Astrophysics Corner, Part 6 – Hitting Space Debris at High Speed

In the soon to be published Dodecedron Books novel  provisionally titled “Kati of Terra Book 3 – Showdown on the Planet of the Slavers”, the spaceship salesperson shows Kati and her team a neat trick:

“Like all space ships, this one is equipped with a field which repels and/or destroys space debris that can damage a vessel travelling at high speeds through regular space.  On most ships its operation is automatic, outside the pilot’s control.  A ship this small, however, has a field that can be turned on and off at slow speeds, and concentrated and directed to take out larger objects, should that be necessary.  If you throw this switch here,”—she demonstrated—“these red keys can be used to do that.

“Now, under attack, a desperate pilot can slow the vessel to a crawl, lure the attacking ship within range, and direct a powerful, destructive beam at its engine, or at some other vulnerable part.  It only works on unshielded ships so don’t even dream of using it on a Torrones, or any other kind of a warship.  And you only get one shot, so it really is a last resort.  But, I have heard the stories—sometimes the final, desperate manoeuvre is what saves your neck.  Keep it in reserve, in case you need it; if you want to be good at it, it is possible to simulate the process with the computer, and practise until you can do the finger work half asleep.”

So, just how much of a problem would it be to hit space debris? Plenty actually.  The energy that a mass carries goes up linearly with the mass, but by the square of its velocity, so a fast moving object can have a lot of kinetic energy in a collision, even if the mass is relatively small.  Below is a table showing the relative kinetic energy of some well-known phenomena, compared to space vehicles colliding with dust at various speeds, including some speeds approaching c (the speed of light, often denoted by “c”, is 300,000 km/sec or 186,000 miles/sec).

For space dust, I used the Wiki result for the size of near earth orbit dust, computed the mass of an object that size with a specific gravity of2.0, then divided that by 10 for interplanetary dust, and by 100 for interstellar dust, on the assumption that the particles that have been measured from near earth space are probably larger than those in deep interplanetary and especially deep interstellar space.  The other masses and velocities are also from Wiki, or just common sense (I think we can all make pretty good estimates for baseballs).

Interestingly, the data indicates that when the space shuttle or ISS collides with a dust particle, the collision should have about the same energy as a baseball being thrown in from the outfield.  I wonder if you can hear that in the ISS?  Perhaps if well-known ISS astronaut Chris Hadfield is reading this blog he can let us know.  A larger particle, such as a bit of space junk in low Earth orbit, could obviously pose a significant problem for those space vehicles.  For example, a 1 mm metal particle could have an impact energy roughly the same as a 10 gram bullet with a muzzle velocity of 300 m/s.  Note that assumes a high relative velocity between the dust particle and the space station – if, for example the particle was travelling in the opposite direction of the ISS.

 

Object	mass (kg)	v (m/s)	v (km/hr)	v (mile/hr)	Energy (Joules)	Energy, relative to bullet
baseball	0.15	40	144	89	120	0.27
bullet	0.01	300	1,080	667	450	1.00
Small Shell	1.00	800	2,880	1,778	320,000	711.11
Howitzer	10.00	500	1,800	1,111	1,250,000	2,777.78
near earth space dust, hitting space shuttle	0.00	10,000	36,000	22,222	52	0.12
interplanetary dust, hitting Helios spacecraft	0.00	100,000	360,000	222,222	524	1.16
interstellar space dust, hitting 1% speed of light space craft	0.00	3,000,000	10,800,000	6,666,667	47,124	104.72
interstellar space dust, hitting 10% speed of light space craft	0.00	30,000,000	108,000,000	66,666,667	4,712,389	10,471.98

 

When we get to interplanetary speeds within the solar system (such as the Helios satellite, which swung around the sun at a very high velocity), the effect of hitting space dust would be that much worse.  The calculation shows that it would be like being hit by a bullet.  By the time we get to potentially achievable interstellar speeds, an impact with a dust particle would be even more substantial.  At 1% of the speed of light it would be like being hit by a small anti-tank shell, while at 10% of the speed of light it would be more energetic than a high mass, high velocity howitzer shell.

