Sunday, September 16, 2007


The Pioneer spacecraft gave us a first glimpse from the outer Solar System. Pioneer 10 was launched March 3, 1972 and encountered Jupiter in December 1973. Its last weak signal was received in 2003, as it headed for interstellar Space. Pioneer 11, launched April 6, 1973; flew by Jupiter in December 1974. This spacecraft then used the Jupiter's gravitational field to slingshot toward a Saturn encounter on September 1, 1979. Last communication with Pioneer 11 was in November, 1995. The two spacecraft are headed in different directions--Pioneer 10 toward Aldebaran and Pioneer 11 toward the constellation Aquila. They carry the famous plaque designed by Carl Sagan. Signals from the Solar System's outer reaches led to the mysterious Pioneer anomaly.

According to radio Doppler data, both Pioneers show a constant sunward acceleration of 8.74 x 10^{-10} meters per second-squared. Interest is slowly growing in this anomaly. Possible sources of systematic error have been accounted for and the acceleration is still there. Presently the archived data is being examined even closer to see if this effect is really sunward or Earth-centred. An error is still possible, so resolution of this issue may have to await better data. Though Voyager 1 has ventured further, that spacecraft is not spin-stabilised and can not corroborate the anomaly. Data from another Space mission may be needed.

For this article we will assume that the effect is real. The problem can be simply explained by inferring that "dark" mass in the Solar System is affecting Pioneer. Data from these spacecraft could indicate density of this mass and how it is distributed. The most important clue is that the acceleration appears to be constant. Gravitational acceleration a is:

a = GM r^{-2}

If mass were distributed spherically, as in the galaxy, mass distribution would be given by: M = $4 \pi \rho$/3 r^{3}. Acceleration a would then be a multiple of r and not constant. If mass were distributed in a disk, we would have:

M = $4 \pi \rho$r^{2}

Now the "r's" cancel out and we have constant acceleration:

a = $4 \pi G \rho $

We can quickly find the density of this mass distribution:

$\rho $= a/$4 \pi G$ = (8.74 x 10^{-10})/[$4 \pi $ (6.67 x 10^{-11})]

$\rho $= 1.04 kg per square meter

Such a disk-shaped mass distribution is not out of the question, since humans know very little about the outer Solar System. Observations of the visible planets and a few probes like Pioneer provide the only data. Recently we have discovered that Pluto is just one of many planet-like objects outside Neptune's orbit. There is far more out there than meets the eye.

We can consider the possibility of primordial Black Holes. The typical mass of such objects is about 10^{12} kg. That is approximately the mass of Uluru (Ayers Rock) in a volume smaller than a proton! We would have approximately one such object per area of 1 million square kilometres. This is about one Uluru mass per area the size of Australia.

Would a Pioneer in the outer Solar System be likely to encounter a Black Hole? Though it is visible for many kilometres, one can spend an entire lifetime in Australia and never see Uluru. A Black Hole's gravitational influence is actually quite small--if you were just 2.6 metres from a 10^{12} kg Black Hole, you would feel no more gravitational pull than you feel at Earth's surface. You could wander an Australia-sized area for a lifetime, and the probability of falling into a Black Hole's influence would be less than the chance of stumbling into Hugh Jackman's bedroom!

If an unseen disk of Black Holes exists, they would not add significantly to the Solar System mass. If this distribution were extended into our neighbourhood, dark mass within Earth's orbit would be only 3.2 x 10^{23} kg. That is negligible compared to the known mass. Earth alone has a mass of 5.98 x 10^{24} kg, and the Sun has a mass over 10^{30} kg. Since Black Holes would be so difficult to find, only the effect of the entire distribution can be detected by Pioneer.

A distribution of "dark mass" is just one idea. Interest in the Pioneer Anomaly has led to many other theories including modified gravity and even changes in the speed of light. (Where have we heard about varying c before?) At present a systematic error is still a possibility. The anomaly is still a fascinating mystery that may point to new physics.

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Blogger Kea said...

Wonderful post! This is certainly a fascinating subject, and you continue to be an inspiring pioneer. I was a small child in the early 70s, and I remember it as an optimistic time, when space was at everybody's doorstep and yet we were somehow still far away from troubles in other parts of the world.

2:37 PM  
Blogger L. Riofrio said...

Thank you again. In Australia and New Zealand one can still find that pioneer spirit of optimism. In the mountains of NZ one must feel very close to nature. I hope that a new generation discovers the wonder of going to the Moon and planets.

7:04 PM  
Blogger Нетурей Карта said...

I think in the spherical universe mass density ro should dependent on r.
"According to the theory of Newton,the number of "lines of forces" which come from infinity and terminate in a mass m is proportional to the mass m.If on the average,the mass density ro is constant throughout universe,then a sphere of a volume V will enclose the average mass ro * V.Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to po * V.For unit area of the surface of the sphere the number of lines which enter the sphere is thus proportional to ro * V/F or ro * R.Hence the intensity of field at the surface would ultimately become infinite with increasing radius R of the sphere,which is impossible."

Albert Einstein, "Relativity: The Special and General Theory"

7:08 AM  
Blogger tristan said...

Hello Ms Riofrio
We sat next to each other for a couple of hours yesterday (at the freezing cold Variety), but didn't quite get to meet! I would love to have shaken your hand and chatted with you. I had to dash out right after the event, and your sandwich looked quite engrossing.

There is a new production out at the Magic Theater which you absolutely must see. Check their website It's a really unusual staging of a play which chronicles the experiences of the ISS crew while they were stranded after the Columbia disintegrated. Here is an interview with the playwright on video podcast:

The W Foundation is also displaying a large collection of space mission artifacts on the ground floor of the theater. The display includes Russian and American pressure suits, satellite components, all kinds of goodies.

I wish that we could have spoken at the Variety. Maybe I will run into you there again. Or maybe at the Magic!

6:30 PM  
Blogger Chris Reed said...

Forgive this theory from a physics layman but I’ve always wondered if the answer to the Pioneer anomaly is much simpler: Drag.

We know space is not really “empty,” especially in our solar system. There are plenty of hydrogen and other protons to go around, as well as other particles (let alone what we don’t know about the properties of dark matter). Is it possible that over the vast distance it has traveled, Pioneer 10 simply got dragged down slightly by these particles?

If not, I wonder if this Pioneer anomaly could also explain the wobbles of Uranus and Neptune that was never satisfied with the discovery of Pluto?

5:30 AM  
Blogger L. Riofrio said...

For Chris: Drag is an idea that should be examined too. Pull from a disk of dark stuff could be considered a big drag too. Now we know that Pluto is just one of many large objects out there, which could affect Uranus and Neptune orbits.

3:27 PM  
Anonymous Anonymous said...

Please write anything else!

9:18 AM  
Blogger L. Riofrio said...


(Added February 10, 2009 by the cat. She likes the posts.)

5:03 PM  

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