<p>Planets are visible during the day and most people will have seen Venus prior to sunset or after sunrise.</p>
<p>The calculation you are attempting is flawed because it takes no account of the bright sky background during the day. Although tbe planet may well have an angular size that is broader than atmospheric seeing, the human eye, with a pupil diameter of 3-4mm in daylight, has an angular resolution of 40 arcseconds at best. That means the &quot;pixel&quot; on your retina that contains the planet, also includes much more signal from the daytime sky, with a brightness of about 3rd magnitude <em>per square arcsecond</em>, which is only slightly fainter than the illuminated surface of the Moon.</p>
<p>Whether you can see a planet against this background is a question of knowing exactly where to look, or of increasing the angular resolution of your observation to minimise the sky background coinciding with the planet.</p>
<p>One way of doing this is indeed with a telescope or binoculars, through which, planets (certainly, Venus, Mars, Jupiter, Saturn) and bright stars are easily visible during the day.</p>

CC BY-SA 4.0
2024-11-12T21:35:17.053Z
It's not about increasing the angular resolution, it's about increasing the contrast.  A point source won't be magnified, while the background light will be spread over a larger area, so the effect of magnifying a point source is that the background gets darker.  Knowing where to look doesn't help much, obviously if you look in a random part of they sky, there are likely to be stars there, but the difference in brightness is so small your eye won't detect it.  Your eye detects brightness levels exponentially, where the added light from a star is a tiny linear increase.
Greg Miller
CC BY-SA 4.0
2024-11-12T23:50:54.497Z
@GregMiller Maybe you misunderstand. Increasing the angular resolution means that rather than, at least, a 40 arcsec diameter patch of sky competing with the planet/star, you have maybe a 3 arcsec patch, even for a modest telescope. And yes, if you know where to look you can see Venus in daylight. How do you plan to increase the contrast witbout increasing angular resolution?
ProfRob
CC BY-SA 4.0
2024-11-14T01:14:21.663Z
To "...is a question of knowing exactly where to look, or of increasing the angular resolution of your observation to minimise the sky background coinciding with the planet" perhaps a third item can be added - the degree to which you can narrow your field of view? cf. [Can an average person see stars from the bottom of a well or through cardboard tubes? Definitive answer required!](https://astronomy.stackexchange.com/q/38504/7982) (where the answer also mentions an exercise seeing Sirius from La Palma at ~2400 meters.)
uhoh
CC BY-SA 4.0
2024-11-12T07:47:45.913Z
2024-11-12T07:47:45.913Z
ProfRob
<p>Let's consider stars. They emit a certain amount of radiation. If you move 2x farther from the star, the radiation reaching you follows the inverse square law so you get 1/4 times the amount of radiation. But the angular size of the surface area of the star is reduced by a factor of 1/4, so the area that emits light has the same surface brightness, as measured by magnitudes per arcsecond squared.</p>
<p>So stars should be visible during the daytime, right, because they should be as bright as the sun as measured by surface brightness? They should have the same surface brightness no matter how far away they are, excluding effects caused by the expansion of the universe.</p>
<p>Not so. Alpha Centauri has a radius of 1.2 solar radii or 8.47 * 10<sup>8</sup> meters,
but a distance from us of 4.344 light years or 4.1 * 10<sup>16</sup> meters, so the angular diameter is about 0.0085 arcseconds. Such a point source of light is no longer a point source after Earth's atmosphere, with typical seeing conditions modifying it to have a radius of about an arcsecond, so the surface brightness after our atmosphere is not the same for Alpha Centauri and the Sun.</p>
<p>However, for planets I can't prove that they shouldn't be visible during the daytime. Consider for example Venus. It is closer to the Sun than our Moon, so it should be brighter than the Moon. However, it has a radius of 6051 km and a distance from us of 38 million kilometers (when the dimmest, when sunlight only reaches the half of the planet not visible to us) to 261 million kilometers, so the angular size should vary from 66 arcseconds to 9.6 arcseconds. The atmosphere doesn't distort much such a large circle of light. So Venus should be clearly visible during the daytime. The same can't be said for Jupiter, since it is only 3.8% as bright as the Moon due to the inverse square law.</p>
<p>But I certainly haven't observed Venus during the daytime, or Mars which should be visible too according to my theory of surface brightness.</p>
<p>So why aren't planets easily visible during the daytime, since at least the inner planets should be brighter than the Moon and Mars should be very bright too, although bit dimmer than the Moon?</p>
<p>Is it because you would need binoculars or a telescope to make what is a point source of light according to our eye, into something larger than a point?</p>

