Looking at the Greenhouse Effect without a control is kind of meaningless. Luckily we can look at Earth compared to a planet (Venus) that is 97% C02 and with an atmosphere that is extremely dense compared to Earth.  We can also look at a planet (Mars) that is 95% C02 and with an atmosphere that is extremely thin compared to Earth. What Greenhouse actions are going on there and do they indicate that Earth is capable of warming due to its particular carbon dioxide levels?

THE FOLLOWING CAME FROM A FANTASTIC PAPER BY PETER STALLINGA. HE TEDIOUSLY DEFINES AND QUESTIONS C02 BASED GREENHOUSE EFFECT MATHEMATICALLY. DIFFICULT TO INTERPRET BUT DEVASTATING ARGUMENT TO EARTH BASED C02 DRIVEN GLOBAL WARMING. 

Stallinga gives good perspective to blackbody temperatures of Planets when he stated:  We must remark at this moment that this is the temperature of Earth as seen from outer space. Irrespective of any greenhouse or other effect. If we, from outer space, point a radiometer at the planet it will have a temperature sig- nature of 254.0 K. (If we also include the visible light that is reflected (aS), then the total radiation power is equal to that of an black sphere with temperature T = 4 S σ 278.3=K ).

Looking at the three planets we can see that it is atmospheric density that drives atmospheric temperature, not presence or concentration of C02 :

Venus -  density 67 kg. / m^3 of which C02 is 64 kg. / m^3. Surface is liquid C02 @ 93 bar / 740 K (BB 227 K).

Earth - density 5 kg. / m^3 of which C02 is .002 kg. / m^3. Surface is gaseous @ 1 bar / 288 K. (BB 254 K).

Mars - density of .02 kg. / m^3 of which C02 is .02 kg / m^3. Surface is gaseous @ .006 bar / 209 K. (BB 210)

ie.  Mars has 10 times the carbon dioxide that Earth does but doesn't heat up. Earth heats up with only 1 / 10th the level of C02 of Mars but with total atmosphere density at 250 times that of Mars. Venus is crazy hot but there is so much gas in total AND it is present as C02 that it is literally liquid at its surface due to high pressure that no radiation reaches its surface from above. Instead the surface is heated from the dense hot atmospheric blanket covering it as a thick skin.

A. Does force of gravity cause the density of the Planets to differ?  

No, it might suggest it with Mars, but with Venus the force of gravity is almost the same as Earth and yet density is 13 times that of Earth.

Force of gravity - Earth 9.807 m/s^2,  Venus 8.87 m/s^2 , Mars 3.711 m/s^2   

B. Is it composition that causes the density of the Planets to differ?

Venus is 96.5% Carbon Dioxide which is a relatively dense gas, Earth's is 78% nitrogen, 21% Oxygen.

Venus would most likely have had more nitrogen, oxygen and even water when it formed, just like the early Earth. What happened was a runaway green house effect that heated the planet up, releasing its surface water to steam, and gas.

That was coupled with its lack of magnetic field, which either never quite formed or shut down. This meant the atmosphere had no protection from the solar wind, which split any water to Oxygen and Hydrogen. These lighter elements were stripped away by solar radiation, giving them enough energy to escape into space leaving only the heavier carbon dioxide remaining.

Venus also does not have plate tectonics, which means that carbon dioxide does not get captured in rocks that go back into the hot mantle. In fact Venus has, and did have volcanic activity the added more carbon dioxide into the atmosphere.

The early Earth has a similar build up of CO2, but life emerged (plant life) that began to break down CO2 to carbon and oxygen. This did not happen on Venus, the carbon just kept building, and the thick blanket of CO2 heated the planet yet further.

With no plate tectonics and plant life to act as a brake, the whole thing became a feedback loop, lighter elements escaped and there was no method to take CO2 out of the system.

We now see a dense thick CO2 atmosphere, and the heat absorbed means no chance of any atmospheric or surface water. Venus was most likely a warmer twin of the Earth early on, it may well have had plate tectonics, and oceans. The water went, the recycling of the crust stopped, and now Venus is the nearest thing to hell in the solar system.

