Orbital Mechanics for Dummies - Orbital Energy

Now we're going to consider the energy in an orbit, and we'll consider two forms of energy: kinetic energy from the speed of motion around the central body; and gravitational potential energy by virtue of the forces in a gravitational field, (which we'll call gravitational  energy for short).

First we need to consider a reference point.  Here on Earth, it is tempting to consider being at rest on the ground to be the zero orbital energy point.  But that means for flight between different planets we have different references to consider and that won't do.  The solution is to consider the reference point to be stationary at an infinite distance from the central body, where the gravitational field is zero.  Then we can use this reference for flight between as many different bodies as we wish.

Kinetic energy is easy, and from high school physics I remember it is given by

E_k = ½mV²

But from our equation [1] we found that in a circular orbit,

V_C² = GM/r

So in such an orbit,

E_k = ½GMm/r = GMm/2r   [2]

This is an important equation and we'll call it [2].  Just take a moment to consider what this means: the kinetic energy of a body in circular orbit is proportional to the masses of the bodies, and inversely proportional to the distance between them.  So as the mass of either body increases, so the kinetic energy increases.  As the distance increases, so the kinetic energy decreases.  This fits with equation [1] which told us that as distance increases, so orbital speed decreases.

Now gravitational energy is a little harder to understand.  It is the work done by gravity to bring a body from infinite distance to a radius r from the central body.  At each step along the way, the gravity from the central body applies a force of GMm/r².  At each step dr along the way from infinity to r, the work done is the force GMm/r² multiplied by the distance dr.  And we add all those steps together by integrating the force from infinity to r as follows:

If calculus puts you off, feel free to take my word for it and skip to equation [3]

E_g = ∫_∞^r GMm/r² dr 

=  GMm  ∫_∞^r 1/r²

= GMm  [-1/r]_∞^r

= -GMm  [  (1/r)  - (1/∞) ]

= -GMm  [  (1/r)  - 0 ]

E_g = -GMm/r     [3]     <= equation [3]

This too is an important equation and we'll call it [3].  Just take a moment to consider what this means: the gravitational energy of a body in circular orbit is proportional to the masses of the bodies, and inversely proportional to the distance between them.  But it has a minus sign, I hear you say.  Yes indeed, and that means that gravitational energy increases (becomes less negative) as an object is lifted away from the central body.  That fits with the idea that energy is required to do work in lifting the object.  It also has some convenient consequences for orbital mechanics which we'll see later on.

Now that was the hardest piece of maths we'll do in this series, and there is no further calculus at all!  Whether you followed the integration or skipped it, please go back and make sure you understand these two energies because they lay the foundation for truly understanding orbits, and all kinds of interplanetary travel.

To wrap up orbital energy, we'll add kinetic energy and gravitational energy together into a single value.

E_o = E_k + E_g

= GMm/2r - GMm/r

E_o = -GMm/2r     [4]

Notice that orbital energy is negative, and increases in value as radius increases.  It's as though this energy represents how far the body is located down into the gravity well of the central body.  And if you imagine raising this energy past zero to a positive value as representing the orbiting body climbing out of the gravity well, then this will lead nicely on to the concept of escape velocity which we'll cover next time.

That's enough for this post.  Next time we'll consider how energy oscillates between kinetic and gravitational energies in elliptical orbits, and look at escape velocity.

Orbital Mechanics for Dummies - Kepler's Third Law

This post is an aside.  Here I show how to prove Kepler's third law of planetary motion from what we have done so far.  Nothing which follows depends on it, and if you choose to skip this post then you will lose nothing of substance from the series on Orbital Mechanics.

Kepler's third law states that

the square of the period of a planetary orbit is proportional to the cube of its distance from the Sun.

