Measuring Solar Power: Newsletter Challenge (08/14/07)

Earth's rotation has slowed and the day is longer?

yes rotation has slowed making jun20th the longest day of sunlight

Earth's orbit is an ellipse so could it be that the point where 20^th June falls is getting closer to the Sun over the 10000 years?

The variation is caused by the changing distance of the Earth from the sun.

The Earth's aphelion (maximum distance from the sun) currently occurs around July 4th. There are a few days short-term wobble in this date, so the change will not be continuously in one direction. However, over the 10,000 year timescale, there are in principle two effects:
First, the Earth's orbit will be becoming less elliptical (more circular), so the maximum distance from the sun will reduce.
Second, there is a systematic variation in the date of the aphelion. But this will be about 7 minutes of arc over this period, which is considerably less than a day.

So my answer is that the reason is that around June 20th the distance between the Sun and the Earth is at its maximum, but that maximum will become closer to average over the coming 10,000 years, as the Earth's orbit becomes more circular. However, the decrease in distance will not be steady as implied, because the date of the perihelion varies by a few days; as June 20th is not actually at the perihelion, the short-term increases due to the timing variation will exceed the effects of general reduction in ellipticity (which is also not monotonic, also due to planetary interactions).

Fyz

3Doug pointed out that every time I wrote perihelion above, I meant aphelion. Apologies.

For those postulating that the quesion is about total energy rather than average power, the increase in day length is very small; orbital differences have much larger effects.

BTW, I was wondering why the puzzle setter chose 20th June rather than July 4th. Perhaps he didn't want to make the answer too obvious? (Or perhaps the setter was concerned about getting too near the date of the Earth's passage through the "invariable plane"?)

Fyz

Could a more likely effect be due to Earth's precession (Milankovitch cycles)? If the Earth is at a 23.4 deg tilt now (ranging from about 21.5 to 24.5 deg) and the cycle is about 41,000 years, AND IF (and I'm guessing re the current point & direction in the cycle) the Earth (or N. Hemispher) will be getting warmer due to the axis shift .... could that be a or the primary factor in the satellite's measurement?

I think the reason for picking June 20th is that it is (or is near to) the Summer Solstice. Over 10,000 years, the reckoning of dates becomes a bit vague -- but the Summer Solstice is a phenomenon of the Earth-Sun geometry. So (I think) the date is meant to imply that the measurement occurs when the Earth is near the Summer Solstice. (Summer Solstice for the northern hemisphere; of course since the satellite is in an equatorial orbit the energy detected is not affected by seasons per se.) The assumption is that dates are related to the seasons, not the position of the Earth along its orbit. If the date is taken to be the position of the Earth along its orbit, then there would be no difference in measured energy since the Earth-Sun distance would always be the same for the same 'date'.

At the present time the Summer Solstice occurs when the Earth is near aphelion. In 10,000 years the Summer Solstice will occur near perihelion, due to the precession of the equinoxes (i.e., due to the precession of the Earth's axis).

So the increase in detected energy is, as a number of responders have suggested, due to the Earth - and the satellite - being closer to the Sun.

Yes, distance from sun was agreed. I'd missed that 20 June was synchronised to Northern hemisphere midsummer, so the rotation of the axis meant that the Earth would be closer to the perihelion (the nearest point of its orbit to the sun). Curiously, the expected reduction in orbital Ellipticity would have been sufficient to ensure an increase - but the effect of being at the nearest point is of course much greater. (I had said this elsewhere - pity I couldn't go back and add it so it ties closely to my original inadequate contribution)

The seasons are caused by the tilt of the earth's axis, not by the ellipticity of its orbit. The Earth is actually closest to the sun during northern *winter* .

In case (as appears to be the case) you missed this: that is part of what we are saying. The other parts are that in 10 000 years time mid-summer will be quite close to the time of closest approach, and the reason is a combination of change in the orientation of the tilt of the Earth's axis, and movement of the axis of the ellipse that defines the Earth's orbit; the final note on that is that the calendar has been defined so that midsummer remains approximately at June 21st (though, if it remains unmodified, the present leap-year plan means that the date will move a few days over the period)

Just a wild guess - could it be that the Earth the Sun are drifting further apart as the gravitational pull between the 2 masses gets lesser, due to the mass of the Sun getting lighter (burning over the 10,000 year)?

