A question about orbits

[Kasuha]

What the hell are you talking about? "The classic argument"? In kindergarten or where? xD

I believe the "classic argument" here refers to Aristotlean theory of gravity and natural motion. That was pretty serious thing by its time and it took centuries to improve.

[cantab]

The point is that the explanation, while simpler, is a fallacy. The classic argument that the reason gravity must make all things fall the same is because of the contradiction that two objects attached together would simultaneously fall at the same speed and yet at different speeds if it was any other way is utterly false.

The argument is rather that the Aristotlean thinking leads to a paradox.

Suppose I join light object A to heavy object B. According to Aristotle, A wants to fall more slowly than B, so A should hold B back somewhat, right? Tied together, A and B will fall slower than B alone. But since I've joined A and B together, I have one object AB, heavier than B (or A) alone. So A and B when tied together will fall faster than B alone.

The most straightforward resolution is that all objects fall at the same rate.

The paradox will still exist in modern thinking if we theorise any force (or at least any long-range force) where the magnitude doesn't depend linearly on how much of a certain property the objects have.

[Aphobius]

I believe the "classic argument" here refers to Aristotlean theory of gravity and natural motion. That was pretty serious thing by its time and it took centuries to improve.

Considering what people are discussing here, it seems it still is a serious thing.

[Claw]

without reading any other posts here:

Go back to school!!!

There are two forces (simplified) on each thing in orbit:

gravity and centrifugal force

if both are equal, you have and perfectly round orbit

if not, the orbit is elliptical and maybe even "hits" the surface of the object you are orbiting.

formula for gravity: F = m * g

zentrifugal force: F = m * v * v / R

like you can see: in both formulas is the mass. if the mass increases the gravity increases too (we all know that), but also the zentrifugal force increases to the same amount!

You might want to be careful about proclaiming who needs to go to school.

[Dunbaratu]

What the hell are you talking about? "The classic argument"? In kindergarten or where? xD

The current physics don't work with such simple "arguments" anymore.

Please pay attention to the thread. I was arguing AGAINST people who claimed it was "too complicated" to give the Newtonian reason, and instead wanted to explain it using the more primitive explanation that in fact doesn't work - the argument that Galileo used to defeat the Aristotelian paradox is itself also NOT right and is as flawed as the paradox itself was. Galileo just has the advantage of being humble enough to actually experiment a little and give it a try, and in so doing behave like a proper scientist. Based on experimentation he was correct that things fall at the same rate, but he had the wrong explanation as to why.

Edited April 18, 2014 by Steven Mading

[Tinyboss]

The point is that the explanation, while simpler, is a fallacy. The classic argument that the reason gravity must make all things fall the same is because of the contradiction that two objects attached together would simultaneously fall at the same speed and yet at different speeds if it was any other way is utterly false.

I think you're confused about the point of the argument. You're correct that it doesn't prove that all objects fall at the same rate. What it does do is disprove the specific notion that objects fall under gravity at a rate proportional to their mass. With respect to your second paragraph, the main idea of the argument is that the "attachment" can be as weak as we like, even a touch, or a touch by a single hair. If you object to that, then you are in the position of deciding how strong the attachment must be before it counts, and that way leads to absurdity.

[Dunbaratu]

The argument is rather that the Aristotlean thinking leads to a paradox.

Suppose I join light object A to heavy object B. According to Aristotle, A wants to fall more slowly than B, so A should hold B back somewhat, right? Tied together, A and B will fall slower than B alone. But since I've joined A and B together, I have one object AB, heavier than B (or A) alone. So A and B when tied together will fall faster than B alone.

The most straightforward resolution is that all objects fall at the same rate.

No. The most straightforward resolution is to realize that whatever the effect is that makes them fall, even if it might make them fall differently if they were apart, it might not be strong enough to overcome the fact that A and B are stuck together. That's why the argument defeating the paradox is insufficient to explain why A and B fall together, because the paradox isn't even a paradox in need of defeating in the first place unless you start from the quite incorrect assumption that both pheonemna - that on the one hand something is making A and B stay together, and on the other hand something is making A and B want to fall at different speeds, are somehow both of equal importance and one can't override the other. My wind tunnel example was illustrating that the paradox isn't even a paradox in need of solving the first place. I shifted to the example of objects in a wind tunnel to illustrate an example where, unlike with gravity, A and B really in fact DO move differently if they're apart from each other, and yet they can still be glued together and the glue can be stronger than the forces trying to pull them apart - thus no paradox - the glue strength beats the wind strength and overrides it. Just like had Newtonian gravity been incorrect and objects in fact really did try to fall at different speeds when apart, they could still have remained glued together anyway if the glue effect was stronger.

That's why the paradox isn't even a paradox in the first place, and therefore the fact that all objects falling at the same speed "solves" the paradox is utterly irrelevant. That's not a good explanation why it happens. The F=ma explanation works much much better, which is why, getting back to what started this in the thread, it's NOT true to say that it's better not to give the F=ma explanation and instead give the Aristotle paradox-defeating explanation.

[Dunbaratu]

I think you're confused about the point of the argument. You're correct that it doesn't prove that all objects fall at the same rate. What it does do is disprove the specific notion that objects fall under gravity at a rate proportional to their mass. With respect to your second paragraph, the main idea of the argument is that the "attachment" can be as weak as we like, even a touch, or a touch by a single hair. If you object to that, then you are in the position of deciding how strong the attachment must be before it counts, and that way leads to absurdity.