Things get worse if an object is moving at relativistic velocities, which just means that it is moving at some appreciable fraction of the speed of light (300,000 km per second or 186,000 miles per second).  That’s because as a physical object approaches the speed of light, its effective mass goes up.  In fact, as the object gets very close to the speed of light, the mass increases without bound - the function blows up, as would anything colliding with it, in a pretty spectacular fashion.  If a space ship was moving at a constant velocity at near light speed, when it hit a stationary dust particle, it would be the same as if a stationary space ship was hit by a dust particle travelling at near light speed.   A lot of energy would be exchanged in a very brief moment.  Here are a few examples of this:

·         At 10% of the speed of light, a 1kg mass would have a “relativistic mass” of 1.005 kg

·         At 50% of the speed of light, a 1kg mass would have a “relativistic mass” of 1.15 kg

·         At 75% of the speed of light, a 1kg mass would have a “relativistic mass” of 1.51 kg

·         At 90% of the speed of light, a 1kg mass would have a “relativistic mass” of 2.29 kg

·         At 99% of the speed of light, a 1kg mass would have a “relativistic mass” of 7.08 kg

·         At 99.9% of the speed of light, a 1kg mass would have a “relativistic mass” of 22.4 kg

·         At 99.99% of the speed of light, a 1kg mass would have a “relativistic mass” of 70.7 kg

At 99.9% of the speed of light, a collision with a dust particle would release tremendous kinetic energy, and this extra relativistic mass would just make things worse.

So, that pretty well finishes off the hope of interstellar travel, does it?  Well not so fast.

Within the solar system, a one week journey accelerating at 9.8 m/s (the acceleration of gravity on the Earth’s surface) would get your ship travelling at about 2% of the speed of light, and you would have covered nearly 2 billion kilometers, which would pretty nearly get you to Saturn and back.  A month of travel, with the first week accelerating to 2% of c, the next 2 weeks cruising at that speed, then the final week decelerating would allow you to cover 12 billion kilometers, which would get you nicely to Pluto and back.

If you could find an energy source to do that, travel within the solar system would be quite reasonable, rather like trans-Atlantic or trans-Pacific voyages of the late 19^th century.  Actually, it would be better, since radio communications would still be near real-time (a day or so at most).  And probably ways could be found to protect the ship from dust collisions – perhaps a multiple-hull structure, like some ocean going ships, so that if one part of the ship  takes a hit, the damage is confined to that area without losing overall ship integrity.  The affected part of the ship could then be repaired in flight.  I don’t doubt that smart engineers could come up with something to handle these contingencies.

As for interstellar travel, most SF assumes something along the lines of warp travel, as in Star Trek.  Einstein’s laws of relativity only say that an object can’t exceed the speed of light relative to “local” space-time.  Various solutions to General Relativity exist, that allow for warping of space, meaning  that effective faster than light travel might be possible.  If so, your ship wouldn’t necessarily be travelling very fast at all within its local bubble of space-time, so all these concerns about hitting objects at high speed wouldn’t come into play.

Other ideas involve worm holes or higher dimensional spaces through which the traveller passes, before dropping back into regular space.  Distances in these higher dimensional spaces are assumed to be much shorter than those in the lower dimensional space, something like how the distance between two antipodes of a sphere (D) is shorter than the great circle distance on its surface (3.14D/2).   With this shortening of distances, the “speed” through these dimensions might not have to be that high, so again, collisions with dust particles might not be a major concern (if there were dust particles in higher dimensional spaces).  Obviously this is all highly speculative, but that’s one of the reasons that SF also stands for speculative fiction.

Anyway, those are some of the escape valves that SF generally uses to get around the problem.  For the foreseeable future, Science Fiction is going to need both science and fiction, to posit long range travel.  But, after all, it’s the combination of the intellect and the imagination that gives Science Fiction its power to inspire and fascinate us.

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Kati 3 will be out in a couple of months.  You don't have to read Kati 1 and Kati 2 to enjoy Kati 3, but it's always nice to read an entire series.  You can get books 1 and 2 from Amazon or Kobo.  Kati 1 is also in print form, for those who prefer that. 

http://www.amazon.com/Kati-Terra-Book-One-ebook/dp/B00811WVXO

http://www.amazon.com/Kati-Terra-Book-Two-ebook/dp/B00D0H15CC

 

 

