The GURPS Basic Set has a simple rule for "hobby" skills. Skills learnt as a hobby can be purchased for half the normal amount of points, to reflect their limited usefulness in play. However, this rule only applies to skills that genuinely have limited usefulness. A character who takes a few Karate lessons in leisure time may qualify for the 50% discount in a non-combat campaign, but will certainly not qualify in a combat-heavy campaign.
Sometimes the distinction between hobby skills that qualify for the point discount and those that don't is not so easy. This can be a problem especially when the GM does not want to reveal too much of the campaign plan to the players in advance.
For example, a player designs a character for a present day campaign, with an amateur interest in Astronomy. Normally this skill is of marginal use, so would qualify for the point discount. But the GM is secretly planning to have the PCs abducted by aliens and have to navigate their way back to Earth and deal with various interstellar hazards - a situation where Astronomy becomes very useful. So does the GM let the player "get away" with a cheap skill, or spoil the campaign surprises by insisting on full cost?
This article discusses a few alternative approaches to hobby skills.
A professional astronomer has (say) Astronomy-15.
An amateur astronomer has Astronomy (Hobby)-11. With the +5 specialisation bonus, this gives the amateur an effective skill of 16 for things like aligning a 3-inch reflector to track Venus correctly, but the -1 penalty for an effective skill of 10 applies for things like remembering the important nucleosynthesis chains in stellar energy production.
This also has the effect that the amateur has invested fewer points in Astronomy, so you don't have to argue with players about whether a particular skill can be taken for half the normal point cost because it's "just a hobby". Just use the normal point costs. And if you want to know all astronomy at a level equal to the professional, but picking it up in your spare "hobby" time, you need to have Astronomy (Hobby) at one level higher than the pro's Astronomy skill, which costs more points, representing the difficulty in learning all that stuff without a structured teaching program.
Also, the hobby astronomer can, with fewer points, have a better chance of aligning her backyard telescope than a professional. This reflects the fact that amateurs and professionals have different learning priorities in their skill. A professional astronomer has little use for a backyard telescope, so could easily be less skilled in its use than a dedicated amateur.
Another example: Computer Programming (Hobby) would give the +5 specialisation bonus for things like hacking together a simple game program, but the -1 penalty for things like network programming or implementing an order (n log(n)) sorting algorithm. In fact, a dedicated hobby programmer can be better at writing games than a professional who has spent most of her programming life working on business accounting software.
A combat example: Longbow (Hobby) is good for things like archery contests - shooting at targets - but poor for shooting at live targets under combat conditions.
The one complication of this system is that the GM must decide on whether any given situation can be addressed adequately by the Hobby version of a skill, or if it requires the complete skill.
Where a professional outdoes an amateur astronomer is in Physics. Possibly also Electronics Operation (Telescopes). You need different knowledge to operate a large radiotelescope or a professional optical telescope than any backyard job. Professional observing also requires operation of detector equipment, followed by intensive data processing and analysis afterwards - Computer Operation and usually Computer Programming skills, plus Mathematics (possibly specialised in Statistics).
The difference is the amateur is operating on default, or max 1/2 to 1 point, in 4 or 5 other skills that the professional has at a competent level.