Okay, thanks! But, can we make Earth so small within the radius of 1 km? Earth looks like Earth. but is so small that has big density. Would that make any difference?
Okay, thanks! But, can we make Earth so small within the radius of 1 km? Earth looks like Earth. but is so small that has big density. Would that make any difference?
Sorry. I kept the comma at 6,772 for the mass at 30000 km range for a decimal point. In German the comma is the decimal point.
Wow, thanks! So two more moon questions:You are totally right. 4.5 billion years ago the Moon was born at just 3.8 earth-radii of distance, 2.5 billion years ago is was 52 earth-radii of distance, and now the Moon is located 60.3 earth-radii away from us. This means that for the first 2 billion years the Moon moved 48.2 earth-radii but for the last 2.5 billion years it has only made 8.3 earth-radii (a huge decrease in receding velocity).
This effect is summarized by the equation (2) of page 601 of this research paper. The a refers to the semi-major axis of the lunar orbit (a.k.a it's distance to Earth) and the dotted a refers to the increase in a (a.k.a the speed at which the Moon recedes from Earth). As you can see the dependence of one another is to the 5.5 power. This means that if the moon recedes at a speed v while been at a distance x from earth, then by the time it has receded to a distance 2x it is receding just a mere 2.2% of the initial receding rate v (45 times slower).
The Moon's atmosphere is so thin as to be completely negligible here. The effect is instead related to scintillation of the remaining crescent of sunlight through atmospheric turbulence -- the same effect that causes stars to twinkle at night. Which should make some sense, as in the moments right before and after totality the remaining crescent is very thin and prone to being distorted like that -- just like the shimmering appearance of planets or the Moon in a telescope under unsteady air, or seeing something through heat haze.Secondly, I was googling shadow snakes, and noticed that this eclipse effect still seems unsolved. What's the likelihood that in addition to the effects from our atmsphere, it is also from the *moon's* atmosphere as well, since the light would be travelling through that first right before reaching the Earth?
I didn't see any shadow bands at all, but YouTube is full of videos of shadow bands recorded during last week's eclipse. Haven't seen one from Madras, though, and they're only visible on bright surfaces:
It is very likely. The moon moves off the earth by 38 millimeters a year. (According to Wikipedia). In 10 billion years this would be only 380000 km, which is about a doubling of the distance. But still far within the hill sphere of the earth.
A small group of people nearby where I was had a sheet on the ground for catching the crescent shape and there were visible shadow bands. It was very interesting to see.
Good point, Wat. Another way of stating this is that the universe with its own space-time is expanding into something which we can call null space-time. In other words, speed is undefined since in this null space-time, our sense of space and time have no meaning.The expansion actually doesn't have a speed in that kind of sense. This is a very common confusion and might be worth spending a few moments on.
Suppose you look at a galaxy which is 100 Mpc away, and you find that it is receding at 7,000 km/s. Then you choose another galaxy that is 200 Mpc away (twice as far). You will find that it is receding at 14,000 km/s (twice as fast). Indeed, for a wide range of distances, you'll find recession velocities that increase according to their distance from you (Hubble's Law).
So, what would you call the universe's expansion speed in this example? Is it faster than light? How do you know?
It turns out we cannot define an expansion speed at all, but rather a speed per distance. That is, the speed depends on distance! The measure of expansion cosmologists use is called Hubble's Constant, and has units of km/s/Mpc.
What this means is that no matter how small the Hubble's Constant is (provided it is not zero) there will always be a distance for which things are receding from us faster than the speed of light. So the notion that the expansion is "faster than light" is totally meaningless.
Things moving away from us due to expansion is a very different type of motion than things literally moving through the space. It's not the things that are moving through space, but the space itself expanding between them, so the speed of light is not being violated (the rule is that things cannot move through the space faster than light).
Alcubierre's drive is based on a similar idea. While it is impossible to move something through space faster than light, it might be possible to distort the space-time such that some patch of it can be transported through the universe faster than light. But to do this, the space-time must be distorted in a very strange way which is most likely impossible -- even if it satisfies the equations of general relativity.
Quark stars and cosmic strings, if they exist might also be able to do thisI think you didn't convert the kilometers to meters (necessary for dimensional consistency, e.g. if speed of light is 3x10[sup]8[/sup] m/s and G is 6.67x10[sup]-11[/sup] m[sup]3[/sup]kg[sup]-1[/sup]s[sup]-2[/sup]). So it must be multiplied by a thousand.
Marko S., I think there would be no object other than a black hole that could make light orbit around it by gravity. A neutron star is closest possible object to a black hole, yet still has not quite strong enough gravity to do this. (Typical mass is 1 to 2 solar masses, within a radius of about 10km, yet the computed size of the photon orbit would be smaller than that radius, so it doesn't exist.)
So, yeah, this situation would not only "look like" a black hole, but must actually be a black hole.