Amazon Top 100 Kindle Books – Exploring Reader Engagement

Recently, Amazon released lists of its 100 top selling titles for Kindle ebooks.  In some previous blogs, we looked at how Indies (self or independently published ebooks) compared to Trads (traditionally published or trade published ebooks) in terms of books sold (as measured by ranking within the top 100), reader satisfaction (as measured by Amazon reviews) and imputed revenues/earnings.  We also looked at how well sales could be estimated from reviews, via several lines of evidence.  (For more information regarding the findings from those earlier analyses, see the previous blogs  Amazon Top 100 Kindle Books - Indies versus Trads Part 1, Amazon Top 100 Kindle Books - Indies versus Trads Part 2, Amazon Top 100 Kindle Books - Indies versus Trads Part 3, and Amazon Top 100 Kindle Books - Relationship between Sales Rank and Number of Reviews.)

Note: Since this blog is a bit lengthy, I will put an “executive summary” at the front, repeating the summary remarks made at the conclusion of the blog.  So, to sum up (prematurely):

·         The top best-sellers get fewer reviews than expected, based on sales rank.  Books further down the list got more reviews than one would expect from their sales ranking.

·         Male writers were slightly more likely to be reviewed, relative to sales, but the effect was small.

·         Indies were slightly more likely to be reviewed than Trads, relative to sales, but again the effect was small.

·         Higher priced books were reviewed more often than would be expected from sales rank. The reverse was true for lower priced books.

·         Non-fiction was reviewed more often than would be expected from sales rank, but the numbers of such books were too small to be able to say whether this was meaningful.

·         Romance and Thrillers were not reviewed as much as would be expected from sales rank.  Science Fiction and Fantasy were “over-reviewed” as were the other categories.

Now for the detailed blog

In this fifth blog we continue to looks at sales rank vs number of reviews rank, in order to explore something we might call reader’s public engagement.   That won’t be a measure of sales or of number of reviews, but rather a blend of the two.  Our intent is to discover what factors might correlate with readers’ tendency tell the world about the book they just read.   Note that this measure of engagement could be either positive or negative – it is the willingness to do a review that matters more than the rating given to the book that is important here.

To this end, we will compare a books sales rank to its number of reviews rank, in the Amazon Top 100 list.  So, for example if a book was in the ranked 15^th in sales but 85^th in number of reviews, we would conclude that readers had low levels of engagement with the book – at least in the sense of engaging in a public space such as the Amazon reviews system.  They may have liked it, but they evidently weren’t motivated enough to review it.  Conversely, a book that was 85^th in sales rank, but 15^th number of reviews rank would have high engagement.   People who read it were evidently more motivated than average to write a review.  Lastly, a book whose sales rank and number of reviews rank were the same or nearly so (say ranked 50^th in both) would be considered to have average engagement.  So, given the limitation of our data, what we are measuring is relative engagement – does the book receive more or fewer reviews than would be expected from its sales rank.

Please note that the number of reviews ranking relates to ranking within that list, not the entire set of Amazon books.  But we don’t have access to those numbers, so we work with the data that we have, rather than the data that we wish we had.

So, let’s look at some data.  First, we will look at how engagement varied by sales rank, grouping the data by decile (i.e. into 10 equal sized categories).  To that end, the table below indicates that books with high sales rankings didn’t tend to receive as many reviews as we would expect ,while those with lower sales ranking received more reviews than we would expect.  For example, none of the books in the second decile of sales (ranked 11^th to 20^th) were ranked in the second decile of reviews – they were all ranked somewhere further down the list. On the table, that is indicated by the column headed “3-RevRan<SalesRank”, which shows that all ten books in this decile had review ranks less than their sales ranks.  This is further reinforced by the column “Sales Rank minus Rev Rank”, which shows that books in this decile were rated 20 places higher in sales than in reviews, on average.   Conversely, only one of the books ranked in the 9^th sales decile (81^st to 90^th rank) was in that review decile – most had review rankings higher up the list.  On average, they were rated 16 positions higher in their review rank than their sales rank.

 

Rank2	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
1	2	2	6	3.0
2			10	20.8
3	4	1	5	11.3
4	4		6	10.6
5	5		5	5.2
6	2		8	6.0
7	6		4	-7.5
8	7		3	-16.4
9	9		1	-15.9
10	9		1	-17.4

 

Next, we will look at the writer’s gender.  The table below shows that there doesn’t seem to be a very pronounced gender effect, though males do seem to be somewhat more likely to be reviewed than females, relative to their sales rank.  On average they are 9 ranks higher in reviews than sales, while females are 4 ranks lower in reviews than sales.  Note that the numbers above don’t balance – that’s because there are more women writers than men in the Amazon Top 100 list.

