"But can't I say it only traveled 9/10 of the way there, and then another 9/10 of what remained, and then another 9/10, and so on?"

This kind of reasoning was discussed already in the 5th century BC in what is known as Zeno's paradoxes. Most famous is the story about Achilles who was never able to overtake the tortoise, since Achilles must first reach the point where the pursued started so that the slower always will hold a lead. Another one is that in order to get from A to B, you must get halfway, and before you get to the midpoint, you need to get halfway to the midpoint, and so on, meaning that you need to complete an infinite number of actions before reaching B, which is impossible.

Based on this Zeno concluded that motion is an illusion.

The color of organic plants/flora/chlorophyll, would they be affected by a world's distance from the sun at all? I don't know if plants would still be green on a hypothetical temperate terra orbiting Jupiter, for instance.

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It would probably depend not so much on the distance, but rather the color of the host star. Increasing the distance diminishes the intensity of the sunlight, making photosynthesis less efficient, but star color affects the wavelength, which suggests a different optimal photosynthetic pigment. You can check this thread for some cool ideas about how that might work.

Thank you for that link! I was looking for it earlier but couldn't immediately find it. Kudos!

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Watsisname, Well, if you think that you can walk thru Earth in a straight line for an infinity time, that's somehow an infinity distance, even if it's a limited surface. That's how I imagine the Universe might be infinity as well, and that's what I'm asking.

HarbingerDawn, exactly! That's the word to explain what was on my mind haha. Take a look at this video, this theory looks interesting. Is it possible or can be easily proved wrong?

It would probably depend not so much on the distance, but rather the color of the host star.

If you're going to have photosynthesis at Jupiter's orbit, it might be best to have plants be deep red, deep blue, or black...

Living among the stars, I find my way. I grow in strength through knowledge of the space I occupy, until I become the ruler of my own interstellar empire of sorts. Though The world was made for the day, I was made for the night, and thus, the universe itself is within my destiny.

pzampella: Ah yes, that makes sense now. Since the surface of the Earth is bounded, we could travel along a straight line (a geodesic, or "locally straight path along the surface") and return where we started. We could also keep following that same path forever.

In cosmology, if we choose a time-like or light-like geodesic (a straight line with speed less than or equal to the speed of light), then we will never return to our origin. This is because the space is expanding as we travel. So in this sense we would keep moving in a straight line forever, always experiencing new surroundings and never returning to where we began.

But we might also ask of "freezing the universe's expansion", or choosing a space-like geodesic (faster than light) with arbitrarily high velocity, so that the expansion is negligible by comparison. In this case, whether we return to our origin depends on the universe's large scale curvature. By observation it appears to be extremely close to "flat", which means it could be infinite in spatial extent (unbounded, so our geodesic will never return to its origin). But the curvature could be very slightly positive, which could make the universe bounded, and in that case the geodesic would return to where it started.

As for the Orange Theory, although it makes for a cool visual, it has no physical basis (what physics explains the nature of the motions shown?), and is easily disproved by observations. The expansion of our universe is homogeneous and isotropic, but Orange model is not. Our universe is also never contracting.

The evolution of the universe (the rate of change of its size, or "scale factor") is most easily understood from the Friedmann equations. Sometime I may make a post explaining them.

I would like to know if any of you know how I would calculate the timeframe within a planet could retain some gases, that is, how I can calculate the gases escape velocity and outflow during a star's lifetime. For example, around a M or K class star, a planet might have enough time to lose enough material during it's regular orbit around the star due to it's mass to become uninhabitable long before the system's HZ shifts outwards due to normal stellar evolution. Another thing I think would be important in anything pertaining this question is the cycle through which the planet's atmosphere goes through, as that affects the escape rate to some extent. You are free to select any example, but I would appreciate it if you were able to share some of the calculations with me.

Another thing that I would like to know is how much a "regular" greenhouse gas such as CO2 or CH4 heats up it's surroundings inside 1 mole of the gas (how much it heats up itself would've been phrased better) (seeing as ppm is relative to the density and mass of the atmosphere and is not constant for all planets, as 1 ppm on Mars isn't the same as 1 ppm on Earth(AKA it heats up the surrounding less due to lower density)). I am also aware that these gases have different heating rates around stars of a different spectrum than the Sun and am curious if there are any formulas that would allow me to calculate a specific gases impact on a planet.

