Let's first eliminate some reasons:
If you have a receiving antenna which is permanently outdoors, then you may want grounding for lightning protection. This is a substantial topic of its own which I am not qualified to describe briefly here. This is largely a separate topic from grounding for RF purposes, though some of the design principles are useful in both cases.
Some types of antennas, deliberately or accidentally, have connections to ground as part of their functional structure. Directional, rotatable antennas such as Yagi, log periodic, or dish antennas, as you would use for satellite work, do not.
There are reasons for grounding applicable here: electrical safety and RFI. Electrical safety is not specific to this application; the usual rules apply, and we'll assume that your line voltage power supplies are properly grounded and everything else (your computer, radio, antenna rotator...) is low-voltage.
That leaves RFI (radio frequency interference). We need to think about grounding and shielding. The purpose of shielding is to prevent noise from entering sensitive circuits or leaving noisy ones. The purpose of grounding is to allow noise which is flowing on some (shield/ground) conductor to preferentially flow to earth rather than into your receiving equipment.
In theory, a receiver does not need a ground at all: if the entire system is enclosed in an impermeable shield, with appropriate filtering at power, antenna, and received-signal-out ports, then grounding has no effect whatsoever.
In practice, anything you can do to reduce the noise power around by redirecting it to earth via a ground connection may be useful.
Caveat: your ground connection needs to not have the effect of conducting noise from a noisy component to a quiet one, which can happen if you wire grounds in daisy-chain fashion rather than separate wiring to a single ground bus/plane/chassis. It's also possible for the ground wiring to end up acting as an antenna for other noise; this is reduced by keeping it as short as possible.
Finally, grounding is useful not only for your receiver but also for other electronic equipment which may be producing noise that would interfere with reception. Of course, you can also “just” shut off that equipment while receiving, which is an easier option for initial troubleshooting.