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Spacecraft Attitude
Well, it started when I wanted to know how can a spacecraft calculate its self-position in space. I started by assuming it'd take reference to stars surrounding it, but I didn't know if the movement of the stars were negligible so it would need to compensate for it, and if so -- how would the measurements take place, and with what kind of resolution.. and so on...
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Concerning the "self-position" of a satellite, you probably mean its orientation in space or "attitude." It is a big subject and much depends on how accurate do you want it to be determined. If you are happy with half a degree, a "sun sensor" and an optical "horizon sensor" may give you enough information--for other uses, star cameras exist and have been used.
A related question is, how do you rotate a satellite from one orientation to another? The usual way is to have gyroscopes, flywheels in constant rotation. Forcing the rotation axis into a new position causes the entire satellite to rotate in a way that preserves its angular momentum, then when you think it has rotated far enough, you return the axis of the gyroscope to its original direction and the satellite stops rotating. You can mount the gyroscope on gimbals and point it in different directions, or have independent gyroscopes for the (x,y,z) axes and spin them up and down. The Hubble telescope, whose attitude (orientation) must be constantly adjusted, has several gyroscopes, and one of the reason for visiting it from time to time is to replace gyroscopes, because their bearings etc. do wear out.
Still another question is how to you express the direction of the satellite in space. You need two angles in spherical coordinates, which express the right ascension and declination of some axis on it, and you also need an angle to characterize rotation around that axis. With those you express (x,y,z) coordinates of points on the satellite. Rotating the satellite in space to a new (x',y',z') requires a calculation with matrices. A simple example is in problem 8 of
http://www.phy6.org/stargaze/Strig6.htm,
which continues at
http://www.phy6.org/stargaze/Srotrans.htm
What makes the Earth rotate?
Hi
Dont mind a question, do you? I was just doing a little competition, and I came across this: What makes the Earth rotate?
Reply
We believe that the entire solar system started as a cloud of gas and dust which gradually pulled itself together by its own gravity. In such a process, a measure of rotation, known as angular momentum, is preserved. Angular momentum of a collection of matter is proportional to its mass, the square of the average distance R of the mass from the rotation axis and to the frequency F of rotations per second (or per year, or century... whatever units you choose).
Any time a rotating cloud of matter gets reduced in size--as it did when Earth originated--R gets smaller. Therefore, to keep the angular momentum the same, F has to increase. It follows that even if the original nebula rotated very slowly, by the time it formed the Earth, it must have speeded up quite a bit.
An analogy can be taken from the tornado, forming during times of severe thunderstorm activity. Usually thunderstorms are associated with vertical hot air rising and giving up energy (see section S-1A in "Stargazers") but there also exist horizontal flows of warm humid air into the storm (low down) and cold dry air out of it (high up).
Usually everything is pretty symmetric, but sometimes a row of thunderstorms is formed ("squall line") and the flow of air in neighboring storms can set one of them slowly rotating. That is all it takes! As humid warm air is sucked into the rotating thunderstorm, its rotation gets faster and faster, and a tornado can result. Unlike hurricanes,though, tornadoes are too small for their direction of rotation to be related to the Earth's rotation.
Energy from the Earth's Rotation?
... just personally, I have had an interest of tapping other sources of energy besides oil, etc. for the earth's energy needs. I have had an idea about gathering the 'rotational kinetic energy' produced by the spin of the earth? Its just something on the side that is an interest.
Reply
Using the energy of the Earth's rotation is an interesting idea, and it is feasible, but the way it's done is probably not what you had in mind. The problem is, to affect the rotation you need some other object which brakes it. It must be outside the earth--nothing on Earth will do it.
Such an object exists: our Moon. The interaction between the Earth's rotation and the motion of the Moon raises tides in the oceans, and schemes to extract energy from tides therefore takes energy from the rotation of the earth and from the orbital energy of the Moon. Such schemes exist, but they are hard to implement (tides are low, salt water is corrosive) and give a low yield.
See also next question, below.
How were planets created?
Dear Dr. Stern,
In your reply to Q 78 you write - "...It was established not when the planets cooled but before that, a relic of the swirling of the cloud of gas and dust from which the solar system (and the sun) formed..."
My question is: From where did the "swirling cloud of gas and dust come? What is the SCIENTIFIC explanation????
Reply