The post states 'incident radiation', not reflected radiation, so it cannot be anything to do with the Earth as a body. It has something to do with its orbit around the Sun. The incident has gone up, the emitted is the same, so the radius has decreased. Hmmmmmmm. OK, let's grab one: the Earth's orbit has decayed over the last 10,000 years and it is now closer to the Sun, caused possibly by the effect of the Earth passing through the Solar Wind, which slows its orbital velocity. So there.

Good thinking that it's the orbit - although "incident radiation" may only mean not-reflected off the moon; in other words the question does not state that it couldn't be due to refraction and reflection off the Earth. however, we have to assume that the questioner doesn't have that much foresight into the Earth's long-term climate change...

Now to detail: solar wind applies a steady outward force - but that is already taken into account in the Earth's orbit. Tidal forces in the in-orbital-plane component of the sun's rotation will tend long-term to move the Earth's orbit away from the sun, but the effect is very small over this sort of period (but larger than any slowing due to lateral interaction with the solar wind - in fact, light enough objects can be accelerated away from the sun by the solar wind). I think we are only left with ellipticity - which is thought to be predictable over this period.

Fyz

Oh well, never mind.

Good thinking that it's the orbit ?

Incident solar power for a day...

The 'day' is getting longer by approx 1 sec every 18 moths according to some estimates.

Longer day=more radiation per day.

So why does it have to be the orbit?

Incident solar power, in terms of watts per square metre of surface, or incident solar energy, which is the integration of that power over a day which, as suggested, is increasing in length. Hmmmmmmm. OK. What about that irritating geostationary satellite? Is its orbital period redicing by the same amount?

Dicing with what, I wonder? If the day is getting longer, the orbital radius would have to increase - unless the Earth gets somehow lighter in the meantime. However, unless something knocks a massive chunk of the surface in the meantime, the effect would still be negligible compared with the that of the Earth's orbit around the sun.

Oh well, never mind.

Sorry for the 'typo': reducing and increasing came out at the same time.

Good observation - power and energy are not the same. Unfortunately, the question introduces a conflict of terms in the phrase: "amount of solar power measured...".

"Amount" is a word that properly applies to integratable quantities ("amount of solar energy received" would be correct), not to the rate at which those quantities accumulate. (And no, "rate of solar power" isn't right, either, but "rate of solar power increase" would be. Also, strictly, 'amount' relates to uncountables - like 'amount of flour', and 'number' should be used for countable - like 'the number of marbles in a bucket.')

So - should we use 'power' as the critical word, or 'amount'?

Given the use of the word 'amount' I suspect that the author of the puzzle was thinking of energy but said power. But that's just my opinion...

Chris

Assuming that the question meant what it said, it's average power, not energy per Earth-day. Even if it was the latter, the variation would be really small compared with the distance from the sun - and indeed other short-term distance changes due to the action of the other planets.

The reason is that I'm pretty certain that you are misinterpreting the changes in the day length. The day is currently longer than its value (based on presumed 1750-1892 values) by typically 1.5-ms. This corresponds to adding a leap-second every 18 months on average*. The rate of slowing is about 1.7-ms per century - so in 10,000 years time the average day length will have increased by 0.17-seconds, which is not a great deal. However, by then, if my sums are remotely accurate, we would need to have accounted for about 3.5 leap-days; so it's to be hoped that the present system of leap-seconds is abandoned relatively soon...

Fyz

Ah.. I must've misread leap second as an actual second increase on every subsequent day...

(Those damn teachers who said I should pay more attention were obviously right....execpt the French Teacher who would sit out in front wearing a mini skirt with her legs crossed...she thought I should pay less, and kept throwing me out....)

Now where was I ..yes..

The question makes no mention of the size of this steady incease.....

That'll do for me.. attention span all used up.

Left-right confusion can be regarded as an aspect of dyslexia. If you display a few of the characteristics, but only mildly, you won't be labelled as dyslexic. If you display them all strongly, but are bright and normal in other ways, even county-employed educational psychologists will recognise you as dyslexic - unless there's a particular squeeze on related budgets, in which case your guardians will be labelled as causing problems by being too pushy and the entire family will be referred to a shrink, which costs more and is utterly unproductive, but comes from a different budget.

