[quote][quote]If and only if the derivative of the distance between two objects (dr/dt) was in exactly the direction same as the distance between the two objects r/[quote]
I think this is not correct.
The derivative of distance is always in the same direction as the distance itself because distance is a scalar.
The derivative of distance is already the component of relative velocity in the direction of the distance, so there is no need to say "If they are in the exact same direction"; by definition they already are./quote]
I just realized that I should have said that if the speed that the objects are moving relative to each other is in exactly the same direction as the distance between the two objects. If the speed the objects are moving relative to each other is in exactly the same direction as the distance between the objects then speed the that the two objects are moving relative to each other is the same as the derivative of the distance between the two objects (dr/dt) but if the speed two objects have relative to each other is in a different direction from the direction of the distance then the speed the two objects have relative to each other is not the same as the derivative of the distance (dr/dt). If there is no overlap between the direction of the speed the two objects have relative to each other with the direction of the distance between the two objects then no gravitons can be exchanged between the objects and so the gravitational force between the objects is 0. If there is some overlap between direction of the speed that two objects are moving relative to each other and the direction of the distance between the two objects then how often gravitons can be exchanged between the two objects depends on how much the directions overlap so the force depends on how much the directions overlap.
Suggestions! (new)

 Posts: 75
 Joined: Thu May 15, 2014 5:45 pm
Re: Suggestions! (new)
Gravitons would be my favorite particle as their existence could prove extra dimensions.
Re: Suggestions! (new)
Yeah, that makes more sense. The derivative of the distance is the dot product of the relative velocity and the axis between the two objects. So, as you said, the more the relative velocity lines up with that axis, the greater the force. If the relative velocity is perpendicular to the axis, then the derivative and the force are 0. For intermediate angles, it is proportional to cos(theta).
Binomial Theorem: ((a+b)^n)= sum k=0>k=n((n!(a^(nk))(b^k))/(k!(nk)!))

 Posts: 75
 Joined: Thu May 15, 2014 5:45 pm
Re: Suggestions! (new)
In this case the uncertainty principle would be σpσv=ħ/2 with σp being the uncertainty in momentum and σv being the uncertainty in velocity.
From the equations p=ma we can get the equation σp=mσa in which σa is the uncertainty in acceleration and m is the mass and from the equation a=mv^2/r we can get the equation σa=(σv)^2/σx in which σx is the uncertainty in position.
From the equations p=ma we can get the equation σp=mσa in which σa is the uncertainty in acceleration and m is the mass and from the equation a=mv^2/r we can get the equation σa=(σv)^2/σx in which σx is the uncertainty in position.
When I said that the force was based on how much the direction of the distance between two objects and the speed the two objects are moving relative to each other I didn't mean what the angle is between the direction of the relative speed and the direction of distance. Instead what I meant is that the force is based on the fact that objects tend to have a non zero volume in position space as well as a non zero volume in velocity space so even if the force depends on what fraction of the two objects have the speed and position in the same direction. When I refer to the fraction of the two objects I mean the fraction of mass of the two objects for gravity and the fraction of electric charge when it comes to electromagnetism.So, as you said, the more the relative velocity lines up with that axis, the greater the force. If the relative velocity is perpendicular to the axis, then the derivative and the force are 0. For intermediate angles, it is proportional to cos(theta).
Gravitons would be my favorite particle as their existence could prove extra dimensions.
Re: Suggestions! (new)
Uncertainty Principle? I thought we were working with macroscopic objects, not quantum mechanics. If we are working with large objects, the uncertainty principle is irrelevant.
The cosine function is just the most natural way to do this mathematically. The closer the velocity is to being 'in the same direction' as the axis, the closer cos(theta) will be to 1.
As you said, different parts of an object are moving different directions. However, when we add up these contributions, we will find that the total velocity is equal to the velocity of the center of mass. So when considering the velocity of an extended object, we can neglect the spread in velocities of the individual parts and only consider the velocity of the center of mass.
Also, to clarify, in our force equation F = da/dt = G*m1*m2*(dr/dt) /r, two objects getting closer experience a force away from each other, and two objects moving farther apart experience a force toward each other. In other words, if dr/dt if negative, the force is repulsive and if dr/dt is positive, the force is attractive. This is necessary for stable orbits.
Suggestion for Andy: Allow us to use dr/dt as a variable in the force equation on the full simulator.
Also, AlternateGravity, why are you assuming that two objects cannot exchange gravitons if moving away from each other?
