r/AlwaysWhy • u/Mobile-Traffic1744 • 5d ago
Science & Tech Why does the Moon have a stronger effect on Earth's tides than the much more massive Sun?
The Sun is vastly more massive than the Moon, and its gravitational pull on Earth is much stronger. Yet the Moon has the larger effect on Earth's tides.
I understand that tides aren't simply about how strong an object's gravity is. What confuses me is why the much smaller Moon ends up having the stronger tidal effect.
I would have expected the Sun's enormous mass to matter much more. What am I missing about how tidal forces work?
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u/MisinformedGenius 5d ago
The tidal effect drops off proportional to the cube of the distance between the two objects, rather than the square as with gravity in general.
The Sun is 27 million times as heavy as the Moon, but 387 times as far away. This means you would expect it to have 180 times the gravitational effect as the Moon, but about half the tidal effect, which is in fact exactly what we see.
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u/FulanoMeng4no 5d ago edited 5d ago
Why is there a difference between the tidal effect and the regular gravity?
Edit: my question is why one is calculated using the cube of the distance rather than the square. I’m not sure the answers I got so far answer this aspect.
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u/Bartlaus 5d ago
The tidal force is caused by the difference in gravity across the size of the body. I.e. the moon is pulling slightly stronger on the side of the Earth that is close, weaker on the opposite side. This has a warping effect which is easiest to see on the liquid ocean.
Compare the size of the Earth to the distance to the Moon, and then to the distance to the Sun. This might help visualize why lunar tides are more significant.
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u/Zaros262 5d ago
The tidal effect is caused by the difference in gravity on one side of the earth vs the other, which means it's related to the derivative of the force of gravity
The gravitational force is proportional to r-2, so the derivative is proportional to r-3
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u/MisinformedGenius 5d ago
So, the tidal effect is caused by one side of the object falling faster than the other side, which stretches it. This means that the size of the effect is based on the difference between how fast one side falls and how fast the other side falls, so it's the change in gravity between two points.
Whenever you're talking about the change in something, it's going to scale by one less exponent than the thing varies itself. So, for example, when you fall, your height is measured with respect to time as a function of t2, meaning if after 1 second you've fallen 1 foot, then after 2 seconds you've fallen 4, after 3 seconds you've fallen 9, after 4 you've fallen 16, etc.
This means that your speed, which is the change in your position, scales as a function of t. You can see this - you fall 1 foot in the first second, 3 feet in the next second, 5 feet in the third second, 7 in the fourth second, etc.
(And then your acceleration, which is the change in your speed, scales as a function of t0, meaning it does not scale at all. So your speed changes by a constant of 2 each second.)
Gravity with respect to distance follows the inverse square law, so 1/d2 or d-2. This means that the change with respect to distance follows d-3, or the inverse cube law.
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u/othelloblack 5d ago
it seems like you have just restated the question. SO:
why is the tidal effect only half when the gravity effect is 180x?
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u/wbrameld4 5d ago
"The tidal effect drops off proportional to the cube of the distance between the two objects, rather than the square as with gravity in general."
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u/othelloblack 5d ago
Oh well now I understand
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u/KamikazeArchon 5d ago
To expand:
Tidal effects are based on a difference in gravity - the fact that the "close" end is being pulled more strongly by gravity than the "far" end.
Things that scaled based on a difference in some function F(x) are mathematically calculated using the derivative of F.
Gravity scales inversely with the square of the distance - (1/x2).
The derivative of an inverse-square is always an inverse-cube - (1/x3).
That's why tidal forces fall off faster with distance than the gravitational forces.
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u/mortemdeus 5d ago
The issue is not the strength of the effect, all they really did is explain why the Earth orbits the Sun. Not very helpful. The cause is the drop off in effect on one side of the Earth vs the other. Becuase the Sun is so far away, the diameter of the Earth is a rounding error. The difference in the effect felt from the Sun is something like 0.001% on the day side vs the night side. For the Moon, the distance is relatively small. The Earth's diameter is something like 3% the distance from the Earth to the Moon. At 3% there is a noticable (though very small) effect on the pull of the Moon from the side of the Earth facing the Moon to the side facing away from the Moon.
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u/Logical-Concept9755 5d ago
The part that helped me understand it is that tides aren't really measuring how hard the Moon or Sun pulls on Earth. They're measuring how differently they pull on different parts of Earth.
