Get a Straight Answer

    I'm 40 years old and passed my junior high and High school and I never understood Algebra, the substitution and replacement rules for the "X" or "Y's"

    When I accessed your page I thought it was just another informative science page, but I'm so surprised by the way how you explain the formulas Off course this came to me about 35 or so many years late but still enjoyable, I really appreciate this small gift that you gave me on this night.

    I will definitely introduce this page to my daughters I'm sure they will really appreciate it too.

    Please keep up your excellent job

Victor

By the way I read the Spanish version
(English spelling and wording were corrected)

...and more:

I'm 32 years-old Mexican living in Mexico.
        Please receive this quick note to thank you for setting up a web page on the Pythagoras' Theorema, but specially for your infinite kindness of providing a Spanish translation.

    I just stumble with the fact that I don't remember my high school math. And I needed it to deduct the measurement for 2 hypothenuses that are part of a sculpture (a triangular prism) of which I'm writing a paper on. After some web-surfing I got directed to your page. And... problem solved, I was able to get the paper written with its right measurements.

Again, thanks sharing your knowledge.
        Rosina

...still more (Spanish, though not math):

    I have just visited your website and am so excited that I found something in Spanish! I teach Integrated Physics and Chemistry at Pampa High School, Pampa, Texas. Every year I have students who are ESL and have very little or no understanding of English, I have been trying to find some resources on Lab Safety and metric measurements in Spanish. I like what you have on your site, but it is not appropriate for these students. Do you know of any resources on the internet in Spanish that I could use as a supplement to my lessons. I would appreciate any information that you could give me.

Thank you ... Diana

...and still more (math, from Africa):

    I accessed the site containing (M-1)Algebra--the basic ideas and it appears to be the stuff that I need to familiarize myself with. I want to write the GMAT exam for MBA, for the 2nd time. Last was in May 2001 and my score was rather dismal. My math knowledge is minimal, and I realize that math in fact seems to be fun. If the basic idea is to isolate all that one does not need in the process of solving a problem and remain with what one needs on both sides, geez, I do wish I had known this ages back. I just hope I will be able to figure out all that you explain.

After visiting NASA solar sailing page I saw your name as a reference.

    Do you know who validated solar pressure? Did anybody actually measure the pressure a (hefty) laser puts on a mirror? Michelson measured the speed of light but did anybody actually measure light's pressure?

Reply

    Light pressure was predicted by Maxwell's theory of electromagnetic waves. It was verified in 1910 by the Russian physicist Pyort Nikolaevich Lebedev. See

Hello Professor Stern,

    I came along to your site regarding seasons while researching a question - How do scientists approximate the time (down to the minute) that seasons change? Can you answer this question or point me in the right direction to find the answer.

Reply

Dear Christiana

    During the year, the Sun seems to follow a large circle around the sky, among the "fixed" stars which define the constellations and whose positions are essentially fixed, because they are so far. That circle is known as the ecliptic, and is described on the web site.

    Because of the Earth's rotation, the sphere of stars also seems to rotate. It has two "poles" around which the rotation takes place, one in the northern half of the sky and the other in the southern half. The first is visible only north of the equator, the second only south of it. The line halfway between the poles is knows as the equator of the celestial sphere, or the celestial equator. This, too, is described in the first sections of "Stargazers".

    These two circles--the ecliptic and the celestial equator--intersect (as any two circles on a sphere must do, if each divides the sphere in two equal halves). The seasons are defined somewhat arbitrarily by this geometry. The two points of intersection are the spring and fall equinox, and when the Sun is there, night and day are equal (hence the name). The first is viewed as the start of spring,: see story on the Persian New Year in the section on the calendar, in the yellow box there. The second is the start of fall, around September 23.

    Summer starts when the Sun is as far north of the ecliptic as it can get--that is the summer solstice, around June 21, the longest day. And winter starts when the Sun is as far south as it can get, and that is when nights are longest, around December 21.

I am really confused on how the accelerator grids function [in ion rockets]. I know that the negative grid accelerates the ions out of the ionization chamber but what exactly does the positive grid do? Does it act as a decelerator or as a repulsive force for the positive xenon ions? Are both grids on at the same time? How do the positive xenon ions get past the positive grid? Does one grid have a higher potential than the other?

    I have been to many websites and I have read that the ions are accelerated as the result of "the potential difference between the grids"... what does this mean?

    Any clarification will be greatly, greatly appreciated.

Reply

"Potential" is a mathematical term also known colloquially as "voltage" because its value is measured in units called "volts." It is somewhat like height in a gravity field: a stone falls from a high location to a low one, and gains energy in proportion to the height difference it crosses. A proton or a positive xenon ion "falls" from high potential to low potential, and gains energy.

    One difference: there also exist negative particles, like electrons, for whom "up" and "down" are reversed. Electrons gain energy moving from low potential (very negative) to high potential (very positive). Except for this reversal, everything is similar.

Still with me?

    So we have two parallel grids, positive (say) on top and negative on bottom. The space in between is where electric forces can be observed, and a region like that is known as "electric field." Electrons released in this space move up (TO the high voltage), positive ions like those of xenon move down (AWAY FROM high voltage).

OK?

    I truly enjoyed your web page on librations of the moon.

You wrote:

"In addition to the preceding modes, there also exist "physical" librations, actual pendulum-like nodding and wobbling of the Moon around its equilibrium position, like the spring-attached head of one of those "bobblehead dolls" popular