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 Originally Posted by CoccoBill
... wouldn't even a slight change in velocity, even the tiniest bit of acceleration or deceleration cause the planet to either get loose or crash?
Most accelerations would only result in a different shape of orbit (a change in the eccentricity of the ellipse), and a different orbital period. Only when 2 bodies are moving near their escape velocity and some interaction accelerates them to or above the escape velocity would they break orbit. Anything which reduces the relative speed would result in another "stable" orbit, or a collision.
Originally Posted by CoccoBill
Well, it's a logical fallacy. The ones with the incorrect speed have indeed already left the orbits or will do so later.
There is a lot of random motion is the early formation of a stellar system, and the localizing of the masses causes more and more instability in the surrounding areas. Planets "clear" their orbits, either by accretion, or by "swinging" smaller bodies away from the orbit. Most of these swings leave the smaller body moving out of the solar system.
Originally Posted by CoccoBill
None of the orbits are stable
The notion of stability is clear in the 2 body problem, but that's not the whole picture. There are thousands of bodies in the solar system. That's not really the issue here, as you've stated. The real issue is that we've been talking about stability without giving a time frame.
"In the long term Pluto's orbit is in fact chaotic. While computer simulations can be used to predict its position for several million years (both forward and backward in time), after intervals longer than 10–20 million years, calculations become speculative: Pluto's tiny size makes it sensitive to small details of the Solar System, hard-to-predict factors that will gradually disrupt its orbit." ... "This does not mean Pluto's orbit itself is unstable, but its position on that orbit is impossible to determine so far ahead."
- Wikipedia "Pluto"
Your info about the orbits of the moon and Earth are solid, to my knowledge.
Originally Posted by CoccoBill
Another effect is that due to the sun being powered by nuclear fusion, it's continuously losing mass.
The mass loss is not strictly due to fusion, merely that its temperature is above absolute zero is enough. Anything with a non-zero temperature is radiating heat (by way of releasing photons through blackbody radiation). Heat is a measure of energy. The object releases energy, therefore the object loses mass, QED.
The mass loss rate of the sun, based on E = mc^2 (m = E/c^2), and dividing both sides of the equation by time is:
Solar photon energy output at Earth: 1,368 W/m^2
Earth's mean orbital distance: 149.6 x 10^9 m
Surface area of a sphere with that radius: 4*pi*r^2 = 2.812 x 10^23 m^2
Total photon power output of the sun: 1,368 W/m^2 x 2.812 x 10^23 m^2 = 3.847 x 10^26 W
Speed of light: 2.998 x 10^8 m/s
Speed of light, squared: 8.988 x 10^16 m^2/s^2
Solar mass loss rate: 3.847 x 10^26 W / 8.988 x 10^16 m^2/s^2 = 4.281 x 10^9 [units]
W = J/s = kg m^2 / s^3 ; [units] = kg/s
Solar mass loss rate: 4.281 x 10^9 kg/s
That's over 4 billion kilograms per second in light alone! Oh yeah, the sun's mass is roughly 2 x 10^30 kg, so dropping 10^9 kg/s is nothing at all.
The fusion processes release veritable torrents of neutrinos, which also contribute to the mass loss rate. Neutrinos are incredibly abundant, but are nearly mass-less and interact so weakly that they are difficult to detect. In fact, billions of neutrinos have sped through your body at nearly the speed of light during the time it took you to read this sentence. If it's night time, those neutrinos passed through the planet before they passed through you. How cool is that!?!
Even still, as you've stated, the total mass loss rate is negligible when compared to the sun's mass. More relevant is the natural evolution of a star like our sun. While remaining constant in temperature, the sun's size and luminosity increase over time. In about 1 billion years, this increase will be enough to boil the earth's oceans.
... but what if global warming is a fraud, and we make the world a better place for nothing?
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