Estimating the Size of The Bre'el Moon

[Mike DiCenso]

Lately in the starship construction thread as well as the tractor beam thread the subject of "Deja Q" and the E-D's first attempt to push the Bre'el moon using her tractor beam and impulse engines was brought up. Of particular note is determining the actual size of the moon itself, which not only gives us the power expended by the E-D in providing a 92 meter a second delta-v to the moon, but also potentially weapons yeilds as the option of destroying moon also came up, but was nixed because the debris would still have largely the same overall mass, and would spread the destruction over an even wider area.

The problem with scaling the moon, at least visually, is that the whole moon is never seen, only relatively small sections with the E-D nearby. The lower end scalings of those mere sections were between 2.5 to 4.1 km. But what of the asteroid as a whole?

To answer that, it turns out through good fortune that we are given a few interesting pieces of information on the moon in the following dialog:

DATA: The satellite's trajectory is continuing to deteriorate, Captain. This orbit will put it within five hundred kilometres of the planet surface.
GARIN [on viewscreen]: We're predicting the atmospheric drag will bring it down on the next orbit.
SCIENTIST [on viewscreen]: Have you been able to find any explanation for this?
DATA: No, Doctor. It is a most unusual phenomenon.
PICARD: Won't the moon disintegrate prior to impact?
SCIENTIST [on viewscreen]: No, it has a ferrous crystalline structure and it will be able to withstand tidal forces, Captain
RIKER: Could we blow it into pieces?
DATA: The total mass of the moon would remain the same, Commander, and the impact of thousands of fragments would spread destruction over an even wider area.
PICARD: How long before impact?
DATA: Twenty nine hours, sir. Projecting it somewhere on the western continent. That would destroy an area eight hundred kilometres in radius.
SCIENTIST [on viewscreen]: That damage would be insignificant, Captain, compared to the seismic repercussions massive landquakes, and tsunami.
GARIN [on viewscreen]: The force would raise a cloud of dust around the planet, leading to a significant temperature reduction. We could be looking at our own ice age.
PICARD: Mister La Forge, is there any way that the Enterprise could coax that satellite

I've high-lighted the important information:

- The asteroid is of ferrous crystilline structure (important for tensile strength and density)

- The area of destruction would span 1,600 km in diameter (800 km radius)

- The area destroyed would be smaller than the tsunamis waves and seismic shockwaves that would reach beyond even that.

How large of an essentially solid iron asteroid would we need to create that level of destruction? Thanks to this website we can run the parameters through to see what it would take.

Assumptions: the moon is coming in at about 45 degree angle, which is common, and will hit at 17 km per second in keeping with the idea that the moon was being continually slowed by atmospheric friction with each pass at perigee. Also, because of the visual FX, the moon diameter parameters cannot be set to anything less than 5 km, and realistically by it's shape it cannot be less than 10 km. Therefore I am starting with a 10 km imput and working up to there, and that by a 800 km radius destruction zone, the Bre'eel scientist means not simply blastwave area and fireball destruction, but cratering. I also assume, since the scientists both mention an impact on the planet's western continent, that the ground zero material will be sedimentary rock, which is a reasonable compromise between the high and low end material densities.

I got the following for a 10 km asteroid of iron composition:

Transient Crater Diameter: 88.4 km = 54.9 miles
Transient Crater Depth: 31.3 km = 19.4 miles

Final Crater Diameter: 159 km = 98.9 miles
Final Crater Depth: 1.36 km = 0.845 miles

Nowhere near 1,600 km, though thermal effects and blastwave would reach you, causing potential death as well as local damage, though well-constructed buildings would still survive structurally. So 10 km still doesn't quite get us where we need to be. Ramping the moon's size to 15 km gives the following:

Transient Crater Diameter: 121 km = 75.3 miles
Transient Crater Depth: 42.9 km = 26.6 miles

Final Crater Diameter: 228 km = 141 miles
Final Crater Depth: 1.52 km = 0.941 miles
The crater formed is a complex crater.

A final crater size of 228 km. Still not big enough. Ramping the diameter to 20 km now gives us a final crater of 293 km, with thermal and blastwave effects of a leathal enough level to exposed people, though well-constructed buildings will likely survive.