Hopefully, the above will cure any illusion that I'm rational and don't suffer from unsupported theories.

BTW, I don't have skin problems with nettles either - though I think they make better soup than tea.

I shall add my off-topic mark to yours; please perform the same service for me.

Note for Codeyn: I recommend you steer clear of matchmaking - it's far too dangerous when you don't know what you are doing. In this case, my wife would probably kill all three of us were you successful.

I remember reading an article about gene dominance and hormone inbalance in a DAF (Fathers Against Dyslexia ((chuckle, chuckle))) newsletter. It stressed non-gender specificity, debunked testosterone as the main culprit. The main point was that in the first 4-6 months postnatal, testosterone levels in males rise to puberty levels. During this time, the brain is (dont beat me up ladies, Its only a term) "masculinized". The result is a larger brain volume, but decreased connection between the hemispheres. If the levels stay lower, the brain is "femininized", and corpus collosum is proportionally larger. A well developed C.C. has been touted as responsible for such favourable traits as: (gulp) Women's intuition, multi-tasking, visual-spatial aptitude, and even musical ability. Dyslexia is usually found to be a problem associated with single task oriented, aggresive masculine brains. It is a problem recognizing codes ("b" and "d" look the same), or relating the code to a specific sound. On different levels, it can be as mild as someone like me who is mostly ambidextrious (no favouring, difficulty identifying L and R), or "I never forget a face, but I get stuck on names", to people who cannot speak because they cannot relate a visual input to a sound. It also has absolutely nothing to do with intelligence, nor communication between the hemispheres as originally thought.

I hope everyone has enjoyed this installment of "useless information" - you've been a great crowd, thank you good-night.

I'm not clear whether it's my elementary reading skills, or your abbreviated reporting - but there seems to be an incompatibility here - i.e.:

"decreased connection between the hemispheres", and
"nor communication between the hemispheres"

You need a very particular definition of intelligence if you are to state that "it (dyslexia) has nothing to do with intelligence". If you define intelligence as the ability to achieve intellectual tasks, dyslexia is most certainly relevant. It certainly interferes with the ability to express yourself in writing. There's also a rather interesting phenomenon with intelligence measurement of at least some severe dyslexics: depending on what they have been doing most recently, they can produce their "normal" score for either video-spatial tasks or on verbal tasks, but apparently not for both on the same occasion; it appears that activity in one area can block communications to those in the other.

Fyz

Yeah that was a bit ambiguous.

1. A masculinized brain always exhibits decreased communication between hemispheres compared to femininized, and sometimes dyslexia.

2. Dyslexia was once considered to be caused by communication deficiencies between hemispheres, due to a proportionally smaller corpus colossum.

3. Intelligence is a property of the brain to plan, solve problems, and think abstractly. It isn't limited to book learning, narrow academic skill, or test taking smarts. Even age old IQ tests are being abandoned now because we acquire a skill for multiple choice tests after a few years of schooling.

what if it's the sun ? .....

would the sun be giving off extra energy in 10,000 years ?

Likely not "supernova" energy..... but would the sun give off more energy as it matures ?

Just a thought.

I understand the Sun is gradually getting hotter, perhaps 20% over last billion years (somebody correct me on that if it's way out) but for the purpose of the problem this was specifically excluded in the wording.

Codey

Not checked your numbers, but twenty-parts-per-million over the next 10,000 years would still be pretty small compared even with short-term (= decades, centuries and millennia in this context) changes in the sun's output, to say nothing of the orbital effect.

Are we assuming linearity in the increase. If so, why?

Not linearity - but "steadily increases" presumably indicates that the 20th June reading averaged over (say) a 100 year period should be greater* than the average over the previous one. In any case, post #3 already identifies one good candidate (the Earth's orbit becoming more circular); therefore, we can afford to reject other effects if their size is theoretically much smaller (not being psychic, we can't say anything with absolute certainty...)

*well, nearly always at least..

Fyz

Hmmmmmmmmmmm. OK. Here's another one. E=MC²! The outpouring of energy over 10,000 years is reflected in a reduction in the Sun's mass which, when poured through Kepler's laws of planetary motion, means that the Earth is further away.....oh, no. That's going in the wrong direction for the stated observation. Forget that one.

