Searched for options for my 2 small scopes and found that Lithium ion were "better".
They cost less and the output does not drop as much after time. They both drop and so expect say around 11.5 maybe 11 volts.
Big problem is cost. A large capacity battery costs a lot. One that appeared in a search here says 12v 100Ah and £778, about $1000. Although I expect lesser cost ones as in other searches I have found Shido 4Ah motor cycle batteries range from £38 to £70.
As your 17Ah lasted 3 hours how long do you want one to go for ? Overnight say 8 hours?
Lithium will discharge for longer and still be usable. Think you can discharge to around 80%. They do not self discharge by a lot and anyway it reads that you will be regularily charging and using whatever.
I use 2 Li batteries and have been happy with them. Never had a problem charging and never detected any heating or warming of the batteries.
Lithium ion batteries do age, they say 500-1000 charge cycles then the efficency drops off. Just that if used regularily that could be say 3 years, likely more with the general weather. But a point.
The size is the question, at a guess you want around 60Ah - bit that is a guess only. Equally equipment seems to get added continuouly.
I would suggest looking at a replacement car battery in Lithium form. Half the reason is they seem to have circuitry to use a standard car battery charger.
May need to identify the construction as LiFePO run at 3.2v so for 12v the battery need a bank of 4. Li-ion run at 3.6-3.7v so 4 in parallel give 14.2v at startup. Just wonder if some try 3 banks and so fall a bit short in voltage terms.
The above came up and looks fairly balanced.
Could you run a protected mains supply to the observatory?
Is charging by mains or by solar?