For example, seeing as I know a planet's GHE and the molar mass of it's atmosphere, as well as it's density and the atmospheric pressure it causes on the planet, I could specifically pinpoint the gases inside the atmosphere if I knew how much a single mole of a given gas (not a specific gas, but any 'simple' gas (3 or more atoms)) heats up the atmosphere and affects the planetary life there. I am aware that the greenhouse effect is due to a 'bouncing' effect within molecules with relatively long, loose bonds, which causes energy to be transmitted in the form of light in a given wavelength (infrared in the case of CO2 and CH4, and some others in the case of water vapor) and would also allow me to see the impact of other, less potent gasses in higher percentages on the planet and it's conditions. (And yes, I am aware that diatomic molecules such as O2 and N2 don't emit heat as they are unable to vibrate, making them thermally inactive)

Another thing, it would be interesting if you could explain to me why it is thought that most larger stars don't possess strong heliospheres, which would imply that convection isn't happening. Is this an effect of the stars size which allows gases to cool more rapidly while approaching the surface, leading to a more stable interior? But then again, the star's plasma is electrically charged, thus it must have a magnetic field that extends away from it, which again, leads me to believe that something's wrong with the piece of information I found that most large stars don't have magnetic fields.

That's...about...Oh yeah.

How would I calculate the time necessary for two objects to become tidally locked, and how would I calculate the energy that the tidal force exhibits on the other body based on it's density and porosity, as well as their orbital distance and rotational speed/difference. I suspect that different rotational speeds in different directions could prolong or shorten the time necessary for this to be accomplished. This would also allow me to calculate how long it'd take for the entire system to collapse due to energy loss through tidal forces, and if the forces are too weak to do so, it'd allow me to see how close they would come to each other before other sources of energy dominated over the system's loss of angular momentum, which is ever-present in any system that involves two orbiting bodies.

And the last thing on my list for now would be the time necessary for a body to clear it's body of asteroids and dust, which is necessary for it to be seen as a planet according to relatively recent developments. What formula would allow me to determine this?

Ok, this is really the last thing, can light that's created through Luciferase enzymes serve other organisms on exoplanets to live off of photosynthesis even without another source of light from, say, a star? I am aware that it would be energetically weaker, but it would be a stable and "programmable" energy source for any plant-like organism, which would open the door for some symbiotic tomfoolery.

That is all for now, I may come back later with more questions...

I'm sorry for the long text, and am deeply sorry if this was the wrong place to post it.

Edited by NikolaAnicic007 - Sunday, 17.01.2016, 14:50

NikolaAnicic007, these are awesome questions, and yes, this is a perfect place to post them. I don't think I can answer all of them, let alone as completely as I might like, but here's what I can say for right now. (And with apologies for the length -- big questions get big answers.)

Atmosphere's can escape by several different mechanisms, so there's no single formula which you can apply everywhere. But a good first approach is to just look at the loss due to the fastest particles escaping (called thermal or 'Jeans escape').

In a planetary atmosphere, there is a certain height (called the exobase, or base of the exosphere), below which molecules collide frequently enough to establish thermal equilibrium, and above which the mean free path is greater than the scale height (so a molecule thrown upwards with enough speed has a good chance of escaping without hitting another one). Molecules in a gas at a given temperature have a Maxwell distribution of speeds. Mathematically, this distribution extends to infinite velocities, but the dropoff happens so fast that in practice there are very few molecules with velocities greater than about four times the mean value, where the mean value is given by

where R is the gas constant, T is temperature in Kelvins, and M is the molar mass of the molecule.

If the mean value is more than 1/4 of the escape speed:

where G is the gravitational constant, M is the mass of the planet (yeah, sorry, same capital M referring to different things -- use whatever other notation you want), and r is its radius,

then this means an appreciable number of molecules will be moving faster than the escape speed, and the planet will lose its atmosphere very quickly. Beyond that, there is an exponential increase in the atmosphere's lifetime. If the ratio of escape speed to mean speed is 4, then it may last thousands of years. 5, millions of years, and 6, billions of years.

This is a rough rule of thumb that works fairly well for most purposes. I made a spreadsheet to calculate this easily in another thread where this discussion popped up -- see here. But if you want to be more precise, especially in the sense of actually calculating the mass loss rate, or flux of molecules evaporating from the atmosphere, then you can use the Jeans formula for the escape rate (atoms per square meter per second). This is

Where N_{ex} is the number density at the exobase, and λ_{esc} is the escape parameter, (v_{e}/v_{o})^2

If you apply this to atomic hydrogen in Earth's atmosphere, you'll get a flux of something like 6x10^{11} atoms per square meter per second, which is comparable to the rate at which this gas is diffused to the upper atmosphere. I.e. it escapes the exosphere at almost the same rate as it gets there in the first place.

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Another thing that I would like to know is how much a "regular" greenhouse gas such as CO2 or CH4 heats up it's surroundings inside 1 mole of the gas

The greenhouse effect doesn't work that way. If you have some small transparent container of CO2, it won't be of any different temperature than the same container filled with N2.

