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No, I don't "believe" in global warming. Sheesh. I don't "believe" in evolution, or in the laws of physics, either. Beliefs are the realm of religion, not science. Read posts #46 and #97 to get an idea on my thoughts on this matter.

Not true. Or rather, true at only two spots on the Earth: The north and south poles. At any point between the equator and one of the poles, the pendulum assembly rotates with a period of one sidereal day (Earth rotation), the pendulum swings back and forth with a period of [math]2\pi\sqrt{L/g}[/math], and this swing precesses with a period of [math]1/\sin\lambda[/math] sidereal days. With three distinct periods involved, describing the motion from the perspective of an inertial frame is a bit tough. There is no coriolis force when explain the behavior of the Foucault pendulum from the perspective of an inertial frame. Doing that is a bit challenging, however. Explain that behavior from the perspective of someone standing on the surface of the Earth and there is (must be) a coriolis force. It's an inherent part of the equations of motion for a rotating reference frame.

You are thinking of the roughly 1/4 day difference between 365 days and the tropical year. The sidereal year and tropical year differ because of the precession of the equinoxes. The Earth's rotation axis is tilted at about 23.44° with respect to its orbital angular momentum vector. It is this axial tilt that results in the seasons. As we want our calendars to be based on the seasons, we use the mean time between successive vernal equinoxes as the defining characteristic of a year. This is the vernal equinox year, which was 365.24237404 days long at epoch J2000.0 (ask, but only if you want to be confused further). The reason we need to add leap days is because that 365.2424 days is not an integer. Julius Caesar introduced the Julian calendar, which inserted one leap day every four years. The Julian year is 365.25 days long on average. This is a marked improvement, but is still off a bit. Our current calendar omits the leap day on years that are divisible by 100 but not by 400. This makes for an average year of 365.2425 days, which is very close to the mark. If the Earth's rotational axis was a constant vector, the vernal equinox would occur at the same location on the Earth's orbit about the Sun every year. However, both the angle and the orientation of the Earth's rotation axis with respect to the Earth's orbital plane changes slowly over time. Ignoring the change in the angle for now, the Earth's rotational axis undergoes a slow precession, the precession of the equinoxes, about the Earth's orbital angular momentum vector. A full cycle takes about 25,771.5 years to complete. This slow precession means that in terms of the Earth's orbit about the Sun, the anomalistic angle between successive vernal equinoxes is about 50 arcseconds shy of 360 degrees. The time it takes to cover a full 360 degrees is of interest as well. This is the sidereal year. The sidereal year was 365.256363004 days long at epoch J2000.0. The difference between the vernal equinox year and the sidereal year means that the constellations used by astrologers now appear in different months than they appeared in when Babylonian astrologers first developed astrology. What about the tropical year? The time between successive vernal equinoxes is 365.242374 days and is growing with time. The time between successive autumnal equinoxes is 365.242018 days and is shrinking with time. The tropical year, 365.242190 days, is the average of the time between successive points over the whole year. So why is the time between vernal equinoxes growing and the time between autumnal equinoxes shrinking? The answer lies in the shape of the Earth's orbit, and this will introduce a fifth definition of the year. The Earth's orbit is elliptical. The anomalistic year is the time between successive perihelion passages. Because the Earth orbits the Earth-Moon center of mass, the exact timing of the Earth's closest approach to the Sun varies a bit year to year. Ignoring this bouncing around, one would expect the perihelion passage to occur at the same point on the Earth's orbit every year. This isn't the case. The anomalistic year, 365.259635864 days at epoch J2000.0, is about 282.771 seconds longer than the sidereal year largely thanks to Jupiter. The date at which perihelion passage occurs (e.g., January 3, 2010) advances about one day every 58 years. This advance is why the time between successive vernal equinoxes is growing but the time between successive autumnal equinoxes is shrinking. Recap [math]\aligned &\text{\bf Year}&&\text{\bf Length (days)} \\ &\text{Julian}&&365.25 \\ &\text{Gregorian}&&365.2425 \\ &\text{vernal equinox}&&365.24237404 \\ &\text{tropical}&&365.24218967 \\ &\text{sidereal} &&365.256363004 \\ &\text{anomalistic}&&365.259635864 \endaligned[/math]

Which site? The only ones referenced are wikileaks (original post, the source of Hovind's "dissertation"), wikipedia (the picture in post #14), and of course this site itself, Science Forums. I don't see any of those as hateful or extreme.

Mark (SKF) was alluding to the figure traced out over one day. To see the analemma take shape, one must remove this daily motion by recording the position of the Sun at a fixed time each day.

Even more importantly, Mark, are you still hung up on the idea of somehow disproving the concept of a sidereal year? Both the sidereal year and the tropical year are clearly definable and easily measurable quantities. That these two quantities differ by about 20 minutes is a fact known to the ancients. If you are having difficulties understanding these concepts and how they relate to general precession, fire away. Your fixation on the motion of the Sun from the perspective of an Earth-fixed frame is hindering your understanding.