In one orbit, the orbiting body travels a distance equal to the circumference of the circle with radius r.  This distance is 2πr.  So the time taken to travel this distance, or the period of the orbit in seconds, P, is given by

P = 2πr / V_C

Taking the square of both sides gives

P² = 4π²r² / V_C²

Now from our last post we know that

V_C² = GM/r

Putting this into the equation for the period squared gives

P² = 4π²r² / (GM/r)

which simplifies to

P² = 4π²r³ / GM

Now if this equation is applied to planets orbiting the Sun, then the square of period of the orbit, P², is directly proportional to the cube of the distance from the Sun, r³.  So we have proved Kepler's third law.

Orbital Mechanics for Dummies - Circular Orbits

Last time we looked at the kinds of basic orbits, and gave a description of how the orbiting body moves in each.  Now we will dip our toe in the maths water.

The first step is to define the parameters of the orbit, according to the following diagram.

M is the mass of the central body, in kilograms (kg).
m is the mass of the orbiting body, in kilograms (kg).
r is the orbital radius between the centres of the bodies, in metres (m).
v is the speed at which the orbiting body moves around the central body, in metres per second (m/s).

There are a few other parameters we'll use along the way:

G is Newton's gravitational constant, and is equal to 6.67 x10^-11 m³/kg/s².

V_C is the speed of a body moving in a perfect circular orbit, in metres per second (m/s).

V_E is the speed of a body moving just fast enough to escape from orbit, in metres per second (m/s).

A is an acceleration, expressed as a change in speed per second (m/s²).

From the previous post we know that for a circular orbit the orbiting body moves under centripetal acceleration which is provided by the gravity field of the central body.  So we need formulae for both centripetal acceleration and gravitational acceleration.

From high school physics we recall that centripetal acceleration is given by

A_C = V²/r

and gravitational acceleration is given by

A_G = GM/r²

Now since centripetal acceleration is provided by gravitational acceleration, A_C = A_G so

V²/r = GM/r²

and because we can eliminate the /r on each side, and in a circular orbit V = V_C

V_C² = GM/r  [1]

There we have it, our first equation for orbital mechanics.  Wasn't so hard, was it?   It's such an important equation that I've labelled it [1] so we can refer to it again.  What it tells us is that the square of the orbital speed is proportional to the mass of the central body, and inversely proportional to the orbital radius.  The constant of proportionality is Newton's gravitational constant.

Example

To try this out, let's work out how fast the International Space Station (ISS) travels around the Earth.  As I remember, it's around 17,500mph.  But can our equation [1] confirm that?

The mass of the Earth is 5.97 x10²⁴ kg.

The radius of the Earth is 6.37 x10⁶ m.

The ISS orbits at 350km above the surface, so the orbital radius is 6.72 x10⁶ m.

V_C² = GM/r = 6.67 x10^-11 x 5.97 x10²⁴ / 6.72 x10⁶ = 59.3 x10⁶.

Taking the square root gives

V_C =7,700 m/s.

Since there are 1,610 metres in a mile, and 3,600 seconds in an hour,

Orbital Speed = 7,700 x 3,600 / 1,610 = 17,200 mph.

That works for me!  Next time we'll take on the giant of orbital mechanics and prove Kepler's third law.

Orbital Mechanics for Dummies - Orbital Basics

I’m going to deal with very simple situations, as these make both understanding and the maths easier, and most real situations can be usefully approximated by these simple cases.  The central body is vastly more massive than the orbiting body, so we can consider the central body to be fixed, and just work on the orbiting body.

The simplest orbit is perfectly circular.  The orbiting body moves in a circle at just the right speed so that its centrifugal force is precisely balanced by the gravitational force between the bodies.  We will call that speed V_C.

Now physics purists will tell us that centrifugal force is an illusion, so to satisfy them we’ll consider acceleration rather than force and describe the orbit as the path where centripetal acceleration is provided by the gravity of the central body.  We’ll do the maths for this in the next post.  For now, here’s the circular orbit as a diagram.

A variation of this orbit is the elliptical orbit.  If at point A the orbiting body accelerates by a small amount, (less than 41% of V_C), then as it proceeds around the central body its extra speed will cause it to climb away from the circular orbit path.  As it climbs against the force of gravity from the central body, the orbiting body decelerates.  It reaches its furthest point at B, directly opposite A, and begins to accelerate back towards the original point A once again.