Instead, the greenhouse effect works by absorbing some of the planet's outgoing thermal flux, and redirecting some of that back downwards. This causes a change in the vertical temperature profile -- heating the surface and lower atmosphere, and cooling the upper atmosphere (because less thermal flux gets there, and with more greenhouse gas these upper layers also radiate thermally more efficiently).

The physics of this is conceptually simple, but is very complicated in practice. It requires computational methods, integrating the absorption and emission of flux over the whole vertical structure of the atmosphere. A good treatment of this can be found in an atmospheric science text, but I won't go in into such depth here. In a more simple model, where the atmosphere is split up into layers, with each layer defined to have one extinction thickness (it absorbs 100% of the outgoing flux), we obtain the following formula for the ground temperature:

Where τ is the number of extinction thicknesses, and T_{E} is the equilibrium temperature calculated by the flux balance for a blackbody,

where L* is the star's luminosity, AB is the albedo of the planet, a is the planet's semi-major axis distance, and sigma is the Stefan-Boltzmann constant.

Finally, the temperature at the i'th layer is just i^{1/4}T_{E}.

You're right that the greenhouse effect will depend on the type of star, but this basically just shifts the incoming spectrum. Most stellar spectra approximate a blackbody spectrum, and for most cases that we might be interested in, this spectrum doesn't overlap much with the planet's emission. So if we're interested in a planet whose atmospheric gases are essentially transparent to that spectrum, then the star's temperature will just be reflected in L*.

QuoteNikolaAnicic007 ()

Another thing, it would be interesting if you could explain to me why it is thought that most larger stars don't possess strong heliospheres, which would imply that convection isn't happening. Is this an effect of the stars size which allows gases to cool more rapidly while approaching the surface, leading to a more stable interior?

I'm not sure! SpaceEngineer may know more about this.

QuoteNikolaAnicic007 ()

How would I calculate the time necessary for two objects to become tidally locked

This is another really complicated process. I hesitate to use a general formula for it because there can be so many factors that influence it (e.g. with the Earth-Moon system, it varies due to changes in the dissipative efficiency within the oceans). But in general, the locking time scales with the sixth power of orbital distance, so it's a very strong dependence. There's a formula on wikipedia if you want to use that.

Other formulas you might use are as follows (from Planetary Sciences, by Pater and Lissauer).

QuoteNikolaAnicic007 ()

how would I calculate the energy that the tidal force exhibits on the other body

The rate of change of angular momentum (or torque), is

Where subscripts 1 and 2 represent the primary body and its satellite, respectively. k_T is the tidal Love number, Q is the dissipation factor, R is the body's radius, r is the orbital distance, omega is the angular rotation rate and n is the orbital angular velocity. (So the sign of omega minus n represents whether the satellite orbits faster or slower than the primary rotates, and the sign(x) function turns this into a +1 or -1 accordingly.)

This torque (if none other are present) will make the orbit expand or contract. The rate at which this happens is

If you specifically want energy, this is transferred by the torque according to n (the orbital angular velocity) times the angular momentum. Or, dE/dL = n.

QuoteNikolaAnicic007 ()

This would also allow me to calculate how long it'd take for the entire system to collapse due to energy loss through tidal forces, and if the forces are too weak to do so, it'd allow me to see how close they would come to each other before other sources of energy dominated over the system's loss of angular momentum, which is ever-present in any system that involves two orbiting bodies.

It generally doesn't, at least not by tidal forces. Tidal force will only cause orbits to collapse if sign(omega - n) = -1. So, if the satellite orbits ahead of the nearest bulge it raises on the primary, or if the satellite orbits retrograde. And for interplanetary distances, tidal forces is trivial, since it follows the inverse cube power of distance.

For looking at long term system evolution and instability, other effects are more important. For planets, the most important things are perturbations by the other planets. There was an awesome lecture on that topic posted here a while back if you're interested. And for small bodies, there are other effects like radiation pressure, PR drag, Yarkovsky effect, YORP, etc.

QuoteNikolaAnicic007 ()

And the last thing on my list for now would be the time necessary for a body to clear it's body of asteroids and dust, which is necessary for it to be seen as a planet according to relatively recent developments. What formula would allow me to determine this?

I don't know offhand a way to calculate the timescale, but for something close to it I would refer you to FaceDeer's post here in the "Defining Planethood" thread. This is regarding the "Planetary Discriminant" and Stern-Levison parameter, which are powerful measures of how effective a body is at clearing its orbit.

I hope that was helpful! And hopefully not too much math.

Oh, and as for the last question on the feasibility of luciferase photosynthesis, I am tempted to doubt it, but I really don't know. That would be really neat if it could work!