A few thoughts to stir the pot:

Fyz, in your first comment (post #3) you first mentioned the date of June 20th being close to the aphelion, then you switch to perihelion. I think most people here know the difference, but for those that don't, this must be a bit confusing.

The satellite's orbit is not just geostationary, it is geostationary over the equator. At the annual date of measurement given, the satellite will pass below the orbital plane when facing the Sun. This means the incident angle of insolation is not optimum for solar power measurment. A better choice would have been on one of the equinoxes.

I have heard that the Earth wobbles on its axis, and Fyz alluded to this, so I presume it is true. If the wobble is moving the nothern end of the axis away from the Sun, that will give a more favorable incident angle of insolation. As the incident angle changes, the satellite measures more solar power.

I wiill now leave this to those more knowledgable than me to figure out if any thing I said is relevant, and if so, how it applies. Meanwhile, I shall research this out in more depth for my own benefit.

Thanks for pointing this out - it was very careless of me. As it's with reference to June 20th, they should all read aphelion, as I'm sure you knew.

I agree that any time other than a solstice would be better, as this is the one time of year that a geostationary satellite passes through the Earth's shadow. However, as we have no way of knowing whether the Earth will cast a larger or smaller shadow in 10,000 years' time, I think we just have to assume it's a red herring. On the other hand, the angle of incidence should be irrelevant to the average power provided that the average area subtended by the satellite is the same now as it will be in 10,000 years (or the satellite is measuring power/unit area - probably omitted to keep the question short). Again, this has to be treated as irrelevant, I think.

Even though the idea of wobble and angle of the earth may change in 10,000 years I don't believe this would matter in this case. To keep these factors from affecting the measurement, the satellite should be aligning itself with the sun so as to point the sensors directly at it. Of course this would assume that the satellite has sufficient fuel to manuever after all those years, but the idea that something man-made can last that long is hypothetical at best anyway. Of course plutonium lasts a long time and that is man-made.

Doesn't a geostationary satellite over the earth's equator always pass through the earth's shadow - regardless of the time of year? That is something I've never considered.

What is the altitude of a geostationary orbit, and what is the distance of the tip of the umbra (full shadow, where no sunlight is present; distinct from the penumbra, where sunlight passing one side of the earth shines, but the sunlight passing the other side of the earth is still blocked)?

Answer:

A. Geostationary orbit: roughly 26,200 miles from the center of the earth.

B. Tip of the umbra: roughly 853,000 miles from the center of the earth, using 93M miles earth orbit radius and earth radius = 1/110 * solar radius.

Given those distances, surely the satellite will always pass through the umbra. The interesting thing is that as the season changes the track of the satellite will deviate from passing through the very center of the cone of total darkness. On June 20th the satellite's path will be furthest from passing through the center line of the cone, and so will be the shortest of its range of paths. Being offset from crossing the centerline of the cone means that any change in the size of the cone will be magnified (the satellite's path is a chord on the circle that is a slice of the cone; the length of the chord varies as the cosine of its distance from the center of the circle).

Minor changes in the earth-sun distance could dramatically alter the amount of time the satellite spends in the full dark of the umbra. The distance to the tip of the umbra is proportional to the sun-earth distance; the transit time across the umbra is proportional to the width, and therefore also to the length, of the umbra. So the time the satellite is in total darkness is proportional to the earth-sun distance.

If you can follow the point of all the above - congratulations. I'd take the time to reorganize it to make clear sense, but I should really be working, so need to stop doing the math (fun though it is).

Chris

The question did not specify any characteristics about the satellite (except that it is able to remain operational for 10,000 years - some mighty technology!). This allows us to assume that it is able to keep is sensor pointed directly towards the son, regardless of the relative angle between the earth's equatorial plane and its orbital plane. So the specific date on which the measurement is made is immaterial.

Now - the question speaks of the "amount of solar power measured" - not the amount of solar power received. Perhaps, the people who built the satellite did a millennial upgrade to their sensor, and it incrementally got more effective, thus increasing the measured power each millennium?

Chris

If the Earth's orbit is elliptical, the date is relevant.

Agreed - but for reason of distance to the sun, not angle of incidence.

