# What is Earth's apparent magnitude from geosynchronous orbit?

How bright is a "full Earth" from geosynchronous altitude (22,200 mi) and would it be dangerous to look at a full Earth for too long from that distance without wearing a dimmed visor?

• I think astronomy.stackexchange.com would be a more likely place to give you the answer.
– SF.
Commented Oct 9, 2023 at 9:07
• Practically speaking: if it's safe to look at the earth from zero miles away, then it should be safe to look at it from any greater distance. (With a possible exception for the reflection of the Sun off of the oceans). Commented Oct 10, 2023 at 15:31
• @RBarryYoung Isn't it safe to look at the Sun from just above its surface? (assuming you wear some futuristic heat-protective suit) Commented Oct 10, 2023 at 16:45
• @Hannes I wouldn't think so. Commented Oct 10, 2023 at 16:54
• Are you using binoculars / telescope at all? Commented Oct 11, 2023 at 12:00

Interesting question!

tl;dr mag -22 maximum, no particular danger except UV because it's still quite a large extended source (not concentrated to a point).

Easy part first:

### Surface brightness for extended (resolved) objects

...and would it be dangerous to look at a full Earth for too long from that distance without wearing a dimmed visor?

It certainly can't be any brighter than it is when you are standing on it looking down!

If I'm hiking I'm looking down a lot, if the surface is rocky it's pretty bright and except for the UV (that can eventually cause Cataracts if I'm not wearing special near-UV absorbing glasses/sunglasses)) I think it's considered safe1,2.

Imagine the following experiment. Walk up to a painted wall of a solid color (white for example) until you're say 50 cm away, not close enough that you make a shadow. Now walk backwards. Does the wall get dimmer? No. While the light from any given square cm reaching your iris does drop as $$1/r^2$$, the number of square centimeters of wall that illuminates a given patch on your retina increases as $$r^2$$.

So to first order, the Earth's apparent average surface brightness is the same whether you are standing at it looking at your feet, or you are in GEO.

This continues to be true until the apparent size of the Earth is so small that it's better described as a point source like a star.

Going even further away, the apparent brightness now starts dropping as $$1/r^2$$ because the whole Earth is contributing to a fixed-size patch of retina, defined by the resolution of your eye (diffraction plus real-world imperfections and other effects)

What is Earth's apparent magnitude from geosynchronous orbit?

Wikipedia's Absolute_magnitude; Solar System bodies (H) gives Earth's maximum absolute magnitude $$H$$ as about -4. That's averaged over the various types of surfaces and assuming full illumination (you're looking at it from the Sun's direction - full-on.

The apparent magnitude is then (assuming maximum illumination):

$$m = H + 5 \log_{10}\left( \frac{d_{ES} \ d_{EO}}{1 \ \text{AU}^2}\right)$$

Here $$d_{ES}$$ is the distance between the Earth and the Sun in AU, so basically 1, and $$d_{EO}$$ is the distance from the Earth to the observer, which is between 0.00024 and 0.00028 AU since we're so close that the sub-satellite point is closer than the terminator by >6000 km. Let's use 0.00026 AU.

$$m = -4 + 5 \log_{10} \left( \frac{1 \times 0.00026}{1^2} \right) \approx -22$$

The fully illuminated Earth can have an apparent magnitude of -22 which is not as bright as the Sun behind you at -29, and a lot brighter than the full Moon seen from Earth's surface at -13 or the Earth seen from the Moon at -18.

However, it's spread out over a huge ~17° diameter circle "like a big pizza pie" while the much brighter Sun fills only ~0.5°. So as mentioned earlier, the surface appears no brighter on average than it does while you're standing on it.

The Sun on the other hand is not only 14x brighter, it packs that into an area 1100x smaller on your retina. So you're definitely in danger when looking at the Sun.

Imagine being in a dark room looking out a round window at a bright reflective landscape on a sunny day.

The difference is that if you look away you'll see pitch black until your eyes accommodate, then if you look again at the window it will look momentarily pretty bright until your eyes "get used to it" again.

However if you turn around 180 degrees you'll be looking directly at the Sun (in this example) so be prepared for that (visor, etc.)

1Of course the brightest surface on Earth is snow, and people take extra precautions (looking through narrow slits or dark glasses) to avoid snow blindness = Photokeratitis

Photokeratitis or ultraviolet keratitis is a painful eye condition caused by exposure of insufficiently protected eyes to the ultraviolet (UV) rays from either natural (e.g. intense sunlight) or artificial (e.g. the electric arc during welding) sources. Photokeratitis is akin to a sunburn of the cornea and conjunctiva.

Bright visible light can also be uncomfortable, and if intense enough can start bleaching the photoabsorbing molecules in our retina. There is also this: Has extended exposure to sunlight and UV in the arctic or antarctic ever caused someone's eyes to change color?

2At least in my case, if I'm hiking on a rocky surface and I'm not looking down a lot, it's considered unsafe! :-)

• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Space Exploration Meta, or in Space Exploration Chat. Comments continuing discussion may be removed. Commented Oct 12, 2023 at 15:44