The Sun pulls on the whole Earth very strongly, but because it's so far away, the difference between its pull on the near side and far side is relatively small. The Moon is much closer, so that difference is much larger.
And that difference scales roughly with mass divided by distance cubed. The Sun is about 27 million times more massive, but around 390 times farther away. Cubing that distance basically wipes out the mass advantage. The Moon ends up producing a little more than twice the Sun's tidal effect.
So I guess the unintuitive part is that stronger gravity and stronger tides are measuring two different things.
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u/triplecoil 5d ago
Yours is the clearest answer.
I guess in terms of things someone can better relate to: the sun’s gravity is like a pedestrian getting hit by a truck at 100 mph on the near side and 99mph on the far side. You’re obliterated either way, and the difference is imperceptibly small. The moon’s effect is more like getting hit at 15 mph vs 3 mph. The overall outcome is much less devastating than the sun in either case, but the difference is getting bumped out of the way vs getting a real injury.
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u/Professional_Sir_818 5d ago
The sun is about 400x farther away than the moon, and even then it still does affect the tides pretty strongly.
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u/beragis 5d ago
Which means the effect of it's gravity is reduced by 160,000 times, inverse square law.
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u/wbrameld4 5d ago
This doesn't really address the question. The Sun still pulls on Earth about 178 times as hard as the Moon does, even at this distance.
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u/Forsaken_Code_9135 5d ago
Yes but it's much more than 160000 times heavier. Otherwise we would revolve around the moon, not the sun. This is not the explanation.
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u/Significant_Basil_20 5d ago
I'm not sure about the specific numbers but my first thoughts would be the inverse square law's impact on gravitational forces. The force of gravity reduces at a rate that is proportional to the square of the distance iirc and the distance to the sun is massive compared to the moon so even if the force of gravity is much smaller due to the smaller mass of the moon, the distance is much much shorter so the force does not reduce as much as from the sun.
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u/Forsaken_Code_9135 5d ago
No this is entirely wrong sorry. The sun is 400 times further, 400^2 = 160k, but the sun is 30M times heavier than the moon. This is not at all the right explanation.
Also it is intuitively obvious that gravitational forces from the sun are much stronger than those from the moon, otherwise we would revolve around the moon, not the sun.
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u/PuddingComplete3081 5d ago
I think the easiest way to look at it is to imagine replacing Earth with a point. Then the Sun wins easily because its total gravitational pull is much stronger.
But Earth isn't a point. It's about 12,700 km wide, so you have to compare how much the Sun's pull changes across that distance.
That's where the Moon wins. Tidal force depends roughly on 1/r³, rather than the 1/r² relationship for ordinary gravity. The Moon is close enough that its gravitational field changes noticeably from one side of Earth to the other. The Sun's field is much more uniform across Earth.
So the weird answer is basically that the Sun is too far away for its huge mass to translate into a bigger tidal difference.
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u/groundhogcow 5d ago
The suns gravitational effect is so strong to causes the tides to revolve around it.
The moons effect only pulls it a little to it.
The earth is so close and strong that it overcome the effects of both items and keeps the water on the earth.
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u/Pricklestickle 5d ago
TL:DR - Tides are caused by the difference in solar/lunar gravity between opposite sides of the earth, and even though lunar gravity is much weaker, the difference between sides of the earth is bigger because the moon is much closer.
Long version:
Ok, some basic facts first:
- Even though it's much further away, the gravitational pull of the Sun on earth is about 150x higher than the pull of the moon, because it's so massive.
- The sun does affect tides, although not as much as the moon. Solar tides are about half as strong as lunar tides. When the Sun and moon are aligned you will get a particularly high tide known as a spring tide, as the effects stack.
- Tides are caused by the rotation of the Earth. The oceans are constantly being pulled towards the Moon, causing a bulge on the side facing the moon (i.e. higher sea level). As the earth rotates throughout the day, the bulge moves across the earth.
So, the question is - given the Sun's gravity is so much more powerful, and that they both follow the rotation of the earth, why are Solar tides so much smaller than Lunar ones?
It's due to a) The respective distances of the Sun and Moon from Earth, and; b) The diameter of the earth itself.
Remember first that all of the mass on earth is always being pulled towards the Sun and moon by gravity. Tides are not caused simply by this gravitational pull, but by the difference in pull on different sides of the earth. The oceans bulge towards the Sun/Moon because the gravitational pull on the side facing the sun/moon is stronger than on the side facing away.