There is no such thing as moving in the exact same direction. There will always be some angle (error) between velocity and the axis between two objects. So we have to define some way to decide how close two vectors are to being 'in the same direction'.what fraction of the two objects have the speed and position in the same direction
The cosine function is just the most natural way to do this mathematically. The closer the velocity is to being 'in the same direction' as the axis, the closer cos(theta) will be to 1.
As you said, different parts of an object are moving different directions. However, when we add up these contributions, we will find that the total velocity is equal to the velocity of the center of mass. So when considering the velocity of an extended object, we can neglect the spread in velocities of the individual parts and only consider the velocity of the center of mass.
Also, to clarify, in our force equation F = da/dt = G*m1*m2*(dr/dt) /r, two objects getting closer experience a force away from each other, and two objects moving farther apart experience a force toward each other. In other words, if dr/dt if negative, the force is repulsive and if dr/dt is positive, the force is attractive. This is necessary for stable orbits.
Suggestion for Andy: Allow us to use dr/dt as a variable in the force equation on the full simulator.
Also, AlternateGravity, why are you assuming that two objects cannot exchange gravitons if moving away from each other?
Binomial Theorem: ((a+b)^n)= sum k=0>k=n((n!(a^(nk))(b^k))/(k!(nk)!))
Re: Suggestions! (new)
I know this may be an odd suggestion, but in the many hours I've spent playing around with the full version, I've come to find that it's quite fun to make solar systems and attempt to send very low mass "probes" from planet to planet, adjusting during transit to try and fall into orbit around another body. Perhaps it's just me, but I thought it would be interesting to be able to actually choose what elements the planets are made of. I was thinking there could be a list of common elements in terrestrial and gas giant planets, and the choice you make could impact the density of the planet, and perhaps the color with assignment. It would be interesting to collide planets rich in different elements to see how it interacts!
I also thought how interesting it would be to have a radiation type of visual indicator in the game. Based on the size of the star, you could have a switch for an infraredtype view that shows surface temperatures of planets, showing habitable zones and giving more insight into what the planets would be like. Pondering on that made me think of how neat it would be to be able to visualize Van Allen belts and color indicated gravitational heat maps... I get too into this game!
I also thought how interesting it would be to have a radiation type of visual indicator in the game. Based on the size of the star, you could have a switch for an infraredtype view that shows surface temperatures of planets, showing habitable zones and giving more insight into what the planets would be like. Pondering on that made me think of how neat it would be to be able to visualize Van Allen belts and color indicated gravitational heat maps... I get too into this game!
 testtubegames
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Re: Suggestions! (new)
Welcome to the forums, encephale  and glad you're enjoying the simulator!
Navigating a probe around *does* sound really fun. I'll have to think about whether I can do that without blowing up the scope too much (the story of this project, right?) I noticed now that you can edit the pos/vel of planets with your mouse, you can kind of drag them around the world, and they follow your mouse... and even that is pretty fun. I should prototype and see what a rocket would feel like in the sim.
You mentioned picking the different elements for the planets  and it made me start thinking about No Man's Sky A massive number of different planets with different properties, based on their makeup.
A radiation indicator is interesting. Since these 'stars' are really just idealized gravitational bodies, I'm not sure if there's a clear way to choose some scientifically accurate temperature of the star. Hmm.
The extra visual settings suggestions are neat  I'd love to figure out a good way to, for instance, draw gravitational equipotential lines, like this: https://en.wikipedia.org/wiki/Hill_sphere. The trick with any crazycomplex visuals like that is they'd probably not render in realtime (you'd have to pause the sim and load them up). Not sure if that'd be something people would be interested in? It wouldn't necessarily fit with the realtime nature of the sim, but it's something I've been batting around.
Navigating a probe around *does* sound really fun. I'll have to think about whether I can do that without blowing up the scope too much (the story of this project, right?) I noticed now that you can edit the pos/vel of planets with your mouse, you can kind of drag them around the world, and they follow your mouse... and even that is pretty fun. I should prototype and see what a rocket would feel like in the sim.
You mentioned picking the different elements for the planets  and it made me start thinking about No Man's Sky A massive number of different planets with different properties, based on their makeup.
A radiation indicator is interesting. Since these 'stars' are really just idealized gravitational bodies, I'm not sure if there's a clear way to choose some scientifically accurate temperature of the star. Hmm.
The extra visual settings suggestions are neat  I'd love to figure out a good way to, for instance, draw gravitational equipotential lines, like this: https://en.wikipedia.org/wiki/Hill_sphere. The trick with any crazycomplex visuals like that is they'd probably not render in realtime (you'd have to pause the sim and load them up). Not sure if that'd be something people would be interested in? It wouldn't necessarily fit with the realtime nature of the sim, but it's something I've been batting around.