CC BY-SA 4.0
2024-11-11T17:51:09.333Z
Venus is visible during the day. If you have not seen it, then you were not looking in the proper direction. Another example is the flashing lights on an airplane at 10 km distance flying overhead should be just as easy to see during the day as they are at night? Are they?
JohnHoltz
CC BY-SA 4.0
2024-11-11T19:30:35.370Z
I don't think your surface area comparison makes sense in this context. If you move twice as far from a source of light, you're receiving 1/4 as many photons regardless of whether all those photons come from a large area or a point source.
Darth Pseudonym
CC BY-SA 4.0
2024-11-11T21:10:53.503Z
@DarthPseudonym - not in the near field. Take a 1 meter by 1 meter electroluminescent panel. Measure intensity 1 cm from the center. Now move to 2 cm from the center - the intensity will not drop to 1/4th.
Jon Custer
CC BY-SA 4.0
2024-11-11T21:50:00.177Z
Okay, I meant large like like the apparent size of the sun or moon, not large like standing directly in front of a spotlight.
Darth Pseudonym
CC BY-SA 4.0
2024-11-11T22:40:13.897Z
Venus is easy to see in daytime if you look in the right direction and focus your eyes to infinity. That isn't easy because a clear sky doesn't offer much to focus on. Another obstacle is that your eyes adjust to daytime brightness so there will be less Venusian light reaching the retina.
doubleunary
CC BY-SA 4.0
2024-11-11T23:35:25.717Z
I've seen Venus hundreds of times during daylight hours. But it's not exactly easy, due to sky brightness. See https://astronomy.stackexchange.com/q/38504/16685 & https://astronomy.stackexchange.com/q/51859/16685
PM 2Ring
CC BY-SA 4.0
2024-11-12T06:26:38.713Z
You would want to consider also the angular Resolution of your detector (eye or camera with telescope). Compare the amount of light per sensor element (Pixel) from sky and star
planetmaker
<observational-astronomy><planet><solar-system><brightness>
Why aren't planets easily visible during daytime?
juhist
# Why aren't planets easily visible during daytime?

(Asked by: username_0 on 2024-11-11)

Let's consider stars. They emit a certain amount of radiation. If you move 2x farther from the star, the radiation reaching you follows the inverse square law so you get 1/4 times the amount of radiation. But the angular size of the surface area of the star is reduced by a factor of 1/4, so the area that emits light has the same surface brightness, as measured by magnitudes per arcsecond squared.

So stars should be visible during the daytime, right, because they should be as bright as the sun as measured by surface brightness? They should have the same surface brightness no matter how far away they are, excluding effects caused by the expansion of the universe.

Not so. Alpha Centauri has a radius of 1.2 solar radii or 8.47 \* 108 meters,
but a distance from us of 4.344 light years or 4.1 \* 1016 meters, so the angular diameter is about 0.0085 arcseconds. Such a point source of light is no longer a point source after Earth's atmosphere, with typical seeing conditions modifying it to have a radius of about an arcsecond, so the surface brightness after our atmosphere is not the same for Alpha Centauri and the Sun.

However, for planets I can't prove that they shouldn't be visible during the daytime. Consider for example Venus. It is closer to the Sun than our Moon, so it should be brighter than the Moon. However, it has a radius of 6051 km and a distance from us of 38 million kilometers (when the dimmest, when sunlight only reaches the half of the planet not visible to us) to 261 million kilometers, so the angular size should vary from 66 arcseconds to 9.6 arcseconds. The atmosphere doesn't distort much such a large circle of light. So Venus should be clearly visible during the daytime. The same can't be said for Jupiter, since it is only 3.8% as bright as the Moon due to the inverse square law.

