What is the maximum viable F-Ratio for a Telescope used to find planetary nebula?

As with all questions in this field, the answer is not so simple.

Both F-ratio and aperture matter.

For a fixed area of sky, increasing the aperture gathers more light regardless of F-ratio. In this case, all the smaller (faster) F-ratio is doing is concentrating that light on a smaller area, essentially improving SNR at the cost of image scale.

Conversely, keeping aperture constant and decreasing F-ratio (such as by using a reducer or simply using a scope of smaller focal length) gathers light from a larger area of sky. This can be useful if your object is large in angular size, since you are gathering more light from it simply by covering a larger area.

For a small, dim planetary nebula, the most important parameter will be aperture. It will fit in the FOV of most reasonable setups and the game is basically to capture as much light from it as you can. This can only be achieved by increasing aperture or integration time. Remember that, so long as the object fits in the FOV, the image scale can be changed by binning, which will be exactly the same as changing the f/ratio at constant aperture. 

For a larger extended object such as the OIII nebular around M31, a faster scope can help. A large aperture f/10 SCT will certainly gather more light from a small, specific area of that nebula than a fast refractor, but the object is so large that it will not be very useful.

George M.:
The maximum f-ratio for detecting a weak unknown planetary nebula in the sky would depend on various factors, including the size and brightness of the nebula, the sensitivity of the observer's eyes or the camera used, and the atmospheric conditions. However, as a general guideline, a larger f-ratio generally results in a narrower field of view but increased image contrast, which can aid in detecting faint objects.In the case of the discovery of the OIII nebula around Andromeda, it was first detected using narrowband imaging techniques that filter out light from other sources and highlight the specific wavelengths emitted by the nebula. While a slow scope like an f/7 refractor or even an f/10 SCT system can be used for this type of imaging, it would likely require longer exposure times or stacking multiple images to achieve the necessary sensitivity to detect such a faint object.Therefore, the choice of f-ratio would depend on a variety of factors, including the specific characteristics of the target object, the observer's equipment and experience, and the observing conditions.

Thank you, ChatGPT.

George M.:
The maximum f-ratio for detecting a weak unknown planetary nebula in the sky would depend on various factors, including the size and brightness of the nebula, the sensitivity of the observer's eyes or the camera used, and the atmospheric conditions. However, as a general guideline, a larger f-ratio generally results in a narrower field of view but increased image contrast, which can aid in detecting faint objects.In the case of the discovery of the OIII nebula around Andromeda, it was first detected using narrowband imaging techniques that filter out light from other sources and highlight the specific wavelengths emitted by the nebula. While a slow scope like an f/7 refractor or even an f/10 SCT system can be used for this type of imaging, it would likely require longer exposure times or stacking multiple images to achieve the necessary sensitivity to detect such a faint object.Therefore, the choice of f-ratio would depend on a variety of factors, including the specific characteristics of the target object, the observer's equipment and experience, and the observing conditions.

Ps:Answer given by ChatGPT