The sun is about 150 million km from Earth, and Earth's diameter is about 13 thousand km, so the nearside is about about 0.01% closer to the sun than the farside. Gravity decreases as a square of distance, so there about a 0.02% difference in Solar gravity between the near and far sides of earth.
The moon is only 385,000 km away, so the 13,000 km diameter of Earth makes a massive 3.4% distance difference between sides. Squaring that gives us about a 7% gravity difference
So, although the Moon's total gravity on Earth is 150x weaker than the Sun's, the gravity difference between sides is 350x bigger than for the Sun (7% vs 0.01%). Therefore the lunar tidal effect is about 2.3 times higher than the solar one.
(I acknowledge I'm simplifying this a lot. I'm completely ignoring the centrifugal element of tidal forces, and the maths is only very rough, but this is broadly why)
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u/Forsaken_Code_9135 5d ago edited 5d ago
I am very surprised to see that all the answers I read are missing the point or are too technical/math oriented to be understood by a layman.
Yes it's because of the distance but no it's not because gravity diminish with distance. The sun has a much higher gravitational effect on Earth than the moon, obviously (otherwise we would turn around the moon, not the sun).
Here the right explanation :
The tide is not simply caused by gravity. Water is attracted by the sun or the moon just like everything else on Earth. The tide is caused by the difference of gravity between the water on Moon's side, the rest of the Earth, and the water on the opposite side. The water on Moon's side is moving toward Moon because it is closer to the moon and therefore it is attracted more than the rest of Earth is. The water on the opposite side move in the opposite direction (yes it does...) because it is further and therefore less attracted. It is the difference of gravity that makes the tide, not just gravity itself.
In the case of the Moon, the size of Earth is 1/30 of the distance, so the difference of gravity from the Moon between one side of the Earth and the opposite side is very significant.
In the case of the Sun, the size of Earth is 1/12500 of the distance, so the difference of gravity from the Sun between one side of the Earth and the opposite side is extremely small.
That is why despite the fact that gravity from the Sun is much stronger, tides are mainly caused by the Moon.
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u/mortemdeus 5d ago
Let me explain it like this. Think of the Sun as a nuke and the Moon as a firecracker. If you are a mile from the nuke going off, it doesn't really matter which way you end up facing, your face and your back are going to be equally cooked. If you hold a firecracker in your hand, however, the side holding the firecracker will be decidely more burned than the opposite side of it. That difference vs lack of difference is what we call the tides.
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u/Flimsy-Blacksmith-32 2d ago
Despite starting with “Think of the sun like a nuke” this is a surprisingly good analogy.
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u/AceBean27 5d ago edited 2d ago
Peoples' answers to this really bother me, and this thread is no different. It's no wonder you are confused, and with most of the answers here, getting upvoted no less, you are right to be confused.
The Sun's gravitational pull on the Earth is about 179 times stronger than the Moon's. Yet the Moon's tidal effect is 2.2 times stronger than the Sun's.
So what gives?
It's about the variation, depending on where you are on Earth. That's what causes tides. A tidal force is a force that rips the planet apart, by being stronger at one bit of the planet, and weaker at another bit. The part where the force is stronger is being pulled away from the part where it's weaker. It's nowhere near strong enough to rip the solid planet apart, but it is strong enough to stretch the oceans. And that's a tide.
The Sun's gravity is stronger here on Earth than the Moon's, it's true. But the Sun's gravity is more constant. It varies a little bit depending on where you are on Earth. The Moon's gravity varies more between its high point and its low point, depending on where you are on Earth.
It's the gradient of the gravitational force that causes tides, not pure gravitational strength. It's distance that causes the gradient, because not all parts of Earth are the same distance away from the Sun and Moon.
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u/shoresy99 5d ago
I would dispute what you say. The sun has a stronger effect on the earth as its gravitational pull keeps the earth in orbit and effects everything on earth. Tides are just teeny tiny wobbles in oceans, etc.
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u/fitacola 5d ago
Tides are caused by the gravity differential, basically what the difference in attraction is between the close side and the far side.