You are adding things to the argument that weren't there. The experimentation that discovered how weak the attachment can be showed that the attachment (and therefore the entire paradox-defeating argument) was not relevant, which is my point. Do the experiment. Drop two objects that aren't even attached. The paradox goes away by only by the experimentation that disproves the premise, NOT by raw logic. By raw logic the paradox wasn't even really a paradox in the first place.

Edited April 18, 2014 by Steven Mading

[Tinyboss]

That's why the paradox isn't even a paradox in the first place, and therefore the fact that all objects falling at the same speed "solves" the paradox is utterly irrelevant. That's not a good explanation why it happens. The F=ma explanation works much much better, which is why, getting back to what started this in the thread, it's NOT true to say that it's better not to give the F=ma explanation and instead give the Aristotle paradox-defeating explanation.

You're still really confused about why people care about this thought experiment. Nobody thinks it's a better explanation than Newton's laws of how things really work. Nobody thinks it's an explanation of anything at all other than the absurdity of the Aristotlean model. The fact that a theory can be dispensed with using nothing but thought actually appeals to some people as an elegant, not to mention cost effective, means of inquiry.

But seriously, if you take nothing else from my posts, please understand that nobody thinks this thought experiment itself is any kind of theory of gravitation.

[Aphobius]

Please pay attention to the thread. I was arguing AGAINST people who claimed it was "too complicated" to give the Newtonian reason, and instead wanted to explain it using the more primitive explanation that in fact doesn't work - the argument that Galileo used to defeat the Aristotelian paradox is itself also NOT right and is as flawed as the paradox itself was. Galileo just has the advantage of being humble enough to actually experiment a little and give it a try, and in so doing behave like a proper scientist. Based on experimentation he was correct that things fall at the same rate, but he had the wrong explanation as to why.

They must be beaten with a stick and sent to school.

[Vanamonde]

As the discussion has long past moved away from OP's question and into the specifics of gravitation, this thread has been moved to Science Labs.

[KASASpace]

Well, I think that as each piece gets added, the difference in velocities of the two different space objects is taken into account.

That's my two cents, and I'm probably completely wrong.

EDIT: It's kind of like when two objects bump into each other. That's kind of what I mean, but one is moving slightly slower than the other in front of the other one, not heading towards each other. Relative velocities.

Edited April 19, 2014 by KASASpace

[Yasmy]

It's approximation time: Start with a 100 km altitude circular orbit, for an orbital radius of r₀ = 700 km, since you have to add Kerbin's 600 km radius to your altitude to get your radius. Your initial velocity is approximately V₀ = sqrt(mu/r₀) = 2246 m/s.

Now make a small velocity change dV to new velocity V₁ = V₀ + dV.

This causes a small change in the radius of the opposite side of your orbit: r₁ = r₀ + dr.

Your new semi-major axis is a = (r₀ + r₁)/2 = r₀ + dr/2.

Plug V₁ and a into the vis-viva equation to find dr in terms of dV:

V₁² = mu (2/r0 - 1/a)

(V₀+dV)² = mu (2/r₀ - 1/(r₀ + dr/2))

Now solve for dr, using V₀² = mu/r₀ to get rid of mu: dr = 4 r₀ dV / (V₀ + 2 dV)

Since dV << V₀, we can approximate this as: dr = 4 r₀ dV / V₀

Thus the fractional change in your radius is approximately four times the fractional change in your velocity: dr/r = 4 dV/V.

Suppose for example you dock equal mass parts at about 0.2 m/s, changing your station velocity by dV = 0.1 m/s.

Then dr = 4 r₀ dV / V₀ = 700000 m * 0.1 m/s / 2246 m/s = 125 m.

If you dock from behind, your apoapsis is raised by 0.125 km, and if you dock from in front, your periapsis is lowered by 0.125 km.

Enough docking, and you can move your orbit quite a bit.

This is not to say that you are not also experiencing a phantom force bug. At least that force should only be present when you are focus on the station or something near it.

Edited April 18, 2014 by Yasmy

[roblamb98]

Hello everyone,

First time posting here on the forums. I have been playing ksp on and off for the past year now. I just started playing again recently and started to build a space station. It's the largest I have built yet but I have noticed my periapsis seems to be slightly dropping since the first piece I sent up. When I started building the station the periapsis was around 99.8 km with my apoapsis being about 101 km. I have brought up quite a few pieces since then, I have a refueling adapter put up, 2 solar arrays, and around 6 or 8 living units (containers, pods, science labs/cuppola). Now my periapsis is currently at 98.973 km, which to me seems like a pretty significant drop. I will be in map mode and I can also see the periapsis slightly dropping. Is this a normal thing that I shouldn't worry about? Or is it something that will affect my station significantly like continually dropping till it de-orbits? I'm not anything close to a scientist, but it seems strange to me that it keeps dropping when I (believe that I am) am in a stable orbit quite a bit above the atmosphere so I shouldn't have to worry about falling back to Kerban. Any help would be greatly appreciated!

Thank you fellow kerbalnauts!

Kerbatron343

maybe docking adds a small change in velocity, which , over time, could slow an orbit