That flies in the face of government policy. There is nothing in neither Obama's Open Government Initiative nor the Freedom of Information Act that says the government will only release data to 'smart' people. There are legitimate reasons for the government to restrict access to data; the FOIA recognizes nine such reasons. That someone is too dumb to understand the data is not one of those nine reasons. BTW, much of the massaged climatology and meteorology data are available, even to dumb people. The raw data, not so much, and the algorithms, even less so.

I don't. I wouldn't be overly surprised if the LHC comes up with something that contradicts the standard model.

Were you that slow, iNow? Seriously, calling this a dissertation is just sad. There are one or two truthful statements here. For example, "Hello, my name is Kent Hovind ..." Fact! Things go downhill from there, rapidly.

Emphasis mine: Curious choice of words, bascule. Beliefs normally are something relegated to the domain of religion, not science. Are your religious beliefs in this matter getting in the way of your scientific objectivity? Regarding my thoughts on this matter, our release of massive quantities of CO2 into the atmosphere almost certainly result in some changes in the climate. How big an effect this represents is a matter of debate, as is whether the net effect is deleterious overall. That this is the biggest problem facing humanity? I'm trying to keep an open mind, but right now, I don't think so. The leaked emails certainly didn't help this religious cause.

Pangloss and Swansont have repeatedly tried to bring this thread back to addressing the what this means as far as climate science, and what it means as far as Science in general. You guys have repeatedly ignored the issue and have instead focused on what the likes of Limbaugh and Beck have to say on the subject. Just because people whose politics you disagree with are pouncing on the subject does not mean the subject is invalid.

I never referred to Fox news. I don't give a crap what they say there. There are plenty of legitimate skeptics out there who have no association with Fox news. And no, you are not allowed to use slurs against them. We have rules against that. That particular word has taken on a foul meaning. They could spout the most meaningless junk imaginable and you should still refrain from calling them by intentionally foul names. All you accomplish in calling names is to make yourself look just as low-brow as the people you are derogating.

No, you aren't. We have distinct rules in the forum against use of fallacies and against using slurs or prejudice against any group of people.

Oh please. Stop with the melodrama, and stop with the association fallacy. You are using that fallacy three times here in one short sentence. You are lumping the legitimate skeptics with those who deny there is no such thing as a greenhouse effect, etc. You are tarnishing their legitimate arguments with a false association with big scary oil. Many of these skeptics have no association with big oil, nor are they creationists. And even if they were, those associations would not detract from their arguments. You intentionally labeled these people with an extremely offensive word to dismiss their arguments.

It is entirely up to you. The choice is yours. You can (a) argue that the concept of a sidereal year is wrong, or (b) try to learn something. Choose option (a) and this thread is toast. I strongly suggest you choose option (b).

In other words, you are a crackpot on an agenda, or at least that is the appearance you give. You've been told multiple times that you are wrong, but rather than try to learn something you are taking the hidden agenda approach.

Not this nonsense, again! Discussed ad nauseum here: http://www.physicsforums.com/showthread.php?t=361891 http://www.physicsforums.com/showthread.php?t=362282 Mark, if you are trying to resurrect your disproof of the concept of a sidereal year, this thread will get the same treatment it got at physics forums. We are quite open to discussion here if, on the other hand, you truly do want to understand the concept.

Executive order 9066 comes to mind.

They really need to fix the font on that graphic. The c's turn into o's. "dogs and oats living together" dang near made me spew on my screen. It's late, and I'm hundreds of pages into writing, what can I say. Let's take the argument that marriage exists because children need a stable family, a mother and a father. What then to do then about those heterosexual partners that either cannot or will not have children? Annul their marriage? Pester them with visits from men in black suits to get busy and have a baby? Personally, my wife and I, along with my daughter-in-law's parents, would really appreciate it if the IRS or some other agency would pester our kids with phone calls that ask "when are you going to give your folks grandchildren?" Our requests seem to fall on dead ears. The "children need a mother and a father" argument might be valid. Children with only one parent do tend to fare worse in many ways than those with two parents. Many a study has shown this. Has anyone done any studies on the outcomes of children with a two mothers, or two fathers? I suspect that the real factor that makes children from stable families perform better economically/psychologically/criminologically/whatever ility you like is not that a child has "a mother and a father"; it is that a child has two parents (period). Even if this is the case, is the difference so significant as to rule out gay marriages? Even if this is the case, there are certainly other avenues of redress that do not require discriminating against an entire class of people. That "even if" begs the question. Those who make this claim need to prove it, and really prove it. Discrimination is in general repugnant. I want to see solid evidence that gay marriage does indeed cause dogs and oats to live together. The real reason to ban gay marriages is of course that you gay people are scary, very scary -- you might make my children or my spouse turn gay (that should be on the chart, BTW).

