These pods aren't missiles or weather radars, but used for electronic warfare. They are mounted on aircraft attachments and connected to control panels in the cockpit. They are not dropped. It's difficult to determine what they are exactly made for, externally they look more or less the same.
Falcon 20 (G-FRAW) pods, in 2012, source
Falcon 20 (G-FRAR) pods, in 2010, source
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Falcon 20 pods, source
Cobham was acquired by Draken in 2020. It's a contractor in operational readiness training for UK MoD and US DoD. The pods may be in-house developed or provided by their customers. From this article:
Although the Cobham jets are civilian, they work closely with the MOD and play a major role in proceedings. They are equipped with onboard systems and special electronic warfare mission pods for radar and communications jamming, threat simulation and electronic surveillance.
As Bianfable mentioned in a now deleted answer, they can also record electronic signals during the exercise for post-exercise debriefing.
The image you included is from the 2021 Joint Warrior exercise in UK. A typical use can be found in this article, the exercise involves both Royal Air Force and Royal Navy:
An example exercise could be to provide general communications jamming before approaching the ship with two Hawk aircraft flying in close formation with a Falcon 20. The Hawks then accelerate away towards the target to simulate air launched, sea-skimming anti-ship missiles. At the same time, the Falcon uses its under wing threat emitter to simulate a specific missile’s seeker.
The aircraft is part of a fleet of 20 Dassault Falcon 20. It frequently participates to this exercise, and is also visible in this video for the 2017 edition, starting at 12:12 carrying different pods, of which one looks similar:
Falcon 20 at Glasgow Prestwick for Join Warrior 2017, source
The gray material used at both ends, and for the fins is a radome material, transparent to waves, covering receiving and transmitting antennas.
Example of pod housing the AN/ALQ-167 radar jammer:
AN/ALQ-167 radar jammer, source