Yes, but the Earth passes through the same channel, for a lack of a better word, in it's orbit in relation to the sun. In other words the orbit does not wobble. Also if I remember one of the programs on the History channel they where discussing the fact that the planets are slowly drifting away from the sun and away from each other. The mirror they placed on the moon during one of the Apollo missions has been used to conclusively determine that the moon is drifting away from the Earth at a couple of centimeters a year. Some how they shoot a laser at the mirror and time the response back. That would be neat to see!

"the orbit does not wobble"? All but one of the Molankovitch cycles are related to the way the Earth's orbit wobbles. Starting from the least relevant: the angle between the orbital plane and the invariable plane (approximately the orbit of Jupiter) changes with time; the minimum and maximum distances from the sun gradually become further around the orbit from year to year, and the difference between the minimum and maximum distances from the sun is currently reducing. But the largest effect over this period (as to my shame pointed out by others) is that the orientation of the Earth's axis of daily rotation is changing with time, and that means that Northern hemisphere summer (and so June 20) will not be approximately at the time of greatest separation to the sun as it is at present - in fact it will be at the time when we are closest - hence a quite significant increase in June 20th insolation.

That would depends on the wavelength of the laser used for the measurement! :)

I would assume the date is a constant to eliminate variations in orbit to make the question easier to answer. Assuming also that the satellite is measuring from the same point and the sensors do not change in calibration my best answer would be solar reflections from the increasing number of satellites and debris in orbit.

The general drift of the earth's magnetic poles (assuming it meanders in the same direction it has for the last 10000 years) would place the satelite in a sunnier trajectory on or about the summer solstice, at the equator, based on (yet another) assumption that the 'intact orbit' is constant to the geographic situation outlined at the onset of the experiment. The Southward drift of the North Pole would dictate that a geostationary satellite would be further north at the perscribed time and would recieve more sunlight as a result. ????????????????????????? PSD

Surely you jest?

Geostationary orbit related to location of magnetic poles
North-South impact of sunlight on a satellite (presumably the leap-seconds result in the calendar remaining adjusted so that June 21st is the solstice)
...

Fyz

To my knowledge, the orbits of satellites are governed by mass, not magnetism.

At least, until you get to some incredibly minor consequences of induced current when moving an object through a magnetic field.

Further, the movement of the earth's magnetic field is not a linear process, so its effect cannot be the one causing the changed measurement made by the satellite.

Chris

The satellite started its 10,000 year cycle of recordings at the coldest point of the shortest Milankovich cycle. As this cycle is roughly 21,000 years long, the satellite, at time of cessation would now be at the warmest part of this Milankovich cycle.

Please be specific, as there are several Milankovich cycles. The causal effects in most of them are more to do with the periodic melting of ice than with overall changes in insolation. (SFIK, the only one that significantly affects annually averaged insolation is the orbital inclination relative to the 'invariable plane', and this would not cause an increase at June 30th over the relevant period - currently, we only pass through the invariable plane around July 7th)

Fyz

The detector is degrading because cosmic x-radiation over time and it is causing a miss reading in photon bombardment.

Mr X I would guess.

Precession of the aphelion, an effect most prominent in the planet Mercury. It is an effect explained by Einsteins general relativity theory.

The change in the time of the aphelion is about two hours over this period. Although the change is in the right direction, other effects are much larger.

Fyz

Ooh, Ooh. A chance for a really dumb answer. Global warming goes slower than Al Gore says. The ice caps melt and the water runs to the equator area where it slows the rotation of the earth, lengthening the day.

The moon is constantly sapping the earth's rotational energy. That is why Devonian corals show shorter days and years. As time progresses, the day simply gets longer. Longer days=more solar power. That's my take on it.

Yes, that might slow the rotation of the Earth but the orbit of the satellite is dependent on its altitude which would not change over that time unless it was manuevered there. So the time it takes to go around the planet would not change.

Every day of every year the earth gets bombarded by micro meters and larger objects. This adds to the mass of earth minimally reducing the radius of the earths orbit over time. A reduced radius does up the level of suns radiation intercepted by the earth and in this case by the solar satellite.

My apologies for not having done my research before my first post.

A geostationary orbit is a geosynchronous orbit with zero decilnation, that is, above the equator, at the altitude mentioned by Odessy2001. The difference between the two types of orbits is explained and illustrated here.

