The Pioneer 10 and 11 spacecraft had exceptional deep-space navigational capabilities .
The accuracies of their orbit reconstruction were limited , however , by a small , anomalous , Doppler frequency drift that can be interpreted as an acceleration of ( 8.74 \pm 1.33 ) \times 10 ^ { -8 } cm/s ^ { 2 } directed toward the Sun .
We investigate the possibility that this anomaly could be due to a drag on the spacecraft from their passing through the interplanetary medium .
Although this mechanism is an appealing one , the existing Pioneer radiometric data would require an unexpectedly high mass density of interplanetary dust for this mechanism to work .
Further , the magnitude of the density would have to be nearly constant at distances \sim 20-70 AU .
Therefore , it appears that such an explanation is very unlikely , if not ruled out .
Despite this , the measured frequency drift by itself places a directly-measured , model-independent limit of \lesssim 3 \times 10 ^ { -19 } ~ { } \mathrm { g / cm } ^ { 3 } on the mass density of interplanetary dust in the outer ( \sim 20-70 AU ) solar system .
Lower experimental limits can be placed if one presumes a model that varies with distance .
An example is the limit \lesssim 6 \times 10 ^ { -20 } ~ { } \mathrm { g / cm } ^ { 3 } obtained for the model with an axially-symmetric density distribution that falls off as the inverse of the distance .
We emphasize that the limits obtained are experimentally-measured , in situ limits .
A mission to investigate the anomaly would be able to place a better limit on the density , or perhaps even to measure it .