C. Is it Composition AND force of Gravity that determines the density of atmosphere in the Planets?

This might make sense. We know on earth that density of the atmosphere is consistent with the force of gravity exerted on it (ie. gets thinner with height), and it makes sense that this works on the other Planets too. With Mars, the force of gravity is much lower than Earth and so we'd expect that the atmosphere next to the surface would be lower than Earth as gravity will not "pull" the molecules together as strongly as on Earth. With Venus, gravity is almost the same and differences are relatively minor, so why is Venus so much more dense? The answer must be that it is carbon dioxide and sulfuric acid, both immensely heavier than the gases composing Earth's atmosphere and "pulling" together under the same force to a much tighter mass than Earth's gases. Mars, even though made up of the heavier gas as well, simply doesn't have enough of it to form an atmosphere deep enough to show the density and the lower force of gravity also doesn't pull it as hard. 

D. Is the mere presence of Carbon Dioxide causing the Planets to be Hot or Cool? 

All in all, purely physical mechanisms are heating and cooling these planets. There is no magical chemistry going on that involves carbon dioxide's magical properties of absorbing long wave IR. 

E. Is it the depth of the Atmosphere that causes Planets to be warm or cold?

We have a problem with visualization. When we think of the Planets we tend to think of a thick "blanket" of gas covering a large ball of solid / liquid material that constitutes the "planet proper". The Atmosphere becomes magnified in size and the Planet minimized as a result. But this is wrong.

The atmosphere is much more similar to a "skin" or even a "wax coating" , similar to the skin of an apple or even the wax coating that is put on the skin of the apple. Compare the depth of the atmosphere to the depth of the Earth.

Radius of the Earth =                     6400 km.

Depth of the Atmosphere =                64 km       =      1% of Earth's total radius.

Depth of Earth's Crust =                      32 km      =       .5% of Earth's total radius.

So, let's use an Apple as a metaphor for the Earth (and other planets) and see if it gives perspective to the relative depth of each of Earth's components. 

 The pith is the core of the apple, the skin is the crust and the invisible wax coating is the invisible atmosphere. 

So, if our Atmosphere is the "wax" that protects the surface from the damaging effects of the Sun (could have  used a car analogy too, I guess) then the "formula" of that wax and the density of that wax will determine the properties not only of Sun shielding but also cooling of the surface below it. 

This is the way to compare. 

HOW DO HUMANS FIT INTO THE PICTURE

As Humans, we live "on" the surface of the Earth but we also live "within" the materials that constitute the protective coating or atmosphere. We scar the surface of the Earth to support our lifestyles but it is the atmosphere that we "feel". It is the Atmosphere that brings us personal warmth, cold, wetness, wind, or transmits the rays of the Sun directly through itself to land upon our bodies and give us heat and perhaps sunburns. The character of the Atmosphere concerns us because it dominates our own personal existence and we don't like the thought of losing its comfort, warmth and well being. 

So, if we think we are adversely altering this life fluid we get concerned - really fast - and we start to run around in circles in our efforts to force things back to "normal". Impossible to do, but nevertheless, we try....

AND WHAT IS IT THAT WE THINK WE HAVE DONE, EXACTLY?

We think we're screwing up the formula, altering the composition of our protective coating and allowing the Sun to penetrate it in ways that it has entered a stage where it and the surface it contacts are warming up. We say that this warming affects the "fluidity" of the coating and as such it creates weather patterns that are discomforting and adversely affect our well being (remember, we're not much more than microbes swimming around in this stuff).

These changes in composition involved increasing the levels of carbon dioxide because of our need to burn fossil fuels to give us energy which drives our societies. By changing the "mix" in this manner we have apparently decreased the quality of the atmosphere we live in and we are beginning to feel the effects of our folly in doing such a thing.  

Our answer to this degradation ? - stop adding more carbon dioxide to the blend by eliminating fossil fuel burning and if possible find ways to remove the C02 we have already added to the atmosphere and "put it back in the ground".