High current draw at start up of DC motor. How to understand if the battery can withstand it?
Car batteries have a high cold cranking current, as Neil says in his answer. 

But they are usually a poor choice for solar storage, where deep cycle or leisure batteries are preferred - they are better able to withstand deep discharge.

If leisure batteries have a CCA (cold cranking amps) rating it is likely to be lower. They should have a max current rating instead. Or, their capacity may be stated at different discharge rates such as C/10 (which would discharge them in 10 hours). C (1 hour) and 10C (6 minutes, which may only deliver half the capacity at C/10). 

C is their nominal capacity, which is often measured at a discharge rate of C/20, i.e. 5A for a 100 Ah battery.

Or the max discharge rate may be expressed as a C rate (10C) instead of a current.

Multiply this rate by the capacity to get the current.

So if you have a battery which allows 10C discharge, and you need 78A, then its capacity must be at least 7.8 Ah. And preferably several times that if you want a reasonably long battery life.