The settings menu key in No Man’s Sky on PC

There was a video here which found that it took 12 hours to walk half way across a planet, therefore it would be one day to travel the circumference.

So based on an average walking speed of 3.1 mph, it would have a 74.4 mile circumference with a 23.68 mile diameter. That's 119.04KM and 37.89 KM.

The planets do appear different sizes, but are all within a similar range.

Buy? Yes. Even if the Steam client won't let you buy the game because your OS is not supported, you can always use your browser to buy the game.

However, if you want to play the game, that is a different issue. According to Steam and GoG, these are the minimum system requirements for No Man's Sky:

MINIMUM:
OS: Windows 7/8.1/10 (64-bit versions)
Processor: Intel Core i3
Memory: 8 GB RAM
Graphics: nVidia GTX 480, AMD Radeon 7870
Storage: 10 GB available space

As you can see, OSX is not supported. So no, you can't play the game on a Mac (yet).

However, assuming your Mac is relatively modern, you can install Windows on it (using Boot Camp). Therefore you won't need a new PC to play the game.