We're still not at 1,600 km for a crater. Ramping up to 100 km gives us a final crater of 1,210 km. Going higher to 150 km gives us a 1,730 km wide final crater. Too big, though it is within the margins of error than one might expect. Taking the diameter down to 140 km gives us almost exactly what we need, a final crater of 1,630 km.

So the Bre'eel moon is +- 140 km. This fits in with the visual FX of a nearly sphereoidal moon, and whose surface when the E-D is close to it appears nearly flat.

Any thoughts?
-Mike

[Roondar]

Well, a few really:

1) We don't know the actual impact speed of the moon - it could be a somewhat smaller moon that impacts faster, altough not faster than 'realistic impact speeds' naturally.

2) A bigger moon only amplifies the problem I mentioned about energy requirements. Power requirements will go up really, really fast if the radius of the sphere grows (not too mention a nickel/iron asteroid would be heavier than my calcs because the thing would be denser than the granite baseline I used).

At your suggested 70 KM radius we're at insane power requirements. I mean, I like Startrek and all but I'm having a real hard time believing the E-D can channel the equivalent of over 3500 GT/Sec into it's frikking tractorbeam.

Just think about it: this is equivalent to the E-D burning up 88219 KG of antimatter (and matter) per second. That just does not make any sense whatsoever. In fact, the whole fuel-required element is what makes all the high-end tractorbeam actions (including the suggested movement of Starbase 74) highly suspect.

[Mr. Oragahn]

There are many problems here, and unknowns.

Momentum will make a difference in as how matter is moved by sheer mechanical forces, compared to a smaller impactor but with a greater speed, changing the penetration pattern and mass of matter heated up at that point of impact.

The angle of impact matters much. If it's at a low angle, we'd likely end with a lot of matter projected along the trajectory of the impactor, but not much in the opposite direction. The shape of the destructed area would be significantly different.

Besides, the chicxulub crater, often estimated at being the fruit of an impact which generated around 100 teratons of energy, is also said to have been caused by a 10 km wide asteroid.
For the note, just as a mean of comparison, a nuke of 100 teratons would have a radius which largely exceeds the radius of destruction mentionned in the dialogue.
The nuke, however, would vapourize the ground and push the atmosphere, while the impactor would, of course, vapourize a lot of matter at the point of impact, but also kick lots of matter up.
Still, this could be useful.

Pictures which could help:
http://tng.trekcore.com/gallery/thumbnails.php?album=60

http://tng.trekcore.com/gallery/albums/ ... jaq000.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq010.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq020.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq021.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq063.jpg (the planet is more distant :/)

http://tng.trekcore.com/gallery/albums/ ... jaq145.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq179.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq189.jpg (schema not to scale)

http://tng.trekcore.com/gallery/albums/ ... jaq210.jpg

http://tng.trekcore.com/gallery/albums/ ... jaq281.jpg (for the science)

We can see in the later caps that the E-D was facing the asteroid, straight ahead. So the profile view featuring the tractor beam and the E-D' portside.
http://tng.trekcore.com/gallery/albums/ ... jaq179.jpg

So you can guess the size of the asteroid. Considering that it's relatively bumpy, but certainly not perfectly spherical:

http://tng.trekcore.com/gallery/albums/ ... jaq000.jpg <- this view shows the E-D from a 3/4 angle. We see both the portside and the front of the ship, even the glowing bow of the starboard nacelle (the glowy special effect is rather grossly splattered upon the image here), so this puts us closer to the asteroid.
We can see that the visible portion of the asteroid is spherical. However, when you consider that we can make this observation, while we are closer to the asteroid than in this screencap, where the surface, at that time, appears flatter, we can conclude that the shape is not homogeneous, and as such, we're dealing with a good potato style asteroid.

