Pioneers

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.