The Great Carina Nebula in viewing range of a planet

How close should a planet be to the Great Carina Nebula for it's inhabitants to look up and see this in the night sky? I'm aware much of the sharpness of the view would be lost due to the atmosphere, but let's say you were on this hypothetical planet (and I'm assuming you can see the falcon shape in the image) and if you put up your hand and it measured exactly the length of your index finger from falcon-head to falcon-tail?

How close is your planet to the nebula?

• This question has been asked in many forms in the past 9 months. Up close, a nebula would appear either as a pale whitish cloud or as nothing. These spectacular photos are created with long exposures and good processing (chemical or computer). Commented Sep 22, 2018 at 5:06
• Ah, okay. Thanks for clearing that up. I assumed that given the right conditions, there would be a planet surface in the universe where nebula could be a significant visual treat in the night sky.
– Moin
Commented Sep 22, 2018 at 5:26
• Actually, Morin, you're not wrong. While we do enhance images to better see what we can, many nebula would be amazing to see "up close." But "up close" isn't all there is. In many cases, light doesn't shine on nebulas in a way to light them up, but that shouldn't stop you from building a story where one has been. But, for your answer, the cross-section of the nebula visible to the planet must be known. After that, it's just trig to figure out how far away it must be. (Maybe light it from behind.... That way the stars aren't in the way.)
– JBH
Commented Sep 22, 2018 at 5:37
• @JBH Thanks a ton!. Not only was your answer helpful, it also gave me a few new ideas.
– Moin
Commented Sep 22, 2018 at 10:52

According to Wikipedia,the Great Carina Nebula is approximately 230 light years in radius. The formula for angular distance (how much of the night sky would be taken up) is : $$angle = atan( distance_{opposite} / distance_{adjacent} )$$. That gives you an answer in radians, which you must multiply by ($$180 \over 3.141..$$) to get the value in degrees.