Back to the Flyby Anomalies

Ah, the flyby anomaly. I had a lot of fun with that back in 2008 and maybe the game is not yet finished. Spacecraft Earth flybys are used by NASA to save on fuel. If they want to get a probe to Jupiter for example, but don't want to launch the heavy fuel needed, then what they do is launch the probe slow, loop it round another planet and bring it in behind Earth in its orbit, and the Earth then pulls the spacecraft forward and transfers some kinetic energy to it. An analogous method was used by Marty McFly in Back to the Future: he hitched a skateboard ride by holding onto a car. These flyby spacecraft are monitored as they zoom past the Earth and in 1990 the Galileo probe gained 4 mm/s of speed more than it should have. This was not a lot given the actually heliocentric (relative to the Sun) speed of 31 km/s, but well outside the uncertainty. This also happened for a few other flybys as well, the largest anomaly being for the NEAR (Near Earth Asteroid Rendezvous) probe which gained 14 mm/s speed from apparently nowhere. Anderson et al. (2008) collected all the data together and showed something that got me very excited at the time: there was a pattern. Spacecraft that came in at the equator, and left nearer the spin axis (the pole), sped up more!

After a lot of thinking and calculation I managed to show that MiHsC predicts something like this. When a spaceship comes in at the equator the mutual accelerations between it and typical masses inside the spinning Earth are big because the acceleration vectors are often along the same line (the Earth mass accelerates towards the spin axis, the craft also towards that axis). So MiHsC predicts the Unruh radiation seen has a short wavelength and fewer waves are disallowed by the Hubble-scale Casimir effect, so the inertial mass is close to the normal mass. Conversely, when the craft exits at the pole, the mutual acceleration between it and the masses in the Earth is smaller since the acceleration vectors are now perpendicular, so MiHsC predicts longer Unruh waves, more of which are disallowed by the Hubble edge, and the craft loses inertia slightly. To conserve momentum it has to speed up. Calculations show that this does a pretty good, but not perfect, job of predicting the flybys without any adjustable parameters (see my paper below). The way I derived this result is not perfect though, since I have not yet calculated the 'total' mutual acceleration including the spacecraft's own acceleration, and this I need to do. For this I could use the brilliant NASA Horizons web-interface, that I've used before, and where spacecraft trajectories are available for free. http://ssd.jpl.nasa.gov/horizons.cgi

What reminded me of the flybys was a recent article, in the Spanish SINC website (see SINC reference below) which piqued my interest by saying that "One of the last [flybys] was that of the spacecraft Juno in October 2013, from Earth en route to Jupiter. NASA has not yet published data on this journey, but everything indicates that its speed as it flew over our planet was once again different to estimates". This was news to me because I pestered ESA and NASA last year and they told me there was no Juno anomaly. It's probable that the comment in the recent article was based more on expectation than evidence, but ESA/NASA have not yet published anything formally on the Juno flyby. MiHsC predicts a small positive anomaly (but as I said before I don't yet consider the motion of the spacecraft itself, which needs trajectory modelling). Time to do some fortran programming..

References

Antreasian P.G. and J.R. Guinn, 1998. Paper no 98-4287 presented at the AIAA/AAAS Astrodynamics specialist conference and exhibition, Boston.

Anderson J.D., J.K. Campbell, J.E. Ekelund, J. Ellis, J. Jordan, 2008. Phys. Rev. Letts., 100, 091102.

McCulloch, M.E., 2008. Modelling the flyby anomalies using a modification of inertia. Mon. Not. Royal. Astro. Soc., Letters, 389 (1), L57-60. Link to pdf

SINC: http://www.agenciasinc.es/en/News/An-anomaly-in-satellites-flybys-confounds-scientists

EmDrives & MiHsC

It's a gamble, but I think it's important to focus on anomalous experimental results since the new stuff always comes from there so I thought it would be useful to recap what I have been thinking about regarding Shawyer's EmDrive results. You should bear in mind that this is an example of me wildly playing around with ideas and I may decide tomorrow it is wrong. So, just to remind you that the EmDrive is a cone-shaped microwave resonant cavity, like a microwave oven built into a megaphone. When microwaves are resonated in there, it has been shown by Roger Shawyer, also a Chinese group and recently a NASA group that a small anomalous force is produced and the cavity moves towards its narrow end. This apparent violation of the conservation of momentum has not been explained.

To explain it, I've assumed the following: the microwaves bouncing around within the cavity have inertial mass (em radiation does: that's why it can push a Solar sail) and their inertia is determined by MiHsC (quantised inertia). In MiHsC the Unruh waves are allowed only if they fit exactly within the Hubble horizon or within a local Rindler horizon, but what if the cavity wall in this case was acting like a horizon? Well, then the microwaves at the wide end would have more inertia than those at the narrow end since more Unruh waves would fit. This means that as a microwave beam goes from the narrow end to the wide end it gains inertial mass. Now I can try something I've used before (for the Tajmar effect) and say, in order to still conserve momentum (mass*velocity) for the whole system, if mass goes up then velocity must go down, and the only way to achieve that is to have the whole structure move towards the narrow end.

I've done the calculation using MiHsC for Shawyer's EmDrive assuming an input power of 850W, a frequency of 2.45GHz and a Q factor (number of times the waves bounce before dissipating) of 5900 and I predict a force of 12.75mN, close to the 16 mN they saw.

Again, do take this in the spirit of 'playfulness'. There are huge questions: How can I throw out the rule book on photons like a hippy on LSD, and then insist on conserving momentum like an accountant with OCD? It could be a just a coincidence that it works, but it is interesting. Comments welcome!