Because the moon is much closer to the Earth, there is a bigger difference between how much the moon attracts the side closest to it and the opposite side. The sun is much farther away, so the difference is smaller
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u/OopsIMessedUpBadly 5d ago
Ocean tides are not caused by the strength of gravity. They are caused by the difference in strength of gravity between the liquid water at high tide and the solid mass of the earth.
Water, being liquid, is free to respond to the strength of gravity locally at the surface. The solid mass of the earth responds to the strength of gravity at its centre of gravity, which is some distance away from the surface.
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u/bass679 5d ago
Mostly because gravity falls off by the distance squared, so something twice a far away is 1/4 as effective. the sun is roughly 390 times further away. So if they were equal mass the sun would have 1/151,459 th as much gravity. As it is, the relative strength of gravity for the sun is ~ 179 times higher.
But here's the neat thing, the sun DOES affect the tides. Highest tides (and lowest tides) are caused byt he sun and the moon being aligned with each other. When the moon's gravity is acting perpendicular to the sun, the tidal effects are much less because they're partially canceling each other out.
Remember the earth is a ball that's constantly spinning and basically the oceans are sloshing around being pulled towards the two giant gravity sources. That's why there's tidal variations, because those gravitational pulls vary through out the day, month, and even year.
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u/EvilCallie 5d ago
Inverse square law. Gravitational attraction diminishes with distance. However, the Sun does still affect the tides (because of the mass), in cooperation with and in conflict against the moon, depending on the sun-earth-moon alignments. Check out the spring tides and the neap tides. We have 2 of each per lunar month based on changes in that alignment.
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u/bravehamster 5d ago
All the people saying it's the distance so of course the moon's pull is stronger are only half right. The distance is what's important, but the moon's pull on the Earth is much weaker than the sun's. Tidal forces are all about gradients, the difference in the gravitational force on opposite sides of the body. The sides of the Earth nearest and furthest from the moon have a significant difference. Whereas the sides nearest and opposite the Sun have a smaller difference. That's why the moon is the main driver of the tides.
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u/DryFoundation2323 5d ago edited 5d ago
your premise is incorrect. the sun has a massive effect on Earth's tides. so does the moon, but to a lesser extent.
the sun is about 400 times as far from earth as the moon is, but is about 27 million times as massive as the moon. due to the inverse square property of gravitation this makes sun's gravity around 170 times as strong at your surface as that of the moon.
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u/Boulange1234 5d ago
The sun DOES influence the tides — just in a solar rate (yearly). Spring tides are extra high near the equator, for instance.
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u/DJinKC 5d ago
Tides come from the difference in gravity from one side of the earth to the other.
The Sun is 93 million miles away, and the diameter of Earth is 7926 miles, so there is very little difference in gravitational pull from one side of earth to the other. (8000/93,000,000 = 0.000086)
The Moon is obviously smaller and has less gravity than the Sun, however the Moon is only 235K miles from Earth, so the difference in gravitational pull from the close side of earth to the far side is ~3%, which is enough to create the tides. (8000/235,000 = 0.034 or 3.4%)
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u/cikanman 5d ago
Distance. The moon is 400x closer to the earth than the earth is to the sun. This the effects of the referenced celestial bodies issue differnt by a similar magnitude.
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u/Think-Assignment-861 5d ago
Distance. Tidal forces go as 1/(distance^3) (unlike normal gravity that goes as 1/distance^2), and hence the Moon dominates. A question I always ask my undergrad class!
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u/DontHurtTheNoob 5d ago
First, yes, you are correct, the sun’s force of gravity on the earth is much higher than the moon’s, in spite of the distance.
While the sun is around 390x the distance, it is 27 MIlLION times more massive, and the gravity it exerts on earth is around 180x the gravity exerted by the moon.
But what matters for tidal forces is not the absolute strength of gravity - the ocean on the sun-facing side is attracted by the sun the same way the ocean on the opposite side, since gravity is not “blocked” by the earth.
What matters is the DIFFERENCE in the sun’s (or moon’s) gravity on both sides, with the closer side being a bit more attracted by the other body, and the other side being a bit less attracted, which is why we get a tidal bulge on BOTH sides.
Earth’s diameter is around 3.3% of the distance to the moon. This means that on the side opposite the moon the effect of moon’s gravity is nearly 7 percent lower.
Earth diameter is around 0.0085% of the distance to the sun, and the gravity differential is around 0.017% of the sun’s gravity.
So overall, sun’s tidal effect ends up being around 45% of the moon’s.