Finally, considering how far the asteroid was from the planet, it's largely possible to get a full frontal impact. :)

[Mike DiCenso]

Most of those images were linked to by me in the two previous threads this one spun out of, and which I linked to above in my first posting. :-)


As for the moon's size, another possible pointer towards a large diameter and or mass is that the moon at a distance of 500 km on it's perigee made the tides rise 10 meters, and some other interesting data comes further from the two scientists:


GARIN [on viewscreen]: The tides reached ten metres on the last orbit. They are already beginning to swell again. We have a lot of frightened people down here, Captain.
PICARD: Your moon has begun moving toward its perigee. We're prepared to make our attempt.
SCIENTIST [on viewscreen]: Our population has already taken shelter, but I'm afraid no shelter will be adequate if you fail. Especially for the people on the western continent.
GARIN [on viewscreen]: Whatever the results, we know you've done your best, Picard. It's appreciated.
PICARD: We'll keep you advised, Doctor. Picard out.
WORF: Captain, sensors are picking up an increased energy output from the Calamarain.
LAFORGE [OC]: La Forge to Bridge.

Interesting in that the impact of this moon may cause such signficant damage that no shelter will be adequate. That certainly fits in with a moon of 100 km or more, and fits in with it being large enough to be sphereoidal (not a perfect sphere, but mostly so.).

Does anyone know a good way to calculate the size of a body based on it's distance and it's tidal effects?
-Mike

[Mike DiCenso]

Well, a few really:

1) We don't know the actual impact speed of the moon - it could be a somewhat smaller moon that impacts faster, altough not faster than 'realistic impact speeds' naturally.

2) A bigger moon only amplifies the problem I mentioned about energy requirements. Power requirements will go up really, really fast if the radius of the sphere grows (not too mention a nickel/iron asteroid would be heavier than my calcs because the thing would be denser than the granite baseline I used).

At your suggested 70 KM radius we're at insane power requirements. I mean, I like Startrek and all but I'm having a real hard time believing the E-D can channel the equivalent of over 3500 GT/Sec into it's frikking tractorbeam.

Just think about it: this is equivalent to the E-D burning up 88219 KG of antimatter (and matter) per second. That just does not make any sense whatsoever. In fact, the whole fuel-required element is what makes all the high-end tractorbeam actions (including the suggested movement of Starbase 74) highly suspect.

Possibly more evidence for uber-antimatter, or at least highly densified storage of fuel reactants.
-Mike

[Jedi Master Spock]

As for the moon's size, another possible pointer towards a large diameter and or mass is that the moon at a distance of 500 km on it's perigee made the tides rise 10 meters

...

Does anyone know a good way to calculate the size of a body based on it's distance and it's tidal effects?
-Mike

Well, tidal effects depend a lot on how the water is distributed. Peak water levels in certain selected locations on Earth (eastern CA) can vary by 16-17 meters.

That said, if we're assuming that this is talking about a ten meter bulge on a typical coastline bordering a very large body of water... that we can very roughly approximate.

In general, the tidal forces are going to be approximately proportionate to mr^-3, but we're much too close for that approximation to be too accurate. That would give our asteroid proportionately 218,000 times the tidal force per unit mass.

The radius of an Earthlike planet is much larger than 500 km. Numerically - throwing it into the calculator - I get only about 39% of the the above using Earth's radius + 500 km as the center-to-center distance - so we'd expect 1e18 kg of mass for tidal forces equal to that of Earth's moon. To have ten times the tidal forces - (average 54 cm tides for a water world the size of Earth orbited by our moon) - we're talking 1e19 kg, or around ten quadrillion tons - putting it in 22nd place among the moons of our system and around 18th place for asteroids.

Which, as I've pointed out, means a ridiculous amount of energy in the warp field. Ignoring everything else in the solar system, that changes the moon's gravitational potential by around ... oh... 6e26 joules. Which is a hair much, in my opinion.

We can play with the parameters a good bit, of course, but that's about what we'd be looking at.

[Mike DiCenso]

Are you sure about that, JMS? 1e19 kg puts this moon in the same size range as 16 Psyche, 324 Bamberga, and 107 Camilla. Assuming the same densities as those three asteroids, it would be around 170 to 300 km in diameter!

I hadn't been thinking it would be that big!

