Expert: Philip A. Stahl - 11/17/2008

Question

I am not a physicist or something but still interested to know things which are not clear. Learned people’s efforts to give knowledge to the mankind is very much appreciated. Some Answers to Oblers' paradox , to me , is very complicated to understand..... My argument is ... from the surface of the moon, which is far from earth only 380,000 km, why sky is always dark - day and night ? and they say it is due to lack of atmosphere, as I understand. But when you  ask why sky is dark at night when looking from earth they will answer you with hundred different way.

And also why the side of earth which is facing the sun its sky is fully bright and other side (night time) the sky is fully dark? why we can not see glow or brightness  of other side of the earth’s sky facing the sun ? which is only 12,000 km away from us while we can see light from stars which are away from earth trillion of kilometers, although light from those stars reach us after millions of years.

Please could somebody explain this to me if my question is making sense to you. Thank you.


Answer
Hello,

Olber's paradox is generally rendered with vastly more complexity than it needs to be, using assorted expanding "shells" and so forth. To me the answer to why the sky is dark at night boils down to a few esential physical principles that require little or no embellishment or expatiation:

1- The inverse square law of light.

Perhaps the most important. This well known law of physics states that any given light source will see its apparent brightness decrease as the inverse square of the distance.

To use a prosaic example: consider a 100 watt lamp visible at a distance of 1 meter. Then if you step back to a distance of 10 meters, the apparent brightness will be reduced to:

100 w  x (1/10)^2  =   100 w (1/100) = 1 watt

in other words it will appear 100 times less bright.

Since the stars occur at vastly different distances this law also applies to them. And the more distant a star the less will be its apparent brightness relative to our location.

2- Dust, dark matter.


Many relatively bright objects are obscured from our view by dust, or by dark matter. This limits how they would normally appear to our telescopes, even Hubble.

Fritz Zwicky in 1933 actually laid the original, observational basis for dark matter. His measurements of galaxy clusters highlighted a 'missing mass'. He found that the mass needed to bind a cluster of galaxies together gravitationally was at least ten times the (estimated) apparent mass visible.

This mass, because it was inferred but not directly detectable, became the first dark matter. Around the same time there were other confirmations, based on observed stellar motions in the galactic plane, by Dutch astronomer Jan Oort. He determined there had to be at least three times the mass visibly present in order for stars not to escape the galaxy and fly off into space.

By the late 1970s, astronomers realized there were forms of matter that didn’t emit light. Among the most talked about candidates were black holes, marking the end stage of evolution for very massive stars. In the black hole, no light escapes and the mass is typically much greater than that of the Sun. One million black holes in the center of our galaxy (probably a conservative number) represents a lot of dark matter. Multiply that by billions of other galaxies, in similar scenarios, and one has an enormous store of dark matter. In fact, given the number of massive stars in our galaxy, it is likely that eventually, 90 percent or more of the stars will have collapsed into black holes, especially with currently accepted lower mass thresholds for black hole formation.

Dark matter itself occurs in either baryonic ('heavy particle' group - e.g. neutrons, protons, etc) or non-baryonic forms, depending on whether it reacts with radiation or not. If not, it's non-baryonic. This non-baryonic matter further breaks down into 'cold dark matter' and 'hot dark matter'.

The terms 'hot' and 'cold' not so much indicative of current temperatures but rather the phase of the early universe at which the particular dark matter 'decoupled'. (An earlier decoupling indicates a higher background temperature - since it's closer in time to the Big Bang).



3- The redshift of light from distant objects, e.g. galaxies.

What happens here is that the more distant an object the more its wavelengths are shifted to the red. Extreme red shifts from extremely distant objects can take portions of their visible spectrum out of view entirely. In other words, a spectral line occurring at say 656 nm is now in the infrared region, thus not as visible.

4- Expanding universe effect:

The universe as time goes on is getting less and less dense as objects recede from each other. Thus, space-time is inexorably increasing between gravitationally bound aggregates like galaxies. We now have evidence, from type 1a supernova data, that the expansion is actually accelerating.

It is believed that a phenomenon known as "dark energy" is responsible for this acceleration. Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided further evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS). (All of which you can google)

Dark energy conforms to an equation of state (cf. 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53) such that:

w = (Pressure/ energy density) = -1   = (p/ rho)


This is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'. In this case, the existence of a *negative pressure* is consistent with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts.

Specifically the term (rho + 3 p) acts as a source of gravity in general relativity, (where rho = energy density).

If we set: 0 = (rho + 3p) then:

p = - rho /3

and if: p < (-  rho /3) we have gravity that repels. This repulsion is what is believed to be driving the accelerated expansion of the universe. The accelerated expansion over time means light sources will get further and further from each other and eventually....wink out.


Now, as to your other questions:

It is not technically correct to assert or say the side of Earth not facing the Sun is "fully dark" because of the phenomenon of astronomical twilight. This means there is still some degree of light "spread" onto what is ostensibly the "night side". Typically such twilight can last up to an hour after sunset, and there is analogously a pre-dawn condition that corresponds to the former. Thus, for all intents, the "fully dark" condition only applies strictly to ~ 10/12 or ~ 5/6 of the time for the side of Earth not facing the Sun. (Of course, this is an average for the equator and times, proportions will vary over the year depending on latitude)


Re: seeing the glow from the other side of Earth (facing the Sun) you can! But you must use the Moon to do so indirectly, in a phenomenon we call "Earthshine". This answer is already getting longer than I wanted, so I will refer you here:

http://en.wikipedia.org/wiki/Earthshine


to read more about it.


You also (earlier) asked: "from the surface of the moon, which is far from earth only 380,000 km, why sky is always dark - day and night ? and they say it is due to lack of atmosphere, as I understand."

This is quite correct! The Moon's lack of any atmosphere means that there will be no scattering of light as there is on Earth, and hence only darkness, except for concentrated sunlight for the sunlit side. If Earth's atmosphere were suddenly siphoned away, the same conditions would hold as on the Moon in terms of dark sky,


"But when you  ask why sky is dark at night when looking from earth they will answer you with hundred different way."

No, not that I am aware of. Again, take note of the answers I have given and if you need further clarification you can get back to me.