WriterSex	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
Female	33	1	36	3.8
Male	15	2	13	-9.0

Now, let’s look at publisher, Indie vs Trad, always an interesting category.  As the table shows, there really wasn’t any difference between Indies and Trads when it comes to this measure of reader engagement.  Indies were slightly more likely to be reviewed than one might expect from sales rank, but the effect was small – a difference of about 5 ranks.

Pub3	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
Indie	12		12	-4.8
Trad	36	3	37	1.5

And here’s a more detailed look at publishers.  There doesn’t seem to be any notable trend in this table. 

Publisher2	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
Doubleday			1	6.0
Hachette	8		11	6.7
Harlequin	1		1	6.5
Harper Collins	3		1	-18.8
Indie	12		12	-4.8
MacMillan	1			-28.0
Penguin	7	1	12	4.0
Random House	7	2	6	2.9
Simon & Schuster	8		5	-2.1
William Morrow	1			-27.0

Next up is price range, broken out as low (under $4.00), moderate ($4.00-$7.99) and high ($8.00 and over).  There does seem to be an interesting trend here – people appear to be more willing to review higher priced books than lower priced books.  Lower priced books sales ranks tended to be about 8 places higher than their review ranks.  For higher priced books, the opposite was true, and moderately priced books had sales ranks and review ranks that were almost identical, on average.  So, there may be some sort of social status effect here, whereby people are signalling their socio-economic status by reviewing higher priced books disproportionately.  Or perhaps they just feel more “invested” in a higher priced book, and thus more willing to spend a few minutes on a review.

Price2	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
1-Low	11		19	8.2
2-Mod	26	3	23	-1.7
3-High	11		7	-9.1

Now we get into the genre categories, which are usually quite interesting.  First up is fiction vs non-fiction. While it is true that most of the Amazon Top 100 ebooks were fiction, the data does seem to show and interesting effect, whereby non-fiction readers were disproportionately more likely to do reviews.  But the numbers are small, so we can only consider this to be a very provisional result.

Fict_or_NF	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
Fiction	45	2	49	0.8
Non-fiction	3	1		-19.5

Here’s a more detailed look at genre.  The main effect here is that Romance and Thrillers tend to be “under-reviewed” while the other categories are “over-reviewed”. 

Genre1	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
Business		1		0.0
Historical Fiction	2			-24.5
Humour	2			-22.5
LitFic	6	1	4	-6.3
Religion	1			-28.0
Romance	19		28	6.4
Self-help	1			-36.0
SFF	6		1	-28.6
Thriller/Suspense/Crime	11	1	16	4.4

A lot of the categories in the previous table were pretty small, so we will repeat them with the collapsed genre categories below.

Genre2	1-RevRank > SalesRank	2-RevRank = SalesRank	3-RevRank < SalesRank	Sales Rank minus Rev Rank
LitFic	6	1	4	-6.3
Other	6	1		-22.6
Romance	19		28	6.4
SFF	6		1	-28.6
Thriller/Suspense/Crime	11	1	16	4.4

Again, the outstanding feature of the data is how Romance and Thrillers don’t get as many reviews as might be expected from their sales rank. The big winner here seems to be Science Fiction and Fantasy.  Perhaps it is not surprising that they get a lot of reviews, as the readers of these categories are often well educated, literate, and confident in their communication skills.  This was also true of literary fiction, though to a smaller extent.

So, to sum up:

·         Best-sellers get fewer reviews than expected, based on sales rank.  Books further down the list got more reviews than one would expect from their sales ranking.

·         Male writers were slightly more likely to be reviewed, relative to sales, but the effect was small.

·         Indies were slightly more likely to be reviewed than Trads, relative to sales, but again the effect was small.

·         Higher priced books were reviewed more often than would be expected from sales rank. The reverse was true for lower priced books.

·         Non-fiction was reviewed more often than would be expected from sales rank, but the numbers of such books were too small to be able to say whether this was meaningful.

·         Romance and Thrillers were not reviewed as much as would be expected from sales rank.  Science Fiction and Fantasy were “over-reviewed” as were the other categories.