I responded with The Most Common Delta V error. High school seniors typically mispatch conics the same way Murphy does. Murphy's level of expertise is somewhere below Orbital Mechanics 101 for liberal arts majors.
Stasse passed this on to Tom Murphy. And got a reply. Stasse quotes Murphy:
I don't dispute the more careful approach used on hopsblog. I put pieces together very simply, which may not represent more clever ways to manage interplanetary trajectories. That said, I stated clearly what I was doing, so that it's an easy job to pick it apart. I'm fine with that. I hope I never appealed to my authority as an orbital mechanics expert, because I am not.By his own admission, Murphy's no expert. Perhaps Murphy hasn't appealed to his authority. But Stasse and his friends certainly have. Murphy goes on:
I just try to put scales on things and sort out roughly how hard things are. At the pace of a post a week (during that time)--on top of a busy job--I could not spend time polishing. 15 km/s (allowing a bit of rounding) is still frikin' hard, so my main point is barely scratched.Murphy's point isn't merely scratched, it's gored. 15 km/s is about what it takes to put a geosynchronous communication satellite in place. This is doable as demonstrated by the large number of geosynchronous sats. Murphy's 20 km/s is about what it takes to land on the moon's surface and come back. 15 km/s and 20 km/s are vastly different delta V budgets.
But 15 km/s vs 20 km/s is isn't the worst Murphy error. He's done much worse. From Grab That Asteroid! in Murphy's Stranded Resources post:
The asteroid belt is over 20 km/s away in terms of velocity impulse. If the goal is to use the raw materials for production on Earth or in Earth orbit, we have to supply about 10 km/s of impulse. We would probably try to get lucky and find a nickel-metal asteroid in an unusual orbit requiring substantially less energy to reel it in. So let's say we can find something requiring only 5 km/s of delta-v. . . .
To get this asteroid moving at 5 km/s with conventional rocket fuel (or any "fuel" that involves spitting the mass elements/ions out at high speed) would require a mass of fuel approximately twice that of the asteroid. As an example, using methane and oxygen, . . .
Does fetching an asteroid take twice the rock's mass in propellent?
Ratio of propellent to dry mass can be found with Tsiolkovsky's rocket equation:
(Mass propellent)/(dry mass) = e(delta V/exhaust velocity) - 1
Let's see -- in Murphy's example delta V is 5 km/s. Exhaust velocity of oxygen and methane is about 3.4 km/s.
e(5 km/s / 3.4 km/s) - 1 = 3.35. So for every ton of asteroid, we'd need more than 3 tons of propellent. At first glance it looks like Murphy is being kind and even under estimating propellent needed.
But methane and oxygen isn't the only propellent. Xenon from an ion engine has an exhaust velocity of around 30 km/s.
e(5 km/s / 30 km/s) - 1 = .18
So about .2 tonnes (or 200 kilograms) of propellent to park a tonne of asteroid. 2/10 is not a "rough approximation" of 2.
But Murphy's error gets worse.
Murphy thinks we'd be lucky to find an asteroid outside of the Main Belt that takes 5 km/s to retrieve. Evidently he hasn't heard of Near Earth Asteroids. There are many asteroids that take much less.
The Keck study for retrieving an asteroid notes some asteroids take as little as .17 km/s. Let's plug in .17 km/s delta V:
e(.17 km/s / 30 km/s) - 1 = .006
So 6 kilograms of propellent to park a tonne of Asteroid. Now Murphy's guesstimate of twice the asteroid's mass is off by a factor of about 350.
Six kilograms is about the mass of two chihuahuas. Two tons is about the mass of two large horses, big horses as in Budweiser clydesdales.
Tom Murphy is a busy guy. So he uses furious handwaving to excuse info that's completely wrong.
Murphy's figures are often off by several orders of magnitude his PhD notwithstanding.
Neither Stasse's appeal to authority nor Murphy's "rough approximation" defense salvage Murphy's arguments.
ReplyDeleteFirstly, you have slightly misunderstood the appeal to authority fallacy which is ‘if an expert says something, then it must be true’. This is a fallacy because obviously an expert can still be wrong, however it is widely accepted that even though an authority can be wrong they still have a higher chance of being right than someone with an unknown level of knowledge. So while Murphy is not an expert on orbital mechanics, a physicist may still have a good reason for not discussing the xenon ion thrusters which you bring up to try to disprove the point. At the point you have shown you know more than Murphy about orbital mechanics, which I believe you have now done, then I am committing the fallacy if I keep suggesting he knows better than you.
Now, a discussion on Ion thrusters.
Ion thrusters have extremely low thrusts as stated on , on the order of a few newtons for the most powerful thrusters. I’ll be nice and assume we use the experimental VASIMR thruster (which uses argon), being BY FAR the most powerful ion thruster available (though it has never yet been used on a mission). VASIMR can produce ~5 Newtons of thrust, but doing so requires 200kW of power, more than twice the 84kW maximum ISS currently produces. To rendezvous with an asteroid using such low thrust is no joke, but if you do you can accelerate a 1 tonne asteroid at (F = ma -> a = F/m = 5 / 1000) = 0.005 m/s^2 or about 5E-4 g. To change an asteroids velocity by .17 km/s would require thrusting for (dV/a = 170/0.005) = 34000 seconds or about 10.5 hours, during which time the asteroid may have moved out of the area for the most efficient ‘burn’, increasing the real delta V cost. Remember how VASIMR uses so much power? The current design spec calls for trickle charging a battery so it can be used for 15 minutes at a time, to power the drive would require either an enormous solar array or a nuclear reactor, both greatly increasing the cost and weight of the vessel and increasing fuel requirements while decreasing available (excess) thrust. For every asteroid you capture this way you still need to launch the fuel from earth using chemical rockets for the initial 10 or so km/s delta V to LEO, and all this only allows you to retrieve the smallest and slowest asteroids.
Can we retrieve a few asteroids? Probably. Can we sustain ourselves on asteroid mining indefinitely? Very doubtful.
The proposed Keck vehicle would 40 kW of power (page 6 of the report).
ReplyDeleteThe first resource Planetary Resources hopes to mine is water. Propellent high on the slopes of earth's gravity well eliminates the initial 10 km/s you mention. Spacecraft could come and go from the earth-moon neighborhood without having to repeatedly ascend/descend a deep gravity well.
If it takes twice the asteroid's mass for retrieval, obviously propellent from an asteroid is a nonstarter. But happily Murphy's rough approximation is wrong.
Sadly VASIMR is bogus,
ReplyDeleteIn Capturing Near-Earth Asteroids around Earth, Hasnain, Lamb and Ross examined whether low thrust ion engines can impart the needed delta V within plausible time frames.
ReplyDeleteOne thing to keep in mind is that heliocentric orbits in our neighborhood have a much lower angular velocity than low earth orbits. A low earth orbit will make a 360º circuit in 90 minutes -- an angular velocity of 4 degrees per minute. A near earth asteroid with an earth like orbit will make a 360º orbit in about a year -- an angular velocity of about 1 degree per day.