The person that mentioned the magnetic poles must not realize that the axis of the Earth's magnetic field does not coincide with the Earth's axis of rotation. For the satellite to have the same period of rotation as the Earth, it must rotate around the same axis. Anyone who uses a compass along with a map knows they must adjust for this difference. Military topographical maps have a triangular diagram that shows the realtionship between grid north and magnetic north.

yes,

declination is the answer

psd

Since the obliquity of the ecliptic plane of earth (its axial tilt) is reducing, wouldn't the fact that the equatorial plane is becoming less inclined to the sun have any impact on the solar output? Not sure about the long term prospects (10000 years) of the tilt, ie would it continue to reduce or indeed would it reverse and begin to increase?

Gary

The obliquity of the ecliptic (angle between the Earth's rotational axis and the Earth's orbital axis) only affects the position of the satellite. The average distance over 24-hours will be unchanged, so there will be very little effect on the average power reaching the Satellite except for the period of time that the satellite passes through the shadow of the Earth. However, 20th June is near the solstice, and with the obliquity being in the range 21-degrees to 24-degrees, the satellite will be about 6000 miles away from the edge of the Earth's shadow. The situation would be different within about three weeks of the equinox, however...

Could the answer be as simple as 'Sensor Drift?

Actually, the answer is a combination of precession of the Earth spin axis (period about 26000 years) and the definition of the calendar. Now June 20 is the time when the Sun appears highest in the sky for an observer in the Northern hemisphere (highest declination). Because of precession, the first point of Aries is changing; this is the point where the Sun passes from the south part of the sky to the north part. If this remains the definition of the spring equinox, or March 21, and the summer solstice as June 20 or 21, then the precession will move the point from the aphelion of the earth's orbit around the Sun to the perihelion. The change in distance to the Sun is small, but significant. The increase in instantaneous power, assuming the solar cells remain at their nominal preformance, is steady though non-linear.

You are basically correct! Precession is caused by the gravitaitonal attraction of the sun and the moon on the rotating earth. This causes the axis of the rotating earth to point to different stars over a period of 26,000 years. However, there is another term. The earth's orbit is an ellipse and perihelion (the closest approach of the earth to the sun) is also moving but in the opposite direction. The combined effect is a 21,000 year period. Wikipedcia has a disscussion on Milankovitch cycles, which are weather related cycles perhaps caused by the earth's orbit and rotation. It has a discussion of the 21,000 year period.

The American Ephemeric and Nautical Almanac ( my copy is for 1975), when discussing orbital motion calls this mean longitude of perigee with respect to the mean equinox of date. Evaluating this term evaluates to a change of 176 degrees in the location of perigee.

In short, today our orbit around the sum, we are almost furthest from the sun on June 20. In 10,000 years, we will be almost closest to the sun!

Guest and GWJ: I take your point - midsummer in the Northern hemisphere (~20 June) is currently close to aphelion (furthest from sun). Reversing the angle of the axis with respect to the orbit will make midsummer come at about the perihelion closest to sun). So I grabbed a red herring with the reduction in ellipticity - though this reduction would just be sufficient that the incident power will be higher throughout the year than it is currently at June 20th.

I raise my hat to you both

.Ω.

^O|^O
.___.

Fyz

Astronomical orbital data are presented with respect to the fixed stars. But our seasons are based upon the current location of the Vernal Equinox which moves with respect to the fixed stars at the 26,000 year period.

You were correct the eccentricity of the earth is now about 0.0167 and it decreases over the 10,000 years to about 0.0113. But at the same time, precession causes the north pole of the earth to point towards the sun when the earth is hear perihelion ( closest approach to the sun).

Another description of this and the Milankovitch cycles appears at the US Naval website. Part of the US Naval description reads:

"We can measure the length of the year in several different ways. The length of the year from equinox to equinox (equivalently, solstice to solstice) is called the tropical year, and its length is the basis for our Gregorian (civil) calendar. Basically, the tropical year is the year of a complete cycle of seasons, so it is natural that we use it for ordinary purposes. But we can also measure the length of the year from perihelion to perihelion, which is called the anomalistic year. On average, the anomalistic year is about 25 minutes longer than the tropical year, so the date of perihelion slowly shifts over time, regressing by about 1 full day every 58 years. The date of perihelion thus moves completely through the tropical year in about 21,000 years."