But I certainly haven't observed Venus during the daytime, or Mars which should be visible too according to my theory of surface brightness.

So why aren't planets easily visible during the daytime, since at least the inner planets should be brighter than the Moon and Mars should be very bright too, although bit dimmer than the Moon?

Is it because you would need binoculars or a telescope to make what is a point source of light according to our eye, into something larger than a point?

**Tags:** observational-astronomy, planet, solar-system, brightness

> **Comments:**
> **username_1**: Venus is visible during the day. If you have not seen it, then you were not looking in the proper direction. Another example is the flashing lights on an airplane at 10 km distance flying overhead should be just as easy to see during the day as they are at night? Are they?  
> **username_2**: I don't think your surface area comparison makes sense in this context. If you move twice as far from a source of light, you're receiving 1/4 as many photons regardless of whether all those photons come from a large area or a point source.  
> **username_3**: @username_2 - not in the near field. Take a 1 meter by 1 meter electroluminescent panel. Measure intensity 1 cm from the center. Now move to 2 cm from the center - the intensity will not drop to 1/4th.  
> **username_2**: Okay, I meant large like like the apparent size of the sun or moon, not large like standing directly in front of a spotlight.  
> **username_4**: Venus is easy to see in daytime if you look in the right direction and focus your eyes to infinity. That isn't easy because a clear sky doesn't offer much to focus on. Another obstacle is that your eyes adjust to daytime brightness so there will be less Venusian light reaching the retina.  
> **username_5**: I've seen Venus hundreds of times during daylight hours. But it's not exactly easy, due to sky brightness. See https://astronomy.stackexchange.com/q/38504/16685 & https://astronomy.stackexchange.com/q/51859/16685  
> **username_6**: You would want to consider also the angular Resolution of your detector (eye or camera with telescope). Compare the amount of light per sensor element (Pixel) from sky and star  

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## 1 answers

### Answer by username_7 on 2024-11-12. Score: 6 | Accepted answer

Planets are visible during the day and most people will have seen Venus prior to sunset or after sunrise.

The calculation you are attempting is flawed because it takes no account of the bright sky background during the day. Although tbe planet may well have an angular size that is broader than atmospheric seeing, the human eye, with a pupil diameter of 3-4mm in daylight, has an angular resolution of 40 arcseconds at best. That means the "pixel" on your retina that contains the planet, also includes much more signal from the daytime sky, with a brightness of about 3rd magnitude *per square arcsecond*, which is only slightly fainter than the illuminated surface of the Moon.

Whether you can see a planet against this background is a question of knowing exactly where to look, or of increasing the angular resolution of your observation to minimise the sky background coinciding with the planet.

One way of doing this is indeed with a telescope or binoculars, through which, planets (certainly, Venus, Mars, Jupiter, Saturn) and bright stars are easily visible during the day.

> **Comments:**
> **username_8**: It's not about increasing the angular resolution, it's about increasing the contrast.  A point source won't be magnified, while the background light will be spread over a larger area, so the effect of magnifying a point source is that the background gets darker.  Knowing where to look doesn't help much, obviously if you look in a random part of they sky, there are likely to be stars there, but the difference in brightness is so small your eye won't detect it.  Your eye detects brightness levels exponentially, where the added light from a star is a tiny linear increase.  
> **username_7**: @username_8 Maybe you misunderstand. Increasing the angular resolution means that rather than, at least, a 40 arcsec diameter patch of sky competing with the planet/star, you have maybe a 3 arcsec patch, even for a modest telescope. And yes, if you know where to look you can see Venus in daylight. How do you plan to increase the contrast witbout increasing angular resolution?  
> **username_9**: To "...is a question of knowing exactly where to look, or of increasing the angular resolution of your observation to minimise the sky background coinciding with the planet" perhaps a third item can be added - the degree to which you can narrow your field of view? cf. [Can an average person see stars from the bottom of a well or through cardboard tubes? Definitive answer required!](https://astronomy.stackexchange.com/q/38504/7982) (where the answer also mentions an exercise seeing Sirius from La Palma at ~2400 meters.)  

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