 

Point A, the closest to the central body, is called periapsis.  Point B, the furthest from the central body, is called apoapsis.

When the orbiting body is at point B, it is travelling more slowly than the circular orbit speed, V_C’, at that radius from the central body.  Now if the orbiting body accelerates again at point B, to V_C’, it will follow a new circular orbit passing through B.

 

This kind of manoeuvre, where an elliptical transfer orbit is used to change between orbits of different radii, is used frequently in space flight.  Some satellites are put into geostationary orbits, where they orbit once in 24 hours and appear stationary over particular points on the equator as the Earth rotates.  When a geostationary satellite is launched, it is inserted into a transfer orbit with apoapsis at the geostationary radius.  Then a dedicated engine is fired at apoapsis to accelerate and achieve a circular geostationary orbit.  A variation of this kind of transfer orbit was used by Apollo spacecraft to reach the Moon.

Finally, if the orbiting body accelerates by 41% of V_C or more, then this speed causes it to climb away as before, but this time it is travelling fast enough that the gravity field from the central body reduces more quickly than the body decelerates, and the body continues climbing indefinitely.  The body has exceeded the escape velocity, V_E, has escaped the gravity field and will not return.

These are the basic principles to grasp for now.  Next time we will look at some simple maths to describe these different cases.

Orbital Mechanics for Dummies - Introduction

I have been following the Dawn mission to asteroid Vesta with keen interest.  The mission team is relying on simulation data because for various reasons accurate measurements of the probe's position are only available occasionally.  The probe is expected to achieve orbital insertion around Vesta today, but without accurate data not available until tomorrow, we can only speculate on whether orbit has been achieved.

For hour-by-hour data, the team relies on the MYSTIC simulator.  This gives vital data including Dawn's speed in relation to Vesta, and its range to the asteroid.

I'm no rocket scientist, but I do have basic skills in physics and maths, and a keen interest in space flight.  A number of years ago, I worked out my own very basic system for understanding orbital mechanics, including the basic equations for simple orbits, from first principles.  I used these, with the simulation data, to show that Dawn appeared to have achieved orbital insertion around Vesta earlier this morning.

I have discussed my calculations with others interested in this mission.  It occurs to me that there may be other keen amateurs out there interested in understanding the basics of orbital mechanics.  So it is my intention to publish a series of posts on the subject.

It won't be for everyone, by a long way.  But if you have a good grasp of high school physics and maths, you should be able to follow along.  My own maths ability reached its limit shortly after high school level, so I haven't included anything too demanding!  It also won't satisfy real rocket scientists, who use levels of calculus way beyond me and can tell you all the fundamentals I've missed out.  However, if my basic version is flawed rather than just simplistic, then I'd really like to be corrected so please do get in touch!

If you're interested, keep an eye out for my following posts which detail my Orbital Mechanics for Dummies...

By the way, the title is not intended to patronize.  I consider myself to be a mathematical dummy, at least compared to the abilities of my peers when I was studying.  My aim is to use my limited skills to understand how orbits work, and how to work out their parameters.  There are plenty of more complete works on the subject, but this is intended to be an easy entry.

Are humans immune from extinction?

Steve Zara made interesting post about a discussion PZ Meyers is having on Twitter.  Steve argues that humans have developed technology which is close to bringing human evolution to a halt, that we will soon leave Earth and colonise the solar system and thereby become immune from global catastrophies.

I would like to explore a counter argument: I maintain that humans are still subject to natural selection.

The greatest selection pressure of all is death of an embryo or foetus from developmental defects - such as a missing circulatory system - which make development impossible.  The majority of fertilised ova do not survive to birth, and many of these don't even make it to implantation.

We have made great strides in combating disease, yet we remain in a microbiological arms race.  Modern medicine provides an enormous selection pressure on human pathogens which are evolving to get around it.  MRSA and C-Diff are examples.

