactly the same thing that happens with a gravity assist. But since it does not change the speed of the satellite with respect to the Earth, the Earth's gravity will slow it down until it swings back the other way. It never gets away from the Earth--it never breaks out of orbit. And "break out of orbit" is what you say you are trying to do.

Velocity with respect to the planet you are trying to swing around is critical. Swinging around the planet is not going to give the satellite more energy with respect to the planet. If it is bound to the planet, it stays bound to the planet, unless you give it more energy from elsewhere. Swinging around the planet when you don't have enough energy to escape the planet will temporarily increase your velocity with respect to the star. And then decrease it again, in a never-ending cycle.

I think some point is missing in that calculation. Exactly - how much energy we want from the strikes? The blasts that destroyed Alexandria was on the megaton-scale, due to their cratering effect. How much velocity we need to make a megaton-size blast from the reasonable-sized projectile?

Back to the original Post

I wonder if it is some sort of futuristic "Y2K" computer reset. A thousand years in some way resets the clocks on ten Picca allowing them to live forever or something like that.

Just a random thought...

will be interesting to see what DW chooses in the end to explain the 1000 year absence of the arch angels.

Dilandu wrote:I think some point is missing in that calculation. Exactly - how much energy we want from the strikes? The blasts that destroyed Alexandria was on the megaton-scale, due to their cratering effect. How much velocity we need to make a megaton-size blast from the reasonable-sized projectile?

A 1 megaton blast is the equivalent to being hit with an object weighing ~21 kiloton traveling at 20 km/s.

You can fiddle with the figures here (Wolfram-Alpha) to get different results.

SWM wrote:

Keith_w wrote:Not to belabour the point, but I really didn't start out suggesting that you could use gravity assist to depart Safeholdian orbit, I suggested that as a way of overcoming the "you cant break out of orbit" suggestion.

Um, what exactly is the differenct from "depart Safeholdian orbit" and "break out of orbit"?

I suggested that it could be used to increase the velocity relative to the local stellar object, until you(?) complained that that wouldn't work either, which it will. I don't actually care that it doesn't increase its velocity relative to the object from which it is using for the gravity assist, I only care if it is increasing its velocity relative to everything else in that solar system, which it will.

This is the simplified explanation from Wikipedia:
A "stationary" observer sees a planet moving left at speed U and a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction (to the left). Since the planet is moving left at speed U, the total velocity of the spaceship relative to the observer will be the velocity of the moving planet plus the velocity of the spaceship with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.
http://en.wikipedia.org/wiki/Gravity_assist

There is an image there which might give you a clearer understanding of my point, especially if you consider the planet to be Safehold.

PS, there is a list in the article of many of the interplanetary probes which have used gravity assist, the last mentioned is the one I like the best:

"The Rosetta probe, launched in March 2004, used four gravity assist manoeuvres (including one just 250 km from the surface of Mars) to accelerate throughout the inner Solar System - enabling it to match the velocity of the 67P/Churyumov–Gerasimenko comet at their rendezvous point in August 2014."

Notice it got to within 250Km of the surface of Mars.

I am fully aware of the list of interplanetary probes that used gravity assist. I know several of the project scientists who worked on those probes. Notice that none of those probes used gravity assist to escape the Earth's orbit. They all used gravity assist on other planets, and they always approached that planet with a speed greater than escape velocity.

Let me show you why the velocity of the object relative to the planet matters. Imagine a satellite in orbit around the Earth with an orbital speed of 5 km/s (well below escape velocity). Sometimes it is moving in the direction opposite to the Earth's motion, sometimes it is moving in the same direction as the Earth's motion. The orbital velocity of the Earth around the Sun is 30 km/s. What is the velocity of the satellite relative to the Sun? When it is moving opposite to the Earth's motion, the velocity relative to the Sun is 25 km/s. When it is moving in the other direction, it is moving 35 km/s. The velocity of the satellite relative to the sun oscillates between 25 km/s and 35 km/s. The act of swinging around the backside of the Earth increases the velocity of the satellite with respect to the Sun--this is exactly the same thing that happens with a gravity assist. But since it does not change the speed of the satellite with respect to the Earth, the Earth's gravity will slow it down until it swings back the other way. It never gets away from the Earth--it never breaks out of orbit. And "break out of orbit" is what you say you are trying to do.

Velocity with respect to the planet you are trying to swing around is critical. Swinging around the planet is not going to give the satellite more energy with respect to the planet. If it is bound to the planet, it stays bound to the planet, unless you give it more energy from elsewhere. Swinging around the planet when you don't have enough energy to escape the planet will temporarily increase your velocity with respect to the star. And then decrease it again, in a never-ending cycle.

Why are you so hung up on the relative to the planet being used to do the G-A? Who cares about relative to the non-Safehold planet (which we don't even know if the exist)? We care about the speed relative to the local stellar object and the other objects in the local stellar neighbourhood, and if that didn't work why would we bother doing it for our own interplanetary probes?

The original suggestion was to use gravity assist a.k.a. slingshot effect around other (possibly existing) planets to use KEWs as an anti-Ghaba device. Then someone said, nono you can't do that because you can't get them out of orbit, at which time I suggested that the G-A could be used to get them out of Safeholdian orbit, and which has been your focus ever since. Fine, you can't use G-A that way. I don't think and never did think that you needed to.

It was just a suggestion and not really a very good one in the first place since the Ghaba would see them coming and get out of the way anyway.

What really surprised me was the lack of imagination shown here. This is science fiction folks. The Terran Federation had compensatory that allowed them to travel at 400Gs. Presumably they had a power source which would allow them to reach that speed, and probably more if it wasn't necessary to protect the protoplasmic objects within.