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

is it possible for a satellite to remain in a perfect geostationary orbit for 10,000 years or could drag slow it down ?

It's so simple - Global Warming, you fools

Would the earth axis change due to annual magnetic field variation?

Would the earth axis change due to annual magnetic field variation?

More likely the other way around. Remember that a magnetic field results from a flow of electrons. If the Earth did not spin, and have a molten iron core, it would not have a sustained magnetic field. The Wikipedia entry on the Earth's magnetic field explains this relationship:

"The field is similar to that of a bar magnet, but this similarity is superficial. The magnetic field of a bar magnet, or any other type of permanent magnet, is created by the coordinated spins of electrons and nuclei within iron atoms. The Earth's core, however, is hotter than 1043 K, the Curie point temperature at which the orientations of spins within iron become randomized. Such randomization causes the substance to lose its magnetic field. Therefore the Earth's magnetic field is caused not by magnetized iron deposits, but mostly by electric currents in the liquid outer core.

"Convection of molten iron, within the outer liquid core, along with a Coriolis effect caused by the overall planetary rotation that tends to organize these "electric currents" in rolls aligned along the north-south polar axis. When conducting fluid flows across an existing magnetic field, electric currents are induced, which in turn creates another magnetic field. When this magnetic field reinforces the original magnetic field, a dynamo is created which sustains itself. This is called the "Dynamo Theory" and it explains how the earth's magnetic field is sustained."

The full article is here.

The poles are predicted to reverse themselves ...

Global warming only works below the ozone barrier doesn't it?

So a satellite in orbit wouldnt be effected.

That is true of most greenhouse effects and the warming due to man's activities. Over geological timescales there are cycles of heating and cooling that are commonly referred to as global warming and cooling*. Some of these are due to orbital variations and others to changes in solar emissions - but the second has specifically been excluded from this challenge.

*In reality, it's all heat coming in and being re-radiated at different rates, so it's always a combination of both...

Fyz

From the CRC Handbook of Chemistry and Physics (1982), the ratio of the aphelion to the perihelion of the Earth's orbit is approx. 1.034. If we square this number to obtain relative radiational flux density we get 1.069. The Handbook also gives the relative observed secular braking of Earth's rotation as -2.8 X E-8 per century or a day with a factor of 1.0000028 longer after the 10,000 years. Clearly the rotation of apehelion effect is overwhelmingly dominant.

Always keep that book handy.

No, the rotation of the aphelion is only a small part of the shift (~17%); and because 20 June is currently so near the aphelion, this this would only provide about 7% of the change on its own. It's the time-movement of June 20th (relative to the "fixed stars") that does the main work. (This is due to its correlation with the precession of the Earth's North-South axis)

The earth's rotational speed steadily slows and a day is slightly longer.

Ken Haselby

Nah. Fyz nailed this one.

Hi TPV

Much as I'd love to take the credit, Codemaster was the first to say it had to be distance from the sun (post #2), Guest identified the largest contributor to the change in distance (post #46), and GWJ provided the confirmatory detail (post #54)

Fyz

Thanks Fyz, I must admit that after my post #2 the discussion got so complicated, aphelions, perihelions and so on, I wasn't sure whether it was confirming my suggestion or not!

Codey

The earth's orbit is self correcting. We just don't know how that works yet.

......how could the answer not be Global Warming? Are you sure?

I am afraid I am in TOTAL disagreement with your answers.

1) First of all the perihelion precession, although it is a well known effect WILL NOT change the perihelion distance and therefore the radiated power to an object tracking the earth, as is the case with a geostationary satellite. All that the perihelion precession will do, is to change the azimuthal position of the of the long axis (apsis) of the earth's orbit in space; the shortest distance from the sun (perihelion) and the longest (aphelion) however will remain unaffected.

There is a different phenomenon viz. orbit circularisation and decay, that occur with VERY LONG time constants (millions of years) due to energy losses e.g. impact with dust and meteoroids. These will eventaully cause the earth to come closer to the sun and therefore increase the "solar constant" and hence the solar power density as perceived by the satellite but these are completely different to the quoted event !

2) The second effect quoted is also not going to make any differenc to the solar POWER received at the surface of the satellite. Although the length of the "day" will increase as described and therefore the "Energy per day" will also increase, the question is talking about POWER not ENERGY.

POWER is the ENERGY PER UNIT TIME and will remain constant, as far as this phenomenon (reduction of the anular rotation velocity of the earth) is concerned.

There is one other phenomenon that WILL increase the solar power VERY slowly with time (again counted in millions of years). This is our Sun undergoing the last cycle of its thermonuclear evolution and becoming a "red giant", eventually engulfing the earth and destroying all forms of life (at least as we know it) by "frazzling" it !

I have an an unfair advantage on most of your participants and by the looks of it on your aditor / contributor, since I happen to be a Space Scientist ( a rear breed indeed)

Better lack next time !

1) Your first point is partially correct. However, all of the orbital elements of the earth's orbit are changing. While I was studying for my degree in astrometry, I used the American Ephemeris and Nautical Almanac frequently. It came out every year with the position of the sun, planets, moon, etc. And it had a series expansion for the sidereal orbital elements of the earth (or position of the sun). In my post #57, I refer to a US Naval web site which refers to some of these cycles. They are caused, primarily, by the interaction of the gravity of the sun on the rotating earth and on the earth / moon system.

The key here is the date of June 20 in summer. That is the only day on which the solar power is measured. Today, that date occurs near aphelion. During the 10,000 years, the earth's north pole will precess until summer in the northern hemisphere occurs near the time when the earth is closest to the sun (perihelion).

The advance of perihelion with respect to the fixed stars contributes a smaller part, but also contributes to the earth being closer to the sun on June 20.

2) I agree with your second comment.

When I say I agree with the second part, I mean that power is energy per time. The length of the day should not affect the power.

The first part of the 'official' answer is partially correct - 20th of June is now near Aphelion. Because of the way the long-term calendar is set up, 20 June will approximately track the precession of the orientation of the Earth's axis. That, combined with the (less significant*) precession of the perihelion itself mean that midsummer (and so June 20th) will be near Perihelion in 10,000 years time (I think it will be at perihelion in about 12,000 years). The principle thus becomes equivalent to the difference in solar power incident on the satellite (this year) at 20th June or at 20th December.
* I think the ratio is about 5:1)

The other part of the official answer is of course junk - both in terms of the principle (as you say, day length wouldn't affect power anyway), but also in respect of the number given - it's closer to 0.17 seconds, so even the resultant change in energy/day would be insignificant compared to random variations.

As a space scientist, you doubtless knew all this - in which case I would suggest that your mode of expression is unhelpful to those less fortunate in their background than yourself.

Fyz

the orbital precession is a valid reason for added heat gain and the I will concede that 50 seconds longer days will also contribute. 50 seconds a day equates to almost 6 hours in a year. Therefore a year is very nearly 365 days not the current 365 + 6 hours which gives us leap year once every 4 years.

This factor must also be accounted for and may make this brainteaser more difficult, in 10,000 years and lengthening days without changing "Leap Year" from every 4 to 5 and then 6 etc. year increments, the calender dates will precess forward in the yearly seasons. In 5,000 years the leap year should occur at 12 year increments, without this change included over the 10,000 years Jun 20th will have become mid fall to winter, spring and back to summer a number of times.

Where on earth do you get 50 seconds from? The expected value is about 0.17. Averaging over a year seems strange - precession will not affect that average.