Completley OT : How can a measurement be this precise ?

Buzby

Senior Member
From the BBC science website, regarding the Cassini mission to Saturn : http://www.bbc.co.uk/news/science-environment-39701671

The intention of this penultimate phase of Cassini's mission is to measure the weight of Saturn's rings, by monitoring the change in velocity as the craft moves between the planet and the rings.

"We're able to tell the velocity of Cassini to an accuracy of a few microns per second. This is indeed fantastic when you think Cassini is more than one billion kilometres away from the Earth."
Cassini will be travelling at a speed greater than 110,000km/h ( 68,000 mph ! ) when the measurements are made, at a billion kilometres from Earth.

How is this done ?.

I'm in awe !.

Buzby
 

westaust55

Moderator
At a real guess, using Doppler effect on radio transmissions while passing through the zones. ?:confused:

Do you know which PICAXE chip are they using :)
 

oracacle

Senior Member
everything exerts a gravitational force, so by measuring the change of speed (ie acceleration in either a positive or negative aspect)
we know the gravitational constant, as a result my guess would be
F= G*Mm/R^2
where:
F = force
G = Gravitational constant
M = mass 1 (ie cassini)
m = mass 2 (ie the rings)
R = distance between the centres of masses

combined with F = ma, they know how much cassini weighs, they will be able to measure the acceleration is gyros and accelerometers, which will give the force being excreted on cassini during entry and exit of the rings, then rearrange and solve for "m" in the above equation.

just a bit of a guess though, that said I don't know if the craft has object detectors of some description for navigating the belts - they will most likely give accurate velocity reading which acceleration can be calculated from giving the "a" of F=ma
 

Buzby

Senior Member
Hi oracacle,

I vaguely understand that lots of force/mass/velocity/gravity calculations will give the answer, but what device can measure "... a few microns per second."

And what about the range of values these calculations need to handle ?. Billions of tons on one side and a few Kg on the other.

Regarding the actual calculations, I think it will use two. One to find the acceleration due to Saturn's pull, and the other for the opposite pull from the rings.
The first calculation will give an acceleration, but the actual accelerometer will read 'low' due to the rings pull, so the second calc uses the difference to find the mass of the rings. ( It's basically what I did in my 'A' level, but that was a long time ago.)

As for navigating the belts, I got the impression it was all pre-programmed from now on, not performed on-the-fly. ( Cassini has almost no fuel left, just enough to change the last orbit into a crash course. )

Newton would proud !.

I'm just amazed !.
 

oracacle

Senior Member
I assumed that it had been navigating the rings up to this point by itself, or at least mapping them to some point. being so far away mean that some form of independent object avoidance would be needed in such a cluttered area of space.
its has quite a suite of sensors as it turns out, it has radar so westys though about Doppler shift may well be spot on. along side that it has a fair amount of optical sensors, the same affect can be measured in light wave lengths (its how IR and laser speed camera work).

IRC speed camera send 43 pulses of IR light in a tiny fraction of second to obtain the speed, so a few micros in a second should not an issue with optical sensors

linky: https://saturn.jpl.nasa.gov/mission/spacecraft/cassini-orbiter/
 

AllyCat

Senior Member
Hi,

IMHO it's not going to be an "instantaneous" measurement and the article says that it will be out of radio contact for almost a day after the pass. My guess is that the "secret" is in the 22 Highly Elliptical orbits before September, shown in one of the diagrams. That makes the orbital period around 1 week, or over half a million seconds; so can the orbital period be measured to within a few seconds? A characteristic of HE Orbits is that the speed drops very considerably at the furthest distance from the planet (when much of the Kinetic Energy has been converted to Potential Energy) which will help to "magnify" the relative speed change.

I don't know if the craft has a radio transponder that would allow a "time of flight" (distance) measurement from Earth, which might be to microsecond or even ns accuracy. But even if not, doppler shift of the radio signals might be able to identify the point of minimum orbital speed to within a few seconds. Of course Microwave communications have wavelengths of only a few cms.

An interesting fact on BBC radio just this week, is that NASA use PI calculated to only 15 decimal places (64 bit floating point?), but that still allows them to calculate the cicumference of a circle to within a few cms, having a radius equal to the current range of the Voyager spacecraft. One has been travelling for 40 years (since 1977), currently at a speed of 17 km (11 miles) per second.

Cheers, Alan.
 

Goeytex

Senior Member
My Take,

The modern scientific community cannot get consistent measurements of "Big G". They never have. The official value of G has changed many times over the years and the official value assigned in 2010 was based upon an average of measurements around the world. However, 2013 measurements by scientists from International Bureau of Weights and Measures showed G to be 240 parts per million greater than the 2010 Official Value. Not sure what it is today. Either they do not know how to measure it, or it actually fluctuates and is not a true constant and may be affected by (Dark Matter, Dark Energy, Plasma Currents, Birkeland Currents or whatever the latest new theoretical force is currently most popular. Seems the only thing that is constant about G is that it constantly changes.

I highly doubt that an accuracy of a "few microns per second" is even possible. However I do not doubt that these Cassini guys actually believe they can do it.
 

srnet

Senior Member
At a real guess, using Doppler effect on radio transmissions while passing through the zones. ?:confused:

Do you know which PICAXE chip are they using :)
As far as I am aware only two PIXAXEs have gone into space. One has gone silent, the other burnt up.
 

rossko57

Senior Member
they know how much cassini weighs
Slap wrist! How much it * masses * ... ;)

I don't suppose they do know that within a few grams - how much dust has it picked up, any debris leftover from separation of parent rocket or Huygens probe, how much fuel left.
Their primary instrument is a radar ranger for mapping detail, I would guess they can range off Titan as well as Saturn and get speed/distance data as good as claimed, over time. Gotta have a good clock on board!
 
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