From the evidence we have, all matter in the universe appeared--very hot, very dense--in the "big bang", about 13.8 billion years ago. I hope you do not expect me to recount all that evidence--expanding universe, microwave radiation etc.
Applying to this event what we know about atomic nuclei tells us that when that matter cooled enough to form atoms, these were mainly hydrogen, some helium and a little lithium. The materials from which planets are made (also, you and me)--elements such as carbon, nitrogen, oxygen and the rest-- --are more complicated, and must have appeared later. Without those elements, no dust would exiss--and no Earth, either, since our planet is largely made up of them.
It is generally held--and again, evidence exists, as well as theory, in which the late Hans Bethe, who just passed away at 98, had a big part--that heavier elements are "cooked," in part in the processes which even now power the Sun, but in addition (and especially the heaviest ones) in the sudden collapse of a supernova, which preceded the solar system. That includes such elements as uranium, which decay radioactively. From the radioactive content of moon rocks, they were dated about 4.7 billion years ago, and it is believed the Earth formed around that time, too.
The material from which the solar system formed must have been the cloud of dust and gas left from the supernova (or maybe from more than one), gradually pulled together by gravity. And it must have been swirling even then, because the amount of swirl--angular momentum--is preserved in mechanical systems. Furthermore, astronomers have observed (using the Hubble telescope, among others), disks of swirling dust which presumably mark the birth of other planetary systems, or perhaps systems of binary stars.
That, in a nutshell, is the "scientific explanation." We weren't there when it happened (the way the Almighty was, perhaps--see Job 38, v. 4), but we have plenty of evidence. You may also look up http://seds.lpl.arizona.edu/nineplanets/nineplanets/origin.html.
Does Precession of the Equinoxes shift our Seasons?
A very good old friend of mine a few years ago told me that the reason our winters are starting to arrive later and later is because in a few thousand years, the axis of the earth will eventually change and our winter season will become summer season and vice versa. I'm no longer in touch with him but I always knew him to be a very knowledgeable person in the fields of cosmology and meteorology. But I have yet to read anywhere or meet anyone who could verify his claim. Is there any truth to his claim? I have noticed the change in the past twenty years so I'd really to get to the bottom of it and understand why this is happening.
Reply
Your friend had in mind a real phenomenon of nature, but it actually happens differently, and the results are not the ones your friend credited to it.
The Earth orbits the Sun in a large flat plane, known as the ecliptic. The reasons we have winter, summer etc., is that the axis around which the Earth turns is not perpendicular to the ecliptic, but makes an angle of about 23.5 degrees to that perpendicular.
Thus in the summer, the northern hemisphere is tilted towards the Sun, the north pole gets 24-hour sunshine and countries north of the equator also get longer days and more concentrated sunlight. Six months later, the axis still faces the same way in space, but now the Sun is on the other side, the north pole is in the shade all the time, the northern hemisphere gets longer nights and sunlight falls there at a more shallow angle, reducing its power to heat the land.
All this is described in "Seasons of the year" at http://www.phy6.org/stargaze/Sseason.htm which also shows how seasons south of the equator are in opposite parts of the year.
Now what your friend is aware of is that the direction of the Earth axis changes. It always makes an angle of about 23.5 degrees with the line perpendicular to the ecliptic plane--but while keeping this angle, it wanders around a cone, whose axis is perpendicular to the ecliptic. It takes about 26,000 years to go completely around that cone. The technical name for this phenomenon is "Precession of the Equinoxes" and it is described in
http://www.phy6.org/Sprecess.htm
Precession, however, does not make the seasons different from what they are now. The picture given in "Seasons of the Year," of the Earth tilted by 23

Get a Straight Answer

Please note!

Items covered:

Spacecraft Attitude

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What makes the Earth rotate?

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Energy from the Earth's Rotation?

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How were planets created?

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Does Precession of the Equinoxes shift our Seasons?

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