I don't have any special equipment.
Just a discone antenna and a SDR RSPDX.
I am using SDR Console with the satelite plugin.
So in theory I can receive from HF, VHF and UHF up to about 1200MHz
For example when NOAA-18 goes past I can receive it no problem.
As can I. But these are designed to be received by small earth stations. A discone is very wideband. I have a 137 MHz QFH antenna on my roof. It does work pretty good off-frequency.
But as you see from the antennas like the Arrow you hold in your hand and aim at ham sats. You're going to need a much more directional antenna cut for the specific frequencies you're intending on receiving.
A discone just has no gain and once you get higher up in download frequencies. You will need a "pair of binoculars" of sorts.
Leading up to a "telescope", or parabolic antenna, and tracking motors. Low noise amplifiers. Super high quality cable in short runs.
It gets.....fun.
Inmarsat is easy to receive. But in the L Band. A Discone just won't do it. In my recent delving into NOAAPORT on C band. I'm lucky to have a steerable big ugly dish that has been carefully upgraded.
By the way. I'm using a Nooelec LANA low noise amplifier. It has no filtering and covers a wide frequency range. And brings in those NOAA & Meteor sats in very well. I use another one like it for Inmarsat.
If you're lucky you can even catch rogue sats that have failed, are tumbling, etc. And there are beacon decoders out there to display a bit of information from them on a pc.
If you search the right terms for those fuzzy sats you're looking to receive. You will find the downlink frequencies.
But remember also that orbiting satellites sometimes have their radios shut down except in range of the receiving ground stations.
Such in the case of Chinese satellites. The NOAA JPSS leo sats with downlinks in the S, X, Ka bands. You're going to need some specialized receiving equipment to even know that they are up there.
Here's a cool site: