Exactly how many hours are in an orbital year?
The number of hours in an orbital year depends on the length of the year, which varies depending on the planet or astronomical object in question. An orbital year is the time it takes for an object to complete one orbit around its star.

For example, on Earth, the length of an orbital year is approximately 365.24 days, or 8,766 hours. However, this value is not exact and can vary slightly due to various factors, such as the gravitational pull of the moon and other planets.

On Mars, an orbital year is approximately 687 Earth days, or 16,466 hours. Meanwhile, on Jupiter, an orbital year is approximately 4,332 Earth days, or 103,968 hours.

So the number of hours in an orbital year varies depending on the length of the year of the astronomical object in question.
How is it possible that the hours don't match the exact number of hours in our calendar? I mean  $24 \cdot 365$  should be the total amount of hours in an orbital year by definition of hour, isn't it?
The number of hours in a year is actually not exactly 24 times 365. This is because the Earth's orbit around the Sun is not exactly 365 days long - it's actually about 365.24 days long. To account for this, we have leap years with an extra day (February 29th) added to the calendar year every four years.

However, even with this adjustment, the length of the tropical year (which is the time it takes for the Earth to complete one orbit around the Sun as measured by the position of the Sun in the sky) is actually slightly less than 365.24 days, and so additional adjustments are made to the calendar over longer periods of time to keep it in sync with the tropical year. For example, every 100 years, we skip a leap year unless the year is evenly divisible by 400 (so the year 2000 was a leap year, but 1900 and 2100 were not). This helps to keep the calendar year length more closely aligned with the length of the tropical year.