For another persepective, not only does it significantly up the E-D's tractor beam power requirements, but also the impulse engine, and weapons (remember that Riker suggested blowing it to pieces). Thousands of teratons here!
-Mike

[Roondar]

Except of course that if weapons yields where in the thousands of teratons region we'd see very different results of said weapons against unshielded targets than we actually do.

[Praeothmin]

Except of course that if weapons yields where in the thousands of teratons region we'd see very different results of said weapons against unshielded targets than we actually do.

Why?
SW weapons are supposed to be Giga and Teratons weapons as well, yet their effects on unshielded crafts are no different then those in ST...

[Jedi Master Spock]

Are you sure about that, JMS? 1e19 kg puts this moon in the same size range as 16 Psyche, 324 Bamberga, and 107 Camilla. Assuming the same densities as those three asteroids, it would be around 170 to 300 km in diameter!

I hadn't been thinking it would be that big!

For another persepective, not only does it significantly up the E-D's tractor beam power requirements, but also the impulse engine, and weapons (remember that Riker suggested blowing it to pieces). Thousands of teratons here!
-Mike

I don't think I made any mistakes.... however... the parameters can be fudged a bit. If we reduce the diameter of Bre'el a bit, shave its mass a little, and play with the geographic parameters (we could say as little as 3x the tidal force and still be in the range for some types of relatively normal coastlines to have 10m tides) we can tweak it by an order of magnitude without changing anything we actually observed to unreasonable values. We might even be able to squeeze out another half order of magnitude by pushing the limits.

[Who is like God arbour]

Except of course that if weapons yields where in the thousands of teratons region we'd see very different results of said weapons against unshielded targets than we actually do.

Even unshielded, a Starfleet ship is not only protected by its hull. There are also structural integrity fields, that are holding a ship together.

For example, in the episode »The Loss«, when the USS Enterprise-D was trying to break free from the influence of the two-dimensional lifeforms, it was reported, that the structural integrity field stress was exceeding 82 million kilodynes.

[Mr. Oragahn]

Except of course that if weapons yields where in the thousands of teratons region we'd see very different results of said weapons against unshielded targets than we actually do.

Why?
SW weapons are supposed to be Giga and Teratons weapons as well, yet their effects on unshielded crafts are no different then those in ST...

Because they're BS numbers. It's only supposed by some sources and some people who lost it a long time ago.

You're not going to convince anyone that these ships are capable of many gigatons of firepower considering the global averaged yields.

Besides, they were mentionning the menace due to debris, indicating a scattering, not a more than generous partial melting or vapourizing.

The most indicative element about the size of the moon is about the tidal waves, but we need to know how close to the planet the moon was the last time it passed over the oceans and raised the waters.

[Mike DiCenso]

It was expected that atmospheric drag and friction were expected to bring the asteroidal moon down on the next orbit. This means that it's perigee probably dropped down to somewhere between 60 and 200 km for that much of an effect by the planet's atmosphere on such a massive moon. This also indicates the possibility that the moon was also coming in at about a 45 degree angle is about right for the entry angle: enough for it to plow through the atmosphere, but not so shallow that it could "bounce" off back into space.

But I don't think that will bring the size of the moon down by more than an order of magnitude or so. How about it, JMS? Do things change radically by bringing down the moon's perigee by a factor of 5 or so?

As for the firepower issue, if you take an asteroid of the 170 x 300 km size range we are discussing here, and run the numbers, even just fragmenting the moon still results in high gigaton to moderate teraton firepower.
-Mike

[Jedi Master Spock]

But I don't think that will bring the size of the moon down by more than an order of magnitude or so. How about it, JMS? Do things change radically by bringing down the moon's perigee by a factor of 5 or so?

Not even that. It's a very small change in radius from Earth-radius+500 to Earth-radius+50 - general order of a 20% amplification in the total tidal forces. When your asteroid is that close to the surface, you're pretty close to the maximum magnitude tidal forces for that pair of bodies.

If the planet is smaller, that difference becomes a little more important, of course.

[Mike DiCenso]

There is nothing I know of in the episode that would indicate that Bre'el IV is anything other than an Earth-sized planet. So currently it stands that we are dealing with a moderately large asteroidal moon of 170 x 300 km.
-Mike