Bingo to Guest and GWJ and Fyz!

Both effects will be significant, but the effect of perihelion date shift is the largest by far.

Jorrie

Global Warming?

Precession.....

I'm curious.

Isn't the sun's diameter supposed to get larger?

I don't know if the effect is meaningful, in terms of the question, over a period of 10k years.

Just tossing my $.02 in.

Obviously aliens will have invented the pot trimmer before us apes did. If the trim pots have not been altered I would say its probably cosmic rays increasing the leakage currents in the photosensor.

THE EARTH'S ROTATION IS SLOWING DOWN.

Aha! Another person who thinks capitalisation (equivalent to internet shouting) makes the argument more convincing? The challenge says power, not energy. Even if it said energy, the expected slowing over this period would be 1.4-ms per century (the actual slowing since 1820 is rather less than this would suggest, and the current rate is rather greater). So the day would be about 0.14 seconds (or 0.00016%) longer - much smaller than almost any of the other effects proposed.

I've seen some viable solutions and would like to put forth my own.

Is it possible the residual atmosphere is masking the satellite? As atmosphere wicks away, that would be reduce the mask and increase the reading.

The date IS IRRELEVANT. The amount of light will increase across the board over 10,000 years regardless if its june 20th or december 20th. Why? Because earths revolution around the sun will slow down (solar drag, collisions with asteroids, etc.) and by laws of planetary motion, the orbital path of the earth around the sun will be moved closer to the sun. THIS IS A MEASURED FACT! Knowing that the earth will be closer to the sun, its painfully simple to apply the inverse square law and show that the sunlights intensity is porportional to 1/d^2, where d is the distance between the earth and the sun. More intensity, more power. Its highly unlikely that in 10,000 years the earth will be along the same axis as it is today (with the sun as an origin) on June 20th, so any arguments about it being a special day in earths orbit around the sun are ridiculous.

No, it is not a measured fact. Over any reasonably long timescale, the dominant effect on the Earth's orbit is due to the tidal effects on the sun, because most parts of the sun rotate around its axis far more than once per year. This is steadily increasing the radius of the Earth's orbit, so any such effect would be a reduction in power. However, over 10000 years, all such effect on the Earth's orbit are very small. The proper answer has been given and well explained elsewhere. Writing your opinions in capitals is not a substitute for checking whether they have any basis in fact. (BTW, June 20th is not a particularly special day in the Earth's orbit - but you would see the opposite effect on Dec 20th)

Any consideration of the suns position in the galaxy? (Andromeda's approaching) or the sun using up the hydrogen and expanding outward as it dies?

I agree with the earth's orbital distance from the sun as the answer due to the simple fact that all orbits will decay with time. Do not however forget the pollution effect from all the reflective space junk being added every year.

All orbits will decay with time"? Well, maybe eventually, if the objects last that long. But in the interim, the moon's orbit around the Earth is growing measurably from decade to decade, and both theory and indirect evidence suggest that the Earth's orbit is growing and will continue to grow at least until the sun becomes too hot for life to continue existing on Earth (because of the rotation of the sun).

What you didn't hear, is that its an inflatable satellite, and is gradually inflating larger and larger, increasing its surface area and registering more radiation. Or the days could be getting longer.

Is it because the sun has no sunspots right now?

What about keeping things more simple... solarpanels get less efficient as they get older... but ofcourse this isn't a very exiting way of looking at it..

If the Earth's orbit is naturally decaying. Every year the Earth will be closer to the Sun.Then at each June 20th and considering the assumptions in the problem the entire day accumulated energy will increase gradually.

The correct answer was given by GWJ (#49) when he wrote:

"...But we can also measure the length of the year from perihelion to perihelion, which is called the anomalistic year. On average, the anomalistic year is about 25 minutes longer than the tropical year, so the date of perihelion slowly shifts over time, regressing by about 1 full day every 58 years. The date of perihelion thus moves completely through the tropical year in about 21,000 years."

The perihelion shift is the key.

The precession of the Earth's pole means that the timing of the seasons will change over time. Presently, June 20 marks the 1st day of Summer for the Northern hemisphere, but in 10,000 years June 20 will be near the 1st day of Winter. BUT, unless the Earth's orbit also precesses, June 20 would still be near aphelion and the average solar power received by the satellite would not change.