That's how things work in (bad) science fiction movies. That is not how things work in the real world. To reenter that way would require using the equivalent of a launch vehicle for reentry. The launch vehicle to launch that big honking reentry vehicle would be immense, orders of magnitude larger than the biggest launch vehicle ever created. If that is how we had to reenter, there would be no reentry. Every flight into space would be a one-way journey. Think of it this way: Why use thrusters to bring the vehicle down to near zero velocity when the atmosphere does that for us for free? In fact, that Mars has an atmosphere that can do most of the work of slowing a lander but the Moon does not is why you will see claims that a trip to Mars is cheaper (fuel-wise) than is a trip to the Moon. Landing on the near airless Moon requires the use of thrusters all the way down. Vehicles that land on Mars can use some kind of aero-assist. Much higher. It is much higher than low-Earth orbit velocity of about 7.8 km/sec. For something reentering from geosynchronous altitude, reentry velocity is about 11.8 km/sec. That's high (higher than the Apollo reentry; it non-intuitively takes more energy to get to/from GEO than it takes to get to/from low lunar orbit) but it is less than the reentry velocity experienced by the Stardust mission (12.4 km/sec).

It does. Even if launched from the equator, that is a relatively small speed compared to the velocity needed to get into orbit: [math]v=r\omega = 6378\,\text{km}\cdot\frac{2\pi}{23.9344696\,\text{hours}} = 465\,\text{m}/\text{sec}[/math] Compared to the velocity of a vehicle low-Earth orbit (about 7785 m/sec), that 465 m/sec is pretty tiny. A geosynchronous satellite has a velocity of about 3,000 m/sec. That 465 m/sec? Not much. Moreover, launching vertically would be mind-boggling costly in terms of fuel. The gravity losses would be immense. A rocket launches vertically not because that is the "best" launch angle. A rocket launches vertically because the rocket would fall over were it tilted at the "best" angle. Suppose the vehicle is climbing. If it weren't thrusting, the flight path angle, the angle between the velocity vector and local horizontal, would decrease over time because gravity will reduce the vertical component of velocity. Because of drag, a non-thrusting rocket will have a zero angle of attack. Gravity and drag will turn the rocket. (Think of how an arrow flies.) Now suppose the vehicle is thrusting. The best angle at any point along the atmospheric part of the ascent is a zero angle of attack. Gravity (and drag) will turn the vehicle so by the time burnout occurs the vehicle is (a) at orbital insertion altitude, (b) is flying more-or-less horizontally, and © has a velocity that is close to (or even exceeds) orbital velocity. How does the satellite get to geosynchronous orbit? The payload of the main rocket is the satellite plus another rocket. That rocket will fire horizontally just long enough to make the orbit be an ellipse with apogee at geosynchronous altitude. The rocket+satellite then coast along this orbit. Ignoring correction burns, it doesn't fire again until it reaches geosynchronous altitude. Then it fires horizontally again to bring the vehicle up to geosynchronous velocity.

Some integer n is finite. Is it even or odd? Your question has pretty much the same answer. You have already been given example of a bounded series than converges and another that does not.

You have an error in that expression Ignoring that, you really should not be using [math]\epsilon[/math] here. Mathematicians use epsilon to denote a small number. This is talking about large numbers. In English, a series diverges to infinity if for any positive bound H, no matter how big, there is always some natural number N such that the absolute values of the partial sums Sn exceed this bound H for all n>=N. So what is the negation of this? Simple: The series is bounded. [math]\exists H\in \mathbb R^+:\,\forall n\in \mathbb N \ |S_{n}|<H[/math]

I didn't explain anything as a simple 1:1 relation. I just asked a question: How to explain the comparable warming from 1910-1940 versus 1975-2005? How do you know that CO2 concentrations are the dominant factor in the 1975-2005 interval? As you said, there other factors at play; the climate is complex. Is it just possible that these other factors dominated over the CO2 forcings during the 1975-2005 period as well? Note well: This is exactly what some legitimate climate researchers claim. Another key question: What is the nature of the feedbacks? This is one of the key questions. The IPCC posits significant positive feedbacks, others such as Lindzen and Choi posit negative feedbacks. The alarmist predictions in the IPCC reports fall apart without those significant positive feedbacks. I'm in the midst of writing a paper (overdue), so my participation is going to be a bit sporadic. I'll be back when I get another case of writer's block.

Janus is right. The vis-viva equation is [math]v^2 = \mu\left(\frac 2 r - \frac 1 a\right)[/math] The velocity of an object in a circular orbit at radius [math]a[/math] is thus [math]v = \sqrt{\frac{\mu}{a}}[/math] The delta-v needed to change a circular orbit at radius [math]a[/math] to an elliptical orbit with apogee [math]a[/math] and perigee [math]r[/math] is [math]\Delta v = v\left(1-\sqrt{\frac{2r}{a+r}}\right)[/math] For a geosynchronous satellite, a=42,164 km and v=3.0747 km/sec. You want to target an orbit with a perigee 60 km to 120 km above the surface of the Earth (RE= 6378 km). Targeting a 60 km altitude requires a delta V of 1.492 km/sec; for a 120 km altitude this reduces to 1.486 km/sec. Both are 1.5 km/sec to two decimal places.