Our abilities to survive modern diets also provides selection pressure.  We have evolved the ability to digest lactose into adulthood within the last 10,000 years, since we domesticated dairy animals.  No other mammal species can do this.

We haven't colonised space yet, and in my opinion it will be some considerable time before off-world colonies become completely independent of humans on Earth, if ever.

We need only a pandemic which wipes out enough people that space travel is abandoned as an expensive luxury.  Then we are all eggs back in the same basket, and vulnerable to global catastrophe.

Finally, the very technologies which allow us to manipulate ourselves and our environments, makes us vulnerable to the failure of those technologies.  A catastrophe which disables modern communication, high-tech industry and global commerce, would leave people with complex prostheses or reliance on drugs for survival, facing imminent doom.

I know how long it takes me to be debilitated when my internet connection goes down, but if it never came back up, or I could never buy car fuel, pay with a credit card or shop for food, I'd be back in the pre-industrial age in days.

I have great confidence in human adaptability, ingenuity and ability to survive extreme conditions.  But I don't think we're any more immune from extinction than the dinosaurs were.

Why versus How

I've just been looking through The Really Simple Guide to Humanism, (which is an excellent introduction btw), and in particular a video on the question Without a God, or religion, why should we care about anything?  About 2/3 of the way through, Colin Blakemore brings up an old point that science should address questions of how and leave questions of why to religion.  Of course, in the context of humanism, this means the why questions are suspicious back doors into religious thinking.  But I fundamentally disagree.  And here's why.

Why addresses issues of greater complexity than how typically does, but that does not mean the question presupposes that the answer makes reference to an intelligent agent.  And the biological answer to why am I here is substantially different from that to how did I come to be here.

How did I come to be here prompts an answer which addresses the biological mechanisms around reproduction.  It may include sexual dimorphism, meiosis, fertilisation, mitosis and embryology.  It is a perfectly valid discussion to have, but has a narrower scope than discussions which why questions prompt.

Why am I here prompts a biological explanation which is far more profound, and addresses fundamental questions of existence, which are not the exclusive domain of religion.  For example, I may answer that you are here because your parents succeeded in making you, that their parents succeeded in making them, and that every one of your ancestors, unlike most of their competitors, succeeded in leaving offspring who also succeeded against the competition to leave offspring.  I could go on to point out that some of the reasons your ancestors succeeded was because they happened to have combinations of genes which made them well adapted to successfully reproduce in the environment they lived in.  Finally, we could consider that your ancestors were also successful, in part, because they passed on the genes which gave them their success, and that you are likely to possess many of those successful genes yourself.

So why am I here can prompt a discussion of the fundamentals of evolution which are often beyond the scope of how questions.  Why would any thinking person want to dismiss that?

Awesome

I am beginning to hate the word 'awesome', with a passion!

How can I be so animated by a word?  Well I'm not, but I resent its use, and try as I can, I can't think of a single instance where there would not be a better choice.

It has no descriptive power and seems to be used as a place holder for a superlative adjective which the speaker can't be bothered to think of. It's this capacity for the word to dumb-down the articulation of the speaker which I resent.  Life and language are rich, powerful and colourful.  The word 'awesome' is mid-grey, colourless, non-descriptive and above all thoughtless.  It could be anything: 'blah' would do just as well.  "Oh your shoes are just blah" says precisely as much as "Oh your shoes are just awesome".  In either case it gives an impression of being disingenuous; of having to say something positive but having nothing positive to say, except perhaps that we have seen 91210.

Just imagine what we could say in its place to describe 'awesome' shoes.  We could say something like: creative; thought provoking; imaginative; beautiful; elaborate; colourful; stylish; unique; fashionable; stunning; irreverent; sexy; outrageous; delightfully expensive;... you get the idea I'm sure.  And if it's not shoes, the possibilities increase considerably.

But what if you want to describe the shoes being so singularly unique that they inspire genuine awe? Then they are truly 'awe inspiring'.

