/sci/ - Science & Math » Thread #14425299

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Please explain to me how geosynchronous satellites are even possible

Anonymous Sun 24 Apr 21:49:21 2022 No.14425299 View Reply Original Report

Quoted By: >>14425435 >>14425482 >>14425725

If the gravity is the only force apparent and the centripetal force of gravity naturally dies out with displacement and hence gravitational acceleration this fucking image should

In any yes any scenario

Should never work

Anonymous

Anonymous Sun 24 Apr 2022 22:41:50 No.14425435 Report

Quoted By: >>14425443

>>14425299
the idea is that it's the previous store owners name so they had to change the sign

Anonymous

Anonymous Sun 24 Apr 2022 22:44:57 No.14425443 Report

Quoted By:

>>14425435
Did you reply to the wrong thread by accident?

Anonymous

Anonymous Sun 24 Apr 2022 22:58:19 No.14425482 Report

Quoted By: >>14425502

>>14425299
As you alter the distance between the orbiter and the planet the orbital velocity changes. There is a sweet spot where this matches planetary rotation.
Hint: Different planets can rotate at different speeds even if they are otherwise identical

Anonymous

Anonymous Sun 24 Apr 2022 23:07:44 No.14425502 Report

Quoted By: >>14425515

>>14425482
Yeah I know what the inverse square law

The problem is that it’s an inverse square relation to begin with

There should never be an instance where an object further away from the object another object is orbiting is somehow travelling faster with no external net forces if there’s simultaneously less force of gravity applied on that object

The most realistic application of geosynchronous orbit I can see is determining how fast an object must be moving relative to another to maintain minimum displacements between each other in orbit. That’s it the rest of the ideas behind this form of motion feel made up or straight bullshit

Anonymous

Anonymous Sun 24 Apr 2022 23:11:23 No.14425515 Report

Quoted By: >>14425537

>>14425502
Objects don't inherently reach geosynchronous orbit, it's a precise combination of position and high velocity. Satellites go from a speed of zero to orbital speed by having a big rocket accelerate them until the desired velocity is reached, at which point the rocket shuts off and it coasts along at that speed, very slowly slowing down due to friction with the interplanetary medium.

Anonymous

Anonymous Sun 24 Apr 2022 23:19:08 No.14425537 Report

Quoted By:

>>14425515
>very slowly due to interplanetary medium

You mean external gravitational forces caused by things like other planets moons and suns?

Anonymous

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Anonymous Mon 25 Apr 2022 00:10:54 No.14425639 Report

Quoted By: >>14425731

you have a planet with mass M and rotational frequency f. (For Earth this is 5.97E+24 kilograms and 1 rotation per day, respectively.)
You have a satellite. From elementary mechanics, you know that the period of the satellite's orbit f' around our planet is and its radius R are related by $f'=\sqrt{\frac{GM}{4\pi^2R^3}}$ You should be able to derive this on the back of an envelope in less than 45 seconds if you forgot this fact. "Geosynchronous" means it looks like the satellite is floating stationary above some fixed point on the surface of our planet.
In other words, you want the satellite orbit frequency to match the planet's frequency of rotation. Since we cannot change M or G, we pick a radius or altitude of orbit such that we can match $f'=f$ . With the known values of G and M, we can rearrange: $f'=f\implies R=\sqrt[3]{\frac{GM}{4\pi^2 f^2}}=42\ \text{thousand kilometers}$ The radius of the earth is already over six thousand kilometers, though, so the desired altitude of orbit of a geosynchronous satellite above the earth is about 35 thousand kilometers.

If it orbits here, it looks like it is floating because it happens to be orbiting at the same rate that the earth is rotating on its axis. that's it. its pretty simple.

Anonymous

Anonymous Mon 25 Apr 2022 00:56:24 No.14425725 Report

Quoted By:

>>14425299
Think in terms of angular velocity, not linear. Just match the two and figure out at what radius it works out

Anonymous

Anonymous Mon 25 Apr 2022 00:59:57 No.14425731 Report

Quoted By:

>>14425639
Not OP but I wonder if OP is worried about this orbit being metastable. Over time the tides from Earth and the orbit of the Moon should shift a GEO sat out of GEO, probably ahead of the Earth's rotation into the "graveyard orbits".
GEO would, I think, need a bit of propulsion to keep it there long term.

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