Rising-Star8471 asked:

Given the numbers from the previous posts, does anyone have
any idea what the mass of an unseen object would have to be
to cause the speed discrepincy?

The mass depends on its distance from Pioneer. A larger
mass would be farther away; a smaller one would be closer.
But the mass would have to be fairly small or it would
affect other bodies in the Solar System. It doesn't.
Also, since the effect on the spacecraft was constant for
more than a decade, the masses would have to be following
the spacecraft at a constant distance behind them. The
masses would have to be approximately in line between the
Earth and the spacecraft, a short distance behind them.
And since the Pioneers were slowing down, in order to
maintain a constant distance, the masses would have to
be slowing down, too.

-- Jeff, in Minneapolis