The downside was that a geocentric orbit placed the spacecraft in a more severe space environment.
As Mercury and Venus are closer to the Sun than to the earth, and move around the Sun much faster than the earth does, they have the widest variations between the geocentric and heliocentric positions.
Can you envisage how concerned you'd become if your satellite TV company started planning its coverage using a geocentric system of astronomy based on the use of Ptolemy's epicycles?
The heliocentric system opens up the possibility of aspect patterns that could never happen in the geocentric system - such as Venus in major aspect to the Sun.
The varying relationship between geocentric and heliocentric longitudes makes it difficult to calculate the exact chance of such a thing happening in any chart, but it is certainly over 95%.
Why did the heliocentric astronomical paradigm replace the geocentric one?
A few taps on the pocket calculator show that the Moon's speed in its geocentric orbit is around 2,300 miles per hour, although variable between perigee and apogee.
Moreover, angular separation rates are constant along a given small circle, and are proportional to the sine of the radius of the circle (measured as a geocentric angle from circle to pole).
Aristotle's geocentric astronomy, which attaches the heavenly bodies to a series of concentric spheres, was not his own creation.
Moreover, in geocentric astronomy there was no way of using observations to find the relative sizes of the planetary orbs; they were simply assumed to be in contact.