The planets the handbook addressed — Mars and Venus — were not missions that were imminent in the early 1960s.

The first successful interplanetary mission, Mariner 2’s flyby of Venus, happened in 1962.

The first successful Mars flyby, Mariner 4, happened in 1965.

Actual Mars landing missions were decades in the future.

The handbook was mathematical preparation for engineering futures that were real but not yet achievable.

That is, in fact, how the most important technical preparation tends to work.

You do not wait until you need the mathematics to develop the mathematics.