An Idiot's thoughts on orbital distance

[dalthor]

We can probably all agree that Bode's Law is fundamentally flawed - it kinda sorta used to work for our solar system, but has been discredited by many other observations.

I've basically thrown out orbital distance FOR NOW. I simply refer to the orbit number these days, and WAG [woeful assumptive guess] the distance, and therefore the travel time. Basically, everything is moving at the speed of story.

Side note: I'll probably go back to using T5 mechanics, pending a scientific breakthrough. lol

I was thinking about orbital distances, and had an idea. I'm not a math person - orbital mechanics give me glazed eyes. This means I have no clue how this would work, or if it is even possible.

I posit using four primary parameters:
- Solar Mass [SM]
- Plant/moon/gas giant/etc Mass [PM]
- Orbital speed (angular momentum or speed???) [OS]
- Distance (from the star)

The orbital distance is a function of those four basic parameters, ignoring other orbital bodies.

Is it possible to come up with a function that can get in the ballpark with orbital distances? I don't need true scientific accuracy, and don't care if it is RW compliant or not.

For example, OS = (SM/PM) / D or D = (SM/PM) ^ OS or some such.

This is just something I've been toying around with. I figured I'd post it because there are some brilliant minds on CotI; maybe somebody here can stand science on its head.

 

[whartung]

I posit using four primary parameters:
- Solar Mass [SM]
- Plant/moon/gas giant/etc Mass [PM]
- Orbital speed (angular momentum or speed???) [OS]
- Distance (from the star)

Actually, the mass of the star and velocity are the two determinants of orbital distance. The mass of the object in orbit (normally) doesn't really matter -- the star really dominates the equation.

Each orbit supports a specific velocity. If you're going to fast, then you're leaving orbit. If you're going to slow, then the orbit is decaying.

You can't have 2 objects in the same orbit going different speeds.

A simply example is to put a weight on a string, and start spinning it around. At high speed, the string is perpendicular to the axis of the rotation, but as you slow it down, the string starts to drift down.

Same thing is involved with orbits.

So.

v = sqrt(Gm/r)

G = Gravitational constant (6.674×10−11)
m = mass of thing you're orbiting
r = orbit radius.

Now, things like Jupiter are big enough that this doesn't quite apply. Truth is in our solar system, Jupiter does orbit the Sun, but it's big enough to skew the Suns path (they actually kind of orbit each other). You can go to https://en.wikipedia.org/wiki/Barycenter for more details on this.

But this is a game, and the above math will work for 99.99999% of the situations.

 

[Blue Ghost]

Orbital distances for what, though? Ships? Moons? Planets? Comets? Polar? Geosynchronus?


What Whartung said; ships orbiting a planet is kind of a no brainer. Technically speaking aircraft or even birds are "in orbit", but are constantly correcting for pull via power output.

 

[jcrocker]

All of the above.

If you've got a planet orbiting the star, the star's mass dominates the equation so much that the planet's mass doesn't really matter from a math point of view.

Same for a ship orbiting a planet, the mass of a type S scout compared to the mass of the earth is much less than a rounding error.

The equations don't differentiate between polar or equatorial orbit. You plug in the values to find the distance of the thing orbiting from the bigger thing it is going around.

The 'orbit equation' I found was: (mv^2)/r = (GMm)/r^2, where m is mass of small body, M is mass of large body, G is gravitational constant, r is orbital radius.

If you're looking for the distance, and I've done the math right, it solved down to r = (GM)/v^2

If your ship is in a fast orbit, it has to be lower down in the gravity well. If your ship is in a slow orbit, it would be far out.

Same with planets and stars - compare the orbital speed of Jupiter to Mercury.

Also, birds and aircraft are not in orbit - I googled "orbital speed of earth" and the first result said "Short version: Earth's average orbital speed is about 30 kilometers per second." Nothing in atmosphere moves that fast, the friction would kill them. No one would need expensive launch vehicles to get to orbit if an aircraft could do it.

 

[BRJN]

2300AD uses a system generation method where the orbit of the next planet out is a multiple of the reference planet's orbit (measured in AU). If you want a 'realistic-looking' system, build a chart that uses IRL ratios for exoplanets.

Important point, though: your travel times only need to be close enough that your players do not stop in bewilderment or disbelief. "It takes 3 days to get to Venus with your ship's 1G drive" is just fine, you don't have to get down to "2 days 18 hours 33 minutes 47 and a half seconds later you settle into orbit"

 

[Blue Ghost]

*snip*

Also, birds and aircraft are not in orbit - I googled "orbital speed of earth" and the first result said "Short version: Earth's average orbital speed is about 30 kilometers per second." Nothing in atmosphere moves that fast, the friction would kill them. No one would need expensive launch vehicles to get to orbit if an aircraft could do it.

An orbit, by definition, is a circular path. Flying objects orbit when they circle something. It's not specific to celestial objects, nor velocity dependent.

 

[whartung]

An orbit, by definition, is a circular path. Flying objects orbit when they circle something. It's not specific to celestial objects, nor velocity dependent.

Yes, that's the generic definition, but the context here is specific to objects in stable orbits, which are velocity dependent.

 

[jcrocker]

An orbit, by definition, is a circular path. Flying objects orbit when they circle something. It's not specific to celestial objects, nor velocity dependent.

I think you may be conflating terms. Your first post was asking about Bode's Law which I don't think has ever been applied to birds.

This is google's definition of orbit: "the curved path of a celestial object or spacecraft around a star, planet, or moon, especially a periodic elliptical revolution."

One example of an elliptical orbit - https://en.wikipedia.org/wiki/Molniya_orbit

 

[Blue Ghost]

All flying object are said to be orbiting. It's not a big deal. I don't understand the OP's question.

 

[aramis]

All flying object are said to be orbiting. It's not a big deal. I don't understand the OP's question.

You also got a basic fact wrong... Orbits are ellipses, not circles.

 

[ShawnDriscoll]

All flying object are said to be orbiting. It's not a big deal.

See circumnavigate, for slower-than-orbit speeds.