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Khurram Wadee

2024-02-24 10:27:30


#xkcd: #OrbitalArgument


https://xkcd.com/2898/


Orbital Argument

xkcd

in reply to Hank G ☑️

vruz
vruz
• •

Waiddaminute, even that is arguably not the definitive answer. The definitive answer is: it depends.

Earth's orbit is an ellipse, and from a mathematical point of view, ellipses have two centres (called foci), not one. From an astrophysics point of view, to simplify, people came up with the concept of the barycentre, which is the common centre of mass around which two or more objects orbit due to their gravitational attraction.

This entry was edited (4 months ago)
in reply to Hank G ☑️

randygalbraith
randygalbraith
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In one of my courses I had to calculate the common center for the Earth Moon system. My recall is that it is several km below the Earth surface.
in reply to Hank G ☑️

Hank G ☑️
Hank G ☑️
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Right the joke is about the barycenter about which two objects orbit each other. It gets even more complicated when you remember that these aren't point masses orbiting each other. So the elliptical approximation of the orbit is for one instant in time, even if we are just accounting for gravity and no other forces. What you end up with when you view the state in terms is an osculating element set over time. If you graph the terms you'll see a larger trend in the orbit state and a much faster oscillating looking component along the the curve as well. The barycenter is constantly changing as well. For systems with very large mass discrepancies, say a man-made satellite around the earth, you can essentially say it is the center of the larger mass.
in reply to Hank G ☑️

Isaac Ji Kuo
Isaac Ji Kuo
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Oh noes, you're doing it also!

The "common center" isn't the barycenter about which Earth and the Sun orbit "each other".

The Sun's position is more or less unaffected by puny Earth.

It's Jupiter and Saturn that causes the Solar System barycenter to sometimes be outside of the Sun. And Uranus and Neptune have an outsized effect because they're further away (the effect is proportional to distance and mass).

in reply to Isaac Ji Kuo

Isaac Ji Kuo
Isaac Ji Kuo
• •

So I see the joke as even more meta ...

I mean ... the thing that's so frustrating is that usually the truth is too complicated to say succintly, so it's just too much effort to feel like correcting the person who spoke up with the right conclusion via the wrong reasoning.

That's the bigger problem ... the Dunning Kruger victim confidently participates in the discussion halfway around the world while the person who knows the truth decides to not bother putting their boots on.

in reply to Isaac Ji Kuo

Hank G ☑️
Hank G ☑️
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@Isaac Ji Kuo Well I was referring to barycenter of two body orbits generically. It's the center of mass of the two objects. And yes, when we calculate that for ridiculously lopsided bodies it essentially collapses to the center of the biggest body. But yes when we calculate solar system barycenter the earth is not really driving it much. While we do often use, if not generally use, solar system barycenter for sun orbiting objects I do believe for cis-lunar we still just stick with the earth center and treat the moon as a secondary gravitational field.
@Isaac Ji Kuo
in reply to Hank G ☑️

Hank G ☑️
Hank G ☑️
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@Isaac Ji Kuo I'm referring to the coordinate system origin for state and force calculations when saying "use solar system barycenter" or "stick with earth center".
@Isaac Ji Kuo
in reply to Hank G ☑️

Isaac Ji Kuo
Isaac Ji Kuo
• •

Yeah, when it comes right down to it, the only way to put it in a small number of words is, "It's complicated."

For example, for cis-lunar it depends on the context, what we use. For most BOE calcs for most orbits, you want to ignore the Moon. Beyond that, for some BOE purposes, the Sun can be ignored but for others it can't.

When it comes to actual mission planning and navigation, BOE type simplifications aren't appropriate. So ... yeah, there's no short way to summarize it.

in reply to Hank G ☑️

Hank G ☑️
Hank G ☑️
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...but to beat the joke to death, it is radically more correct to reduce the physics to say the earth orbits the sun than the other way around.
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