Help with the physics of a fictional geocentric solar-system

[TopQuark_]

Hello. This might seem like a silly topic, but I could use some help to build a geocentric model of a solar system.

Wait! Hear me out!

I'm doing bit of of creative writing, and have a story idea for a sci-fi in which a system is discovered that has a star, moon, and several planets orbiting one inhabited planet. It is sort of a mystery of how this is possible, but I won't bore you with that. Needless to say, it is all caused "dark energy force" (so essentially magic).

For the purpose of this model, gravity, and therefore Kepler's Laws, can be ignored. The central body can be considered a fixed point reletive to the "satellites".

The main information I actually want is the amount of force that would have to be exherted on the star by the "magic" to keep it in its path (I suppose it's not technically an orbit) in its twenty-five hour period. The star's mass and orbital axes are approximate to those of our solar system.

I have a feeling that the solution is simpler that it seems, but my math skills aren't the strongest, and taking gravity out of the equations is really doing my head in.

Please don't burn me for my heretical thoughts. I'm not a Flat-Earther, I swear! ;)
(Also, I'm new here, so apologies if this is in the wrong subforum)

 

[Dynamics101]

So we can assume the star has the same mass of our sun, the moon has the same mass as our moon and the planet has the same mass as earth? And they are all orbiting the planet, right?

 

[TopQuark_]

So we can assume the star has the same mass of our sun, the moon has the same mass as our moon and the planet has the same mass as earth? And they are all orbiting the planet, right?

For the purpose of this model, yes. Later, I can make some adjustments to the values so I'm not just copying our solar system. Though 'orbit', in this case, is a bit of a misnomer. More like "made to move in a circle", as 'orbit' would imply gravity is the acting force, and would therefore limit things like speed. Now that I think about it, wouldn't the star have to be moving a significant portion of the speed of light to make a revolution in twenty-five hours?

 

[davenn]

I'm doing bit of of creative writing, and have a story idea for a sci-fi in which a system is discovered that has a star, moon, and several planets orbiting one inhabited planet. It is sort of a mystery of how this is possible, but I won't bore you with that. Needless to say, it is all caused "dark energy force" (so essentially magic).

For the purpose of this model, gravity, and therefore Kepler's Laws, can be ignored. The central body can be considered a fixed point reletive to the "satellites".

The main information I actually want is the amount of force that would have to be exherted on the star by the "magic" to keep it in its path (I suppose it's not technically an orbit) in its twenty-five hour period. The star's mass and orbital axes are approximate to those of our solar system.

since you are ignoring real physical laws and making it all magic ... there are no real numbers that can fit this scenario
continue to use your "magic" and make up numbers as you go


Dave

 

[Dynamics101]

I think it'd depend on the distance between the star and your planet. If you want the massive sun to revolve around your planet, we can assume that the dark energy force has the ability to do so. Okay since we have ignored keeplers law and all that gravity stuff we can treat it like a ball on a string attached to a stick (I will use the approximate distance from the Earth to the moon).
1. Since we want a full revolution every 25 hours (90,000seconds). Let's use angular velocity; w = change in radius/ change in time
W = 2pi/90,000seconds. --> 6.98x10^-5rad/s
2. When angular velocity is multiplied by radius we can get velocity; W * R = V
6.98x10^-5rad/s * 3.8x10^8m = 2.653x10^4m/s
3. Using the force equation (F = ma) and writing acceleration as v^2/R we get
F = m(v^2/r).
mass of sun = 1.9x10^30kg
F = (1.9x10^30kg)*(2.653x10^4)^2 / (3.8x10^8)
F = 3..519x10^30 Newtons
This much force. LOL.

 

[TopQuark_]

I think it'd depend on the distance between the star and your planet. If you want the massive sun to revolve around your planet, we can assume that the dark energy force has the ability to do so. Okay since we have ignored keeplers law and all that gravity stuff we can treat it like a ball on a string attached to a stick (I will use the approximate distance from the Earth to the moon).
1. Since we want a full revolution every 25 hours (90,000seconds). Let's use angular velocity; w = change in radius/ change in time
W = 2pi/90,000seconds. --> 6.98x10^-5rad/s
2. When angular velocity is multiplied by radius we can get velocity; W * R = V
6.98x10^-5rad/s * 3.8x10^8m = 2.653x10^4m/s
3. Using the force equation (F = ma) and writing acceleration as v^2/R we get
F = m(v^2/r).
mass of sun = 1.9x10^30kg
F = (1.9x10^30kg)*(2.653x10^4)^2 / (3.8x10^8)
F = 3..519x10^30 Newtons
This much force. LOL.

Indeed. It's even sillier if you use the Earth-Sun semi-major axis as the radius.

V = (6.98x10^-5rad/s)(1.5x10^12m)
= 1.05x10^8m/s
≈ 1/3c

F = (1.9x10^30kg)(1.05x10^8m/s)^2/(1.5x10^12m)
= 1.397x10^34N

Sorry, I don't have a ton of experience with angular velocity. Is acceleration defined as 'v^2/R' because this is circular motion, making this centripital force?

This probably won't even be the story's actual in-canon explanation for this crazy concept. Dark energy has an effect on gravity, so it probably would work by manipulating the bodies' gravity fields. I'd have to seriously mutilate general relativity to offer a legitamate-sounding explanation for this, so I'm not even going to touch it.

 

[Dynamics101]

Yes, centripetal acceleration is defined as that. I think it should work for your story, Dark energy should account for these things. And If I'm reading your story I'd like to have general understanding for the dynamics of your system. Not too much detail, but enough to make me wonder. [emoji5]

 

[AidenFlamel]

Hello. This might seem like a silly topic, but I could use some help to build a geocentric model of a solar system.

Wait! Hear me out!

I'm doing bit of of creative writing, and have a story idea for a sci-fi in which a system is discovered that has a star, moon, and several planets orbiting one inhabited planet. It is sort of a mystery of how this is possible, but I won't bore you with that. Needless to say, it is all caused "dark energy force" (so essentially magic).

Actually I've been going over this same concept for a few weeks if not months now. The thing is, I'm trying to create this extensive epic fantasy world but at the same time, i need to know how everything works in my head... And having a Geo-Centrical planetary system would be great for my world setting... though there are so many things to take into account. To bad we couldn't get to a more satisfying answer than "dark magical force is capable of ejercing x*10³⁰ Newtons and that's why..." Thanks for the thread anyway