I can see no point in the word 'awesome' at all.

Homoeopathy Consultation

The Medicines and Healthcare products Regulatory Agency (MHRA) has called for consultation on changing the regulation of homeopathic products.  Replies must be submitted by Fri 18 Feb 2011, so this post is up to the wire.  Read the consultation document here http://bit.ly/g0rSig

Here is a proposed reply, for those wishing to add support for evidence based medicine in this regard.

To: andrea.farmer@mhra.gsi.gov.uk

Ms Andrea Farmer
MHRA, Area 5M
151 Buckingham Palace Road
Victoria, London SW1W 9SZ

...date...

Dear Ms Farmer,

I am writing to you about the MHRA consultation document entitled "Review of Medicines Act 1968: informal consultation on issues relating to the PLR regime and homoeopathy".

As a member of the public who values evidence based medical practice, and recognises the dangers inherent in misleading claims for medical efficacy, I am deeply concerned by the current orchestrated campaign in support of unproven homoeopathic treatments, and their potential to delay or avoid the application of proven medical therapies, which is led by self-interested homoeopaths.
I consider it to be a fundamental duty of a democratic society to ensure that patients and clinicians are provided with clear information about potential remedies which is founded on reliable scientific evidence. This includes homoeopathy, the efficacy of which, as you know, is not supported by the current scientific consensus.

I contend that the marketing of any substance which may be offered for sale or application, with an implied or explicit claim of medical efficacy, and which may be considered by patients or clinicians to be suitable as a substitute for, or an addition to, conventional therapeutic remedies, should be subject to the same Marketing Authorisation (MA) requirements as the therapeutic remedies for which they may be substituted.

Therefore I strongly urge the MHRA to move homoeopathic products to full Marketing Authorisation (MA) requirements, rather than the NRS or simplified scheme.

Yours sincerely,

...name...

...address...

The human fingerprint in global warming?

The human fingerprint in global warming

There are highly polarised views on the subject of climate change, with extremists on both sides accusing the other of misinfomation and worse.

So I was very interested to read the article on the left here which explains the science behind the claim that human activity is contributing to climate change. Helpfully, it even gives explanations at basic, intermediate and advanced levels. And for the science buffs out there, the levels do concentrate on different aspects so all levels are worth a read.

 This prompted a good discussion with a relative who is skeptical of human influence on climate.  Neither of us are extremists, both enjoy exploring ideas, and we had an enjoyable dialogue.  So I though it may be worth relating the conversation here:

Billy: For anyone interested in the Climate Change debate, an excellent explanation of the science behind the consensus that it is caused by human activity. In basic, intermediate and advanced forms, dig as little or as much as you like! http://www.skepticalscience.com/its-not-us.htm

Harvey: Ooooh scary scary - how will we cope with a degree extra over the next few decades!

Billy: Ah, no longer denying climate change, or that it is man-made, but now saying it doesn't matter. Climate skepticism to climate apathy. That's progress of a sort, I guess. ;-)

Harvey: Here is my kitchen logic:

I hope we can agree on the fact that oil will run out within circa 60 years forcing a switch to another fuel, almost certainly one that does not emit CO2. Agree?

Given that even your wildest predictions for temp rises in the next 60 years amount to not very much, what the heck is all the fuss about?

Billy: I guess the known oil reserves may well run out in 60 years, but there are ever more places opening up to exploration. Plus there extraction of coal is largely a matter of economics: as easy coal runs short, prices go up, so currently uneconomic resources become viable again. But you're right, there is a finite limit.

I don't make predictions for temp rise: I don't have the knowledge or data to make predictions. I could join you in the kitchen and make a stab at it. First of all, I'll see if I can find a published prediction with a reasonable pedigree. I'll get back to you...

Billy: Okay. Starting with the supposed link between CO2 levels and increased global temp. Bear with me, because this may give us an idea of how much warming can be expected.