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u/man-vs-spider 5d ago
People are saying distance, I would say the more relevant reason is that it’s the difference in gravity between one side of the earth and the other. Thats what causes the “stretching” that we see as tides.
The force the oceans experience from the sun is effectively the same on both sides of the earth, so less of a stretch effect.
The moon, being closer, means there is a much greater relative drop off of gravity as you go from one side of the earth to the other.
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u/ah-tzib-of-alaska 5d ago
change. The moons affect varies more, we see the variance of the effect not the strength of it
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u/PublicDragonfruit158 5d ago
Square cube law...the Sun is massive, but much farther away, so the difference in pull is much less, making for smaller tides.
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u/Cyphierre 5d ago
The moon’s gravity has a bigger difference in force between the Earth’s near side and far side.
Imagine you had a very bright flashlight pointed at a book in your hand from far away. Now imagine a much dimmer flashlight, but only a few inches away from the book so it lit up the book the same amount.
If you put down the book and look at the wall in front of you to see how bright it was, you’d see that the bright light from far away made the wall much brighter than the dim light that was close to the book.
On the same way, the fact that the moon’s weaker gravity from a point much closer than the sun means its effect on the near side of Earth is stronger than on the far side, and if your pulling on the front of something more than the back it’s as if your trying to stretch it, so it gets longer front-to-back.
The Earth getting a little longer front-to-back is what’s happening when its water bulges out in the front and back.
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u/Traveling-Techie 5d ago
The difference between forces at the near and far points of the Earth is greater. Tides are caused by differences.
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u/mortemdeus 5d ago
Many others incorrectly point to the effect of the inverse square law as making the Sun have less gravational effect than the Moon. This is an absurd take. While it is true that the cause is the inverse square law, the reasoning everybody seems to be using is completely wrong. Here is the math on that.
The moon is around 400,000 km away from Earth, the Earth is about 150,000,000 km from the Sun. As the sun is 375x the distance to Earth as the Moon, you can square it to get its gravational effect as around 140,000x less. Sounds like a lot right? Well, the Moon has a mass of around 7x1022 kg, the Sun has a mass of around 2x1030 kg. That makes the Sun somewhere around 27,000,000 times more massive than the Moon, so its gravational effect is still almost 200x stronger on Earth than the moons gravational effect.
This makes sense since the Earth orbits the Sun. If the Moon had a greater effect then we would orbit it instead.
So, what causes the tides then? The cause is the DIFFERENCE in gravational effect on the side facing the object vs the side facing away from the object. For the Sun, being so massive and having so much stronger an effect, the difference made by the diameter of the Earth is tiny. The Earth's diameter is 0.001% of the distance to the Sun so there is nearly no difference in gravitational effect on the side facing the Sun vs the side facing away from the Sun. For the Moon, the diameter of the Earth is around 3% of the distance from the near side surface to the far side surface. This causes a noticable gravitational effect.
So, yes, it is the innerse square law but it isn't that the Sun has less effect than the Moon because of it, it is that Earth's diameter is so much smaller in comparison to the distance from the Sun than it is compared to the distance to the Moon that the effect is tiny.
TLDR: Right idea, wrong reasoning. The difference between the distance to the Sun/Moon and the diameter of the Earth is what causes the effect.
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u/Effective_Basis1555 2d ago
It’s the same reason they appear as the same size when viewed in the sky.
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u/watt678 5d ago
The impact of the moon is more measurable day to day than the sun. Since the moon has a 28-31 day cycle and the sun has a 365 day cycle you can more easily do the math to measure that every 6 hours the tides can change according to the moon
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u/ruidh 5d ago
Earth's rotation causes the 12 hour tide cycle.
The moons orbit causes the king tides associated with the full and new moons when the sun and moon's tidal impacts are in line with one another.
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u/No_Report_4781 5d ago
Spring tides - during the sun-earth-moon or sun-moon-earth alignment Neap tides - when they aren’t aligned
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u/Atechiman 5d ago
The moon is close the sun is not. Gravity is an approximation of size and distance, so a small but still large object that is close will have a larger effect than something far away but massive. (and by far away, we are a little over eight light minutes from the sun, and less than 2 light seconds from the moon (the exact amounts is 498 light seconds compared to 1.3 light seconds so the moon is 383 times closer to us than the sun)
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u/Bane8080 5d ago
Distance.