Skip to main content

Spacecraft Flyby Anomolies

I ran into the sources for today's post while searching for the answer to a great question posed by +Bruce Elliott regarding yesterday's post[1] about flux pinning and stable superconductor levitation.  Bruce's question was:
"...Of course, like any good post, it leads to more questions. So here's my next one: I would think that since the the induced currents resist any change to the magnetic field, that they would have an effect analogous to friction, i.e. any attempt to change the position of the conductor (or magnet) would be similar to moving an object through a very viscous fluid - hard to do, but once done, the object stays put in the new position.
What we see in the NASA video, however, is that when the levitating magnet is poked, it oscillates slightly. This looks more like the motion of an object in a potential well, like a mass on a spring. This suggests that the superconductor "remembers" the equilibrium position (and the corresponding magnetic field flux) and that the induced currents continually direct the magnet back to that position. Why would the currents not maintain the new position, like a rock being pushed through mud?..."
I don't have a solid answer yet, because I got sidetracked looking for some of the source material for the answer.  Before I take us down the sidetrack though, let me explain very briefly the answers I'm trying to track down regarding flux pinning.  First, pinning and pinning strength vary with the construction of the superconductor.  If a ceramic YBCO superconductor is made from rather loosely packed material, or if there are a lot of defects, then there are lots of sites in the material where magnetic field can penetrate and get pinned.  The superconductor in the video that Bruce mentions[2]

was very large and very porous, so it's easy to 'pin' a magnet to it.  Flux pinning sites are easily formed.  On the other hand, if the same type of superconductor is made from a single crystal domain, then there are far fewer pinning sites due to defects, and it's actually very difficult to levitate a magnet over it unless the magnet is placed there before the superconductor is cooled, allowing the magnetic flux lines to penetrate while the material is not in its superconducting state.  You can see this kind of behavior in the following reserach video from Cornell.

The difficulty with which magnetic field can penetrate the superconductor is overcome by suspending the magnet above the superconductor while it is being cooled.

Two more points and I'll get to the sidetrack of the day.  The first point is that suspended magnets can move quite easily as long as the magnetic field in the path they move is constant.  This leads to things like the train track demo shown in yesterday's post.  The second point is that there is a potential well, much like Bruce mentioned, formed as a result of pinning.  Cornell researcher +Joseph Shoer discusses both of these things in an excellent poster presentation.

Now, for the sidetrack.  While looking for more videos of Cornell's supercondcutor research, I came across a paper about several spacecraft flyby anomalies that have been recorded since 1990[5][8].  Basically, while tracking various spacecraft including the Galileo and Cassini missions it was discovered that the resultant speed of the spacecraft after passing by the Earth to modify its orbit, was a few mm/s faster or slower than was expected.  These aren't huge differences mind you since the spacecraft speed was on the order of km/s. None the less, there's not a solidly known reason as to why this is happening yet.  One commentator from the European Space Agency has offered some perspective as to the cause of the anomoly  in Nature's news column circa 2008[6]:
"Trevor Morley, an engineer at the European Space Agency's (ESA) operations centre in Darmstadt, Germany, notes that the trajectories of spacecraft flybys are calculated using detailed models that must incorporate a lot of phenomena, including the pull of other planets, relativistic effects (changes in time and length for objects travelling near the speed of light), and even the radiation pressure of sunlight striking the craft. One of these may be incorrectly accounted for, or there may be an effect missing from the equations entirely."
That hasn't stopped a number of articles from being written studying the data and hyptohesizing that the cause might be anythign from Lorentz forces acting on electrically charged spacecraft, to dark matter to gravitational anomalies [7][9].  The last referenced paper is from Dr. Nieto who I mentioned a few weeks ago in reference to coherent states, quantum mechanical phase operators and the Pioneer anomaly[10][11].

1.  Yesterday's post

2.  Video of NASA superconductor

3.  Cornell superconductor levitation video

4.  Poster presentation

5.  Atchison and Peck paper

6.  Nature on the anomaly

7.  Dark Matter and anomalies
Adler S. (2009). Can the flyby anomaly be attributed to earth-bound dark matter?, Physical Review D, 79 (2) DOI: 

8.  PRL article on the anomalies
Anderson J., Campbell J., Ekelund J., Ellis J. & Jordan J. (2008). Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth, Physical Review Letters, 100 (9) DOI:

9.  Nieto on graviton and photon mass limits
Goldhaber A.S. & Nieto M.M. (2010). Photon and graviton mass limits, Reviews of Modern Physics, 82 (1) 939-979. DOI:

10.  Nieto post

11.  Nieto post


Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr. 

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…