The physics of CO2 heat absorption are well understood, and easily demonstrated in the kitchen. But if for a moment we set that aside, is there evidence of correlations between CO2 and temp from the past to back it up?

Vostok temp, CO2 and dust. Petit et al, 1999

I found a paper by Petit et al in Nature, (Nature 399, 429-436 3 June 1999) http://bit.ly/fdIy3Y. The important part is a chart http://bit.ly/cW44Ur showing changes in temperature, CO2, dust, all revealed in ice cores from the Vostok ice station in Antarctica.

There is a striking correlation between changes in CO2 and changes in temp. When CO2 rises by 100ppm, Vostok temp rises by 10°C. Now Vostok temp is not global temp, but it's a good place to start.

Take a look at the data, and the peer reviewed paper it comes from. Do you see what I see? If not, do you have similarly reputable evidence for a different conclusion?

Harvey: Like I said before, I don't buy into the causal link between CO2 and significant climate change. But suspending judgement, what is your best guess at climate change over the next 60 years...? if this is small then it doesn't matter who is right....

Billy: Did you see the chart in my previous post? Do you have better evidence to the contrary or does the evidence perhaps not matter? If you do have contrary evidence then I'd be delighted to see it.

I'm not a climate scientist, so following you into kitchen science is rather dubious, but perhaps it's the best I'm equipped to do. Taking the recorded trend showing that in the 30 years from 1975 to 2005, global average temp rose 0.6°C, then if we simply extrapolate that over the next 60 years then there could be a further rise of 1.2°C, making a 1.8°C rise since our childhoods.

You may say that 1.2°C or 1.8°C is not much, and on any individual day that may be true. But if you are familiar with the normal distribution curve, if you were to take the number of days of extreme high temp in the 2000s, (say the top 1%), shift the curve right by 1.2°C, you'll see that there is a large increase in the number of days with extreme high temp (above the same temp limit as before). Given that a heatwave in 2005 killed 3000 people in France, such a rise is anything but trivial. And that's leaving out the effects on agriculture, desertification, energetic extreme weather events, changes to the distribution of air and ocean currents and sea level rise through melting ice over land masses.

Furthermore, your assertion that we'll run out of fossil fuels in 60 years is far from certain. Known coal reserves are estimated at between 150 and 400 years, and that ignores any reserves yet to be discovered.

My projection ignores any positive feedback effects of warming, which could include the release of CO2 from thawing polar permafrost and the release of methane from the sublimation of deep ocean methane hydrates. The record from the last 420,000 years shows sharp and large temperature rises, with slower and moderate temperature falls. Such positive feedback effects could explain these sharp rises. Once the climate begins to warm, there is good reason to suspect it could continue to warm substantially, as it has before.

The climate science, based on peer reviewed scientific studies, rather than the opinion columns of novelists like James Delingpole, seem to suggest that we are indeed changing our climate. But if you choose to take your science from the Mail or Telegraph rather than Nature or Science, then I can understand your point of view.

Harvey: Yes, I did look at the chart... great to see that over thousands of years the variation in temperature was well within the range of -11 to +3°C. This is in-line with your estimate of 1.2°C rise over the next 60 years, which is pretty underwhelming.

Peak oil production. Hubbert, 1956

I also think 60 years is a pretty conservative estimate about when the oil is likely to run out: http://en.wikipedia.org/wiki/Peak_oil (are you really saying we will then use coal as a starting point for oil?!).

So we are left with the fear of an increase in extreme climatic events...which will never grab attention compared with the far greater and more immediate threats now facing mankind, such as Malaria or a host of preventable diseases, etc..

The church grabs our attention by suggestion we will go to hell if we don't listen to their doctrine.... which does kind of grab your attention for a few minutes. A rise in temp of 1.2C before the problem starts to go away does not grab the attention and that's why digging into the science (taking us away from our beloved Mail and Telegraph) is about as likely as a straight hockey stick ....

Billy: Ah, I think we need to understand what effect a comparatively small rise in MEAN GLOBAL temperature could have. It certainly does not mean that your peak daytime temperature in Switzerland, or mine in England, would rise by 1.2°C. That alone would be underwhelming, I totally agree with you there.