Since the perihelioin point precesses, though, the dates of perihelion and aphelion change over time. And in 10,000 years June 20 -- which at present is near the date of aphelion -- will be near the position of perihelion. And thus the slight eccentricity of the Earth's orbit will cause the satellite to receive more power.

And by the way, the length of the day over these 10,000 years will only increase by about 0.1 seconds.

Guest said," Presently, June 20 marks the 1st day of Summer for the Northern hemisphere, but in 10,000 years June 20 will be near the 1st day of Winter. "

Our calendar is based upon the seasons. June 20 will always be the 1st day of summer. But, the perihelion of the earth's orbit will move in time from early January to late June.

Similarly, the precession of our north pole will point to different stars on the sky. Since the earth will not appear to move -- at least to those of us on the planet -- this means that the Vernal equinox (the first day of spring) will appear to move through the constellations of the zodiac. Or simply the summer constellations will become those we see in December. And the winter constellations will be seen in June.

GWJ wrote:

"Our calendar is based upon the seasons. June 20 will always be the 1st day of summer."

Not any more. The length of the day is fixed by atomic clocks, and likewise the length of the year. June 20 has not always been the 1st day of Summer. Over time the start of each season will creep through the calendar.

Then GWJ wrote:

"Similarly, the precession of our north pole will point to different stars on the sky. Since the earth will not appear to move -- at least to those of us on the planet -- this means that the Vernal equinox (the first day of spring) will appear to move through the constellations of the zodiac. Or simply the summer constellations will become those we see in December. And the winter constellations will be seen in June."

This is certainly true, but keep in mind that (aside from the proper motions of stars) the constellations on the Ecliptic will always remain on the Ecliptic. As the Earth's axis precesses the constellations along the Celestial Equator will change, along with the "Pole Star". A line drawn through the center of the Earth towards the center of the Sun, on June 20, points to a spot in space near the star Eta Gemini. And in 10,000 years at the same point in its orbit (June 20) it will still be pointing towards Eta Gemini. (But by then, due to the precession of the perihelion point -- which is not the same as the precesssion of the Earth's axis -- The Earth will be near perihelion on June 20, not at aphelion.)

SFIK, the Gregorian calendar was defined so that the solstices would occur as close to the same date every year as practical. Of course, there are short-term variations, because corrections were defined only once every four years, and also because the orbit is non-circular and varies from year to year. In addition, the algorithm was not defined as exactly as would currently be possible; therefore, if no modifications to the calendar are agreed in the meantime, the solstices will have moved by about four days in the coming 10,000 years, so the NH summer solstice will be around June 17th. It doesn't seem to me that that significantly affects the outcome.

In the same vein, leap seconds are added up to twice a year as required to maintain the average times of midday and midnight on the Greenwich meridian as close to 12:00 and 0:00 (or 24:00 take your pick) as possible; various effects (tidal being most significant) mean that individual times will vary quite a lot (at least a few minutes, I believe). Of course, in 10,000 years time you'll need to add leap-seconds roughly every week (or about four seconds monthly if we maintain the present system).

Guest wrote:

"A line drawn through the center of the Earth towards the center of the Sun, on June 20, points to a spot in space near the star Eta Gemini. And in 10,000 years at the same point in its orbit (June 20) it will still be pointing towards Eta Gemini. (But by then, due to the precession of the perihelion point -- which is not the same as the precesssion of the Earth's axis -- The Earth will be near perihelion on June 20, not at aphelion.)"

The earth's orbit about the sun defines the ecliptic. The constellations of the Zodiac are fixed ( Except for proper motion as you mentioned. And the movement of our sun about the galactic center. Both of these are small effects over 10,000 years.). BUT precession of the poles does cause movement of the constellations from season to season. Refer to Wikipedia for a discussion of equinoxes or solstices. In part the one for solstices notes,"

"First point of Cancer and first point of Capricorn. One disadvantage of these names is that, due to the precession of the equinoxes, the astrological signs where these solstices are located no longer correspond with the actual constellations. "

The summer solstice was called the First poihnt of Cancer because it occurred in the constellation of Cancer when the Greeks first observed it. However, precession has moved it into Gemini. In 10,000 years the summer solstice will be near the constellation of Capricorn.