Orbital period Puns

How did Kepler know the mean radius to the Sun for the planets, and how long they took to go around the Sun?

Hey all!

I'm incorporating TRAPPIST-1 e into the worldbuilding for my sci-fi setting and I was wondering what the effects would be of a year lasting a week and a day lasting 1/4 of a year on Earth. The atmospheric content is very similar to Earth and so is the gravity, but I don't know what I want the axial tilt to be yet. My setting is hard sci fi, so I'd like to make the composition of my inhabited exoplanets to be as realistic as possible. That being said, I know that it is often the case with exoplanets that one has to do a lot of speculating as to the true nature of these distant celestial bodies (which is to say, fill in the gaps). This presents a unique opportunity though: the ability to pick and choose the unknown attributes of TRAPPIST-1 e to create some really interesting worldbuilding. I'd love to hear any advice/first thoughts you guys have.

Thanks so much! :)

I have data that spans several years, with time of passage (specifically time of ascending node) measurements taken at random times (constrained by observation dates). We also have a model of the orbit that tells us the expected values for the time of passage. Using the best-fit orbital model, we are left with some residual; I.e the time of passage at time x is slightly early/slightly late. I reckon this is due to a white noise process occurring in orbital period, meaning if the time of orbit x is slightly smaller than in the model, the time of passage will be earlier than the model prediction. Anyone out there familiar with how deduce the white noise in period from time of passage measurements?

Can also be written as: there is a random walk in time of passage, governed by white noise in period. What is the best way of describing/parameterising the white noise in period?

I was thinking about how to insert 5 relay satellites around the sun along Kerbin's orbit (to make a 6 pointed relay network, including Kerbin), and I figured my best options were to drop the orbital periods of the satellites to either 5/6 or 1/6 of a year.

I realize it's probably impossible to get the orbital period down to just 1/6 of a year, given the same aphelion as Kerbin, but that raises the question: what is the lowest possible orbital period I could get?

Is there a orbital period calculator or formula where I could enter a couple parameters such as ap, pe, body that I would be orbiting to get an orbital period?

Title

How do you find your ideal ap bassed on orbital period

Press play to start time: https://www.desmos.com/calculator/nrud5aim80

The equation for the spiral is short and sweet: r = (2πt/ø)^(2/3)

Here is another application of the equation for musical notes/frequencies. I call it the virtual monochord.

https://www.instagram.com/tv/CCE8P84pnPU/?utm_source=ig_web_copy_link

Hey, I'm currently working on a habitable exomoon orbiting a large jupiter-like gas giant. Where do I even begin calculating the orbital speed- and period? And what units of measure would I need to use?Incase needed:

Gas giant

Mass: 4.82 (9.14836 × 10^27 kg)
Radius: 2.17 (151706.87 km)
Gravity: 1.023 (jupiter is 1 for mass, density, radius and gravity)
Density: 1.382 (1.838 g/cm³)

Habitable moon

Mass: 0.37 (2209.64 × 10^24 kg)
Radius: 0.62 (3950.02 km) ­(earth is 1 for mass, density, radius and gravity)
Gravity: 0.596
Density: 0.96 (5.29 g/cm³)
Eccentricity: 0.0082
Semi-major axis: 9.3 R
Periapsis: 8.67 R (R= planetary radia)
Apoapsis: 9.93 R

I a super easy scenario, a person born on a world with a precise 548 earth-day orbit would have a birthday nearly every 18 earth-months. From an Earth-born point of view, if that person were born on January 1st, 2400 they would turn 1 on July 2nd of 2401. Then they'd be 2 on Jan 1st of 2403. But with Earth's Leap Days, their "birthday" would drift beginning in 2407.

And that's just in a scenario where we simplify all the variables down to just these.

With a Bajoran 26 hour day, every 12 days on Bajor is 13 on Earth. But what if Bajor has a shorter orbit than Earth? A Bajoran could celebrate their birthday more than once an Earth-year!

Thus, time is merely relative (we knew that) to arbitrary points in space based on the local conditions and observed repetition of consistent patterns.

The orbital period of two masses orbiting each other is supposed to be

2 * π * √(a^3 / (G * (M + m)))

where a is the semimajor axis of the orbit and M and m are the masses of the two bodies. If I plug in the values for Saturn and the Sun (a = 1.43353 * 10^(12) m, M = 1.9885 * 10^(30) kg, m = 5.6834 * 10^(26,) the result is

2×π×√((1.43353E12)^3÷(6.6743E-11×(1.9885E30+5.6834E26))) = 935,970,871 seconds, or 10,833 days

This is several months away from the actual period, which is 10,759 days. Where is the error in my math? Or are there other factors not captured by Kepler's Third Law? I'm trying to write a virtual planetarium using the recent great conjunction as a test case, and I suspect this is a source of error.

What is the name of the moon with the longest orbital period?

2 points

Submitted by u/orangevg

#0556 - February 10, 2021 - Theme: Science/Nature

JOIN OUR DISCORD! discord.gg/X592eNS

Give feedback on this question!

We are always looking for staff members! Apply here!

title says it all

Given a map such as an image in this post (the logistic map), how would I go about determining the point where period-doubling bifurcation occurs?

Eq-1

From the Eq-1, the stationary points are x0=0, x1=(r-1)/r. The stability requirement is |r-2rx|<1.

So x0 is stable if -1<r<1. x_1 is stable for 1<r<3. I can tell that there is a transcritical bifurcation at r=1.

From reading, there is a period-doubling bifurcation at r=3. I do not know how I would know that if I had not read about it. I coded a model for Eq-1 and it is clear that there is a period-doubling bifurcation at r=3 but how would I go about proving that there is a period-doubling bifurcation at r=3 if I could not code it? Thanks!

I have two stars in a system: one that's 1.05 solar masses and 0.95 solar masses orbiting on average 0.12 AU and 0.13 AU away respectively from the barycenter.

An Earth-like planet orbits on average 1.44 AU away from the barycenter with an eccentricity of 0.0001.

Every year on this planet is about 631 Earth days or 686 local days (each day on this planet has 22 Earth hours).

What equations do I need to figure out how long it takes for the two stars to complete orbits around the barycenter? What about for how often they eclipse each other in the sky of this planet?

I'm having issues with my relay satellites drifting out of sync, which limits my signal coverage. I've read on this sub that you need to match the orbital period as closely as possible and that MJ can do it to the hundredth of a second.

But how? The only method I can see is to look at the Orbit Info window while piloting one satellite, write down the period, then try to manually match it by piloting the other satellite(s).

Is there a way to just have MJ do this for me? I'm in career mode, but I've fully unlocked all of the MJ functions up to rendezvous autopilot.

Press play to start time. The distance of the planest is plotted in light seconds:

https://www.desmos.com/calculator/nrud5aim80