2000 year global temperature. Rhode, 2005

The mean temperature http://bit.ly/WM6bT appears to have risen by 0.7°C from the past 2000 year mean to 2004. This swamps the medieval warm period (0.3°C warmer) and the Little Ice Age (0.3°C cooler). Neither of these periods would been identified if the actual temp in a particular place had changed by only 0.3°C.

These periods saw far greater localised changes, including droughts, famines, removal of and re-establishment of Atlantic pack ice, and growth and abandonment of Viking settlements in Greenland and Newfoundland. If that is what 0.3°C fluctuations can do, a rise of 1.2°C from now, totalling a 1.9°C rise from the past 2000 year mean, is likely to be more severe.

Why haven't we seen these changes yet? I don't know that we haven't. Most likely the changes so far are brushed off as being random variations, but there SEEMS to be a large amount of small pieces of evidence for change. Extreme hot-Summer and cold-Winter weather in Europe, increasing anoxia in the Gulf of Mexico (due in part to pollution but also due to water temp rise), increases in flash floods, generally strengthening El Nino cycles, retreating glaciers, breakup of Antarctic ice shelves and measurable rise in sea level. I don't know how long it takes for the Earth to respond to temp rises, but I can't conclude it's not already happening.

We use oil for many things, not just transport. Many power stations are oil- and gas-fired. And as these decline, without a change in approach, coal is very likely to take over. Even if we switch to H2 or direct electric drive for vehicle power, these both require power generation, and that could well be from coal which could last hundreds of years more.

Temperature of Planet Earth. Fergus, 2008

The -11°C to +3°C variations you see at Vostok (I see -9°C to +3°C, but whatever) correspond to 3°C swings in mean global temp http://bit.ly/dRl3Wf. These global swings correspond to ice age glaciations which saw half of Europe, (including the UK and Switzerland) under ice kilometres thick. In the last 100 years we have changed the global temperature by half that already, and there is little sign of it failing to continue.

On that basis, personally I think a further 1.2°C rise, on top of the 0.7°C rise which appears already to have taken place, is anything but underwhelming.

That's why I think digging into the science is not only justified, but a responsibility for a thinking consumer. Even if that's not the way for churches or newspapers! Not everyone needs to agree on the conclusion, but I would not sleep well if I didn't make the effort to understand enough to justify the conclusion I've come to. But what to do about it......? I don't know where to start on that one!

Harvey: Your latest graph shows a span in temp over the past 2000 years of circa 1.2°C, a time that has been relatively unremarkable in terms of climate. Truly underwhelming as a threat to threat to civilization.

Billy: I wouldn't call differences between fully developed agriculture in Greenland during the Medieval Warm Period, and annual festivals on the frozen Thames in the Little Ice Age unremarkable, and that was during the period when the range was 0.8°C at most. The increase to 1.2°C has been in the last few decades, and I don't know what lag to expect between rises in mean temp and changes in climate behaviour.

Atmospheric CO2. Mauna Loa, Hawaii

While I think there is good reason to expect substantial effects from the 30% increase in CO2 we've undoubtedly caused already http://bit.ly/4uOScd, I do depart from the 'end-of-the-world' extremists, and the laughably gullible 'day after tomorrow' panickers. Millions may die, nations may revolt, wars may be fought, islands may be inundated, species may become extinct, but mankind will survive and thrive in adversity just as it did through previous ice ages. We're as good at adapting as rats are!

Harvey: And here we converge! Thanks, that was fun...

Billy: Knew we'd get there in the end. :-)

Shermer's Hierarchy of Needs

In his blog article The 'Point' is beside the point, Michael Shermer presents a truly updated, neo-darwinian version of Maslow's Hierarchy of Needs which provides a foundation for discussing a humanist (non-theist) basis for ethical individual and social conduct. Click the image below to read the article.

Leave Your Child Behind