Yes I have been thinking of this also. You need tides for sea life to move onto land and I'm not sure the sun alone would've been enough. Not only that, but the moon was a celestial pin-cushion for many an asteroid that could have hit Earth. The aftermath of an asteroid collision accelerates evolution, but the impact itself kills off up to 90% of all life, so without the moon evolution might have been in a perpetual start-stop-start-stop sequence.Somebody asked me today (somewhat jokingly) whether I think it's a coincidence that the Sun and the Moon have almost precisely the same apparent size. Of course it's a coincidence, but the question becomes more complicated the more thought it's given. The Moon seems to have had an important role in the evolution of the Earth including the evolution of life. Had there been no moon, or a moon either significantly different in size or distance, we wouldn't be here (true even for small differences in the early history of Earth), but could we at all be here? Do planets which have a moon and star of roughly the same apparent sizes have better conditions for life? I.e. do favourable tidal forces and solar heating coincide with similar apparent sizes?
For sure, there's a helpful analogy for the expansion as a 3D space expanding into some higher dimensional space we can't perceive. It's also possible (actually preferred teaching among most cosmological texts) to just treat it as a 3D expansion with no higher dimension at all. This is necessary and sufficient to explain it with math (basically you have three spatial dimensions in the space-time metric, and the "scale" of them is a function of time.) This fits into general relativity and gives the right predictions, but conceptually it can be a bit difficult to imagine how it works that way.
Good point, I forgot about those! Strings in particular could cause some really weird and strong distortions of the space and light around them.
This is a fascinating question! Some years ago my astrobiology professor raised the same question for the class, and he seemed to be a big proponent of the idea. I'm a bit doubtful but think there's definitely aspects which are important. It is a very difficult thing to research and find robust answers for.
I've heard people suggest this before and it sounds appealing, but when we run through the numbers I think it's pretty doubtful. The Moon currently covers only about 0.0005% of the sky. (Yes, really! I find this a surprising and neat bit of trivia). The full "solid angle" of the sky is 4*pi steradians, and the Moon is about a half degree wide, or a solid angle of about pi*(0.25deg*pi/180)^2 = 0.000019*pi steradians. The ratio of the two is about 5x10[sup]-6[/sup], or 0.0005%.
Yes, and I don't know how much we can deduce from a sample size of one I remember many years ago it was thought that every solar system we would find would have inner planets close to the sun and gas giants much farther out. Of course, we now see that solar systems come in all shapes and sizes and varieties. I would like to think that lifebearing planets possess a similar variety.For sure, there's a helpful analogy for the expansion as a 3D space expanding into some higher dimensional space we can't perceive. It's also possible (actually preferred teaching among most cosmological texts) to just treat it as a 3D expansion with no higher dimension at all. This is necessary and sufficient to explain it with math (basically you have three spatial dimensions in the space-time metric, and the "scale" of them is a function of time.) This fits into general relativity and gives the right predictions, but conceptually it can be a bit difficult to imagine how it works that way.
It's also a bit limiting -- although it correctly predicts everything we can observe and currently understand with the universe, it doesn't let you go much further. It's when you get into the deeper models of gravitation and cosmology that the interesting speculative stuff comes into play, like the higher dimensions, multiple universes, colliding branes, and so forth.
Good point, I forgot about those! Strings in particular could cause some really weird and strong distortions of the space and light around them.
This is a fascinating question! Some years ago my astrobiology professor raised the same question for the class, and he seemed to be a big proponent of the idea. I'm a bit doubtful but think there's definitely aspects which are important. It is a very difficult thing to research and find robust answers for.
I've heard people suggest this before and it sounds appealing, but when we run through the numbers I think it's pretty doubtful. The Moon currently covers only about 0.0005% of the sky. (Yes, really! I find this a surprising and neat bit of trivia). The full "solid angle" of the sky is 4*pi steradians, and the Moon is about a half degree wide, or a solid angle of about pi*(0.25deg*pi/180)^2 = 0.000019*pi steradians. The ratio of the two is about 5x10[sup]-6[/sup], or 0.0005%.
Expressed another way, that means it would take about 200,000 full moons to fill the sky! It also means that out of a million asteroids that would hit Earth, only about FIVE of them would be blocked by the Moon.
Even if we look very far into the past the Moon's shielding ability wouldn't improve much. There are large uncertainties in the evolution of the Moon's orbit since its formation, but even assuming it was just 1/4th of its current distance 3 billion years ago (probably way too generous), its screening ability would be about 80 out of a million. And at the Roche limit of ~9500km, it still blocks less than 1% of them.
So I don't think the Moon could ever have done much to protect Earth from asteroids, but it certainly does do a lot for producing tides and keeping the Earth's obliquity in check. It's an interesting question whether this naturally leads to an expectation that a complex life arises when Moon and Sun are of similar angular size, but I haven't seen a lot of strong research on it.
Me, too.
I try not to think of it as the universe creating space -- that provokes a whole nest of difficult questions like "how does it create space?" or "where does that new space come from?". There aren't meaningful answers to those questions, nor does describing it that way make the math any easier.
It's more like the problem of comparing velocity with acceleration. The units don't work. There is definitely a "rate" to the expansion of the universe (e.g. it seems to be about 70 km/s/Mpc), but it is not a "speed". It is a "speed per distance". Something twice as far away recedes twice as fast. Because space itself expands, the farther away two things are, the faster they move away, so you can't ascribe a unique speed to the whole thing. Instead you ascribe a speed per distance to the whole thing, but that's incomparable to plain "speed" as in speed of light.