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# Absolute magnitude of a light bulb

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### #1 EricSi

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Posted 11 June 2021 - 12:56 AM

For my fellow nerds who might find this amusing:

The output of the sun is 3.82 x 10^26 Watts, so 3.82 x 10^24 times as much as a 100 Watt light bulb.

Magnitudes are based on the fifth root of 100, or (10^2)^.2 = 10^0.4.

Therefore for a brightness ratio of r, the difference in magnitudes m is given by 10^(0.4 x m) = r, or m = 2.5 log r.

Thus, in this case m = 2.5 x (24 + log 3.82) = 2.5 x (24.58) = 61.46.

Since the absolute magnitude of the sun is 4.83, the magnitude of a 100 Watt light bulb at a distance of 10 parsecs is 61.46 + 4.83 = 66.29.

Only 35 magnitudes too faint to be seen by the Hubble!

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### #2 Dynan

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Posted 11 June 2021 - 01:11 AM

You, Eric, are amazingly intelligent...and certainly have too much time on your hands.

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### #3 Sleep Deprived

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Posted 11 June 2021 - 01:25 AM

Yeah, but how many angels can fit on the head of a pin?

### #4 MillHey

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Posted 11 June 2021 - 03:47 AM

Hi Eric,  so how close would the Hubble have to get to be able to see it?

### #5 chrysalis

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Posted 11 June 2021 - 03:55 AM

For my fellow nerds who might find this amusing:

The output of the sun is 3.82 x 10^26 Watts, so 3.82 x 10^24 times as much as a 100 Watt light bulb.

Magnitudes are based on the fifth root of 100, or (10^2)^.2 = 10^0.4.

Therefore for a brightness ratio of r, the difference in magnitudes m is given by 10^(0.4 x m) = r, or m = 2.5 log r.

Thus, in this case m = 2.5 x (24 + log 3.82) = 2.5 x (24.58) = 61.46.

Since the absolute magnitude of the sun is 4.83, the magnitude of a 100 Watt light bulb at a distance of 10 parsecs is 61.46 + 4.83 = 66.29.

Only 35 magnitudes too faint to be seen by the Hubble!

An interesting further exercise would be this:

Calculate the light bulb wattage equivalent to that of sunlight falling on the earth's surface. Then extend that to the surface of Pluto - in order to get a good feel of what the lighting power of the Sun would be from 2.48 billion miles.

This would provide a realistic visual impression of the Sun not at magnitude -26.9 but at (whatever the apparent magnitude of the Sun is as seen from Pluto).

And for more fun - determine the ratio between that and the appearance of the ground on  Earth during a Full Moon at it's highest.

### #6 Tony Flanders

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Posted 11 June 2021 - 06:15 AM

Since the absolute magnitude of the sun is 4.83, the magnitude of a 100 Watt light bulb at a distance of 10 parsecs is 61.46 + 4.83 = 66.29.

Only 35 magnitudes too faint to be seen by the Hubble!

Which means that at 1 parsec the bulb would appear 100 times brighter: mag 61.29, and 30 magnitudes (a factor of 100^(30/5) = 10^-12) too faint for Hubble.

From which we conclude that the maximum distance at which the Hubble Space Telescope can see a 100-watt light bulb is one millionth of a parsec, which works out to 0.2 a.u., or 30,000,000 km.

So when Venus is closest to Earth, the Hubble would be able to see a 200-watt light bulb on Venus, but not a 100-watt light bulb. Ignoring the fact that Hubble would likely be permanently damaged by pointing so close to the Sun.

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### #7 EricSi

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Posted 11 June 2021 - 01:27 PM

An interesting further exercise would be this:

Calculate the light bulb wattage equivalent to that of sunlight falling on the earth's surface. Then extend that to the surface of Pluto - in order to get a good feel of what the lighting power of the Sun would be from 2.48 billion miles.

This would provide a realistic visual impression of the Sun not at magnitude -26.9 but at (whatever the apparent magnitude of the Sun is as seen from Pluto).

And for more fun - determine the ratio between that and the appearance of the ground on  Earth during a Full Moon at it's highest.

Pluto's orbit is at an average distance of about 40 AU, so the sun would be 1,600 times fainter than it is here (2.5 log 1600 = 8.01 magnitudes, making it -18.9). That's brighter than I would have expected.

The full moon is about 400,000 times fainter than the sun is here (magnitude -12.7).

So even from Pluto you would have a pretty bright but tiny (roughly 40" or 45") source of light.

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### #8 chrysalis

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Posted 11 June 2021 - 01:36 PM

Pluto's orbit is at an average distance of about 40 AU, so the sun would be 1,600 times fainter than it is here (2.5 log 1600 = 8.01 magnitudes, making it -18.9). That's brighter than I would have expected.

The full moon is about 400,000 times fainter than the sun is here (magnitude -12.7).

So even from Pluto you would have a pretty bright but tiny (roughly 40" or 45") source of light.

So can you equate the luminance of the Sun at -18.9 with an approximate earthly lighting condition? 1/1600th of the sun's light shed onto the earth's surface would approximate what: a cloudy day? A cloudy day at sunset or afterward? Dusk? Wonder if this correlation is possible. I'm sure it could be done (somehow) in terms of lumens/square meter, but that just provides a number, not a real-world example so we in the audience can perceive it and experience an "Aha!" moment...

### #9 Mister T

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Posted 11 June 2021 - 04:58 PM

For my fellow nerds who might find this amusing:

The output of the sun is 3.82 x 10^26 Watts, so 3.82 x 10^24 times as much as a 100 Watt light bulb.

Magnitudes are based on the fifth root of 100, or (10^2)^.2 = 10^0.4.

Therefore for a brightness ratio of r, the difference in magnitudes m is given by 10^(0.4 x m) = r, or m = 2.5 log r.

Thus, in this case m = 2.5 x (24 + log 3.82) = 2.5 x (24.58) = 61.46.

Since the absolute magnitude of the sun is 4.83, the magnitude of a 100 Watt light bulb at a distance of 10 parsecs is 61.46 + 4.83 = 66.29.

Only 35 magnitudes too faint to be seen by the Hubble!

That is why you should use LEDs!

### #10 KBHornblower

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Posted 11 June 2021 - 08:53 PM

So can you equate the luminance of the Sun at -18.9 with an approximate earthly lighting condition? 1/1600th of the sun's light shed onto the earth's surface would approximate what: a cloudy day? A cloudy day at sunset or afterward? Dusk? Wonder if this correlation is possible. I'm sure it could be done (somehow) in terms of lumens/square meter, but that just provides a number, not a real-world example so we in the audience can perceive it and experience an "Aha!" moment...

The light level from the Sun at Pluto is similar to that of ordinary indoor household lighting at night.

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### #11 spacemunkee

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Posted 13 June 2021 - 05:17 PM

Now if we can just find those light bulbs on another planet... Those horrible 7k LED's should stand out pretty well!

https://www.scientif...-other-planets/

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