According to 1905 Relativity, a single material point must be always at rest
in [Relativity]
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From: valls on 28 May 2010 12:48 On 27 mayo, 14:56, Darwin123 <drosen0...(a)yahoo.com> wrote: > On May 27, 10:08 am, va...(a)icmf.inf.cu wrote:> On 25 mayo, 19:16, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > On May 25, 5:42 pm, va...(a)icmf.inf.cu wrote: > > > > > On 21 mayo, 15:00, Darwin123 <drosen0...(a)yahoo.com> wrote:> On May 20, 6:17 pm, va...(a)icmf.inf.cu wrote:> On 20 mayo, 11:57, Darwin123 <drosen0...(a)yahoo.com> wrote:> On May 20, 12:28 pm, va...(a)icmf.inf.cu wrote:> On 20 mayo, 08:50, harald <h...(a)swissonline.ch> wrote:> On May 20, 3:19 pm, va....(a)icmf.inf.cu wrote: > > He simply denotes stationary frame a reference one> in which the equations of Newtonian mechanics hold good (the first > > By the way, the presence of an external force accelerating > > the centre of mass of some inertial system doesnt affect at all the > > holding of Newtons laws in it when the same acceleration is shared by > > all the bodies composing the system. > > By the way, this statement is not true. > If we have a set of measuring instruments (clocks and rulers) that > accelerate in the exact same way relative to the stationary frame, as > defined by Einstein, then each is acted on by an outside "force". Each > an every instrument in this frame has to be subject to a force equal > to the mass of this instrument times this acceleration. If there is no > such force, then the instruments are not obeying the first and second > laws. > If these instruments are used to examine another body to which no > force is applied, then these instruments will determine that this new > body is accelerating in a direction equal and opposite the > acceleration of the frame. > The acceleration of this new body, isolated from forces, violates > Newton's first law. A body in motion without any outside force > accelerated. > Thus, the acceleration of the instruments relative to the > stationary frame can be measured using an accelerometer. The > accelerometer is a device that uses a body that is isolated from the > forces that accelerate the instruments in the accelerated frame. > For instance, suppose we have a set of positively charged clocks > and rulers accelerated by a homogeneous and stationary electric field. > Now, it is impossible to measure the acceleration using any of these > positively charge instruments. However, we can take another body and > place it in an enclosed metal container. Then, this body won't be > accelerated by the electric field. It hits the side of the metal > container. The impact tells us the acceleration of the frame. > 1) A body in motion tends to remain in motion, unless acted on by some > outside force. > Ever Consider the Solar System (SS) motion in the Galaxy. Taking into account the great distance between SS and the rest of the Galaxy, the gravitational acceleration the Galaxy provokes in all bodies composing the SS is with an extraordinary accuracy practically the same. This is why the SS is the more accurate inertial frame known by men. I write when the SAME acceleration is shared by all the bodies composing the system. That is the condition for any accelerated system to be internally an inertial frame. My statement is true. The unique not true is the existence of a system in the real world with a mathematically exact same acceleration in all its bodies provoked by the rest of the Universe in it. RVHG (Rafael Valls Hidalgo-Gato)
From: PD on 28 May 2010 13:32 On May 28, 11:06 am, va...(a)icmf.inf.cu wrote: > On 28 mayo, 09:01, PD <thedraperfam...(a)gmail.com> wrote: > > > On May 28, 8:55 am, va...(a)icmf.inf.cu wrote: > > > > On 27 mayo, 10:52, harald <h...(a)swissonline.ch> wrote: > > > > > On May 24, 12:47 pm, va...(a)icmf.inf.cu wrote:> On 21 mayo, 04:35, harald <h...(a)swissonline.ch> wrote: > > > > > [..] > > > > > > > > By the way, we are considering here only 1905 Relativity (and > > > > > > > I was born long after that epoch). 1905 Einstein can support only 1905 > > > > > > > Relativity. > > > > > > > Exactly, that is what I referred to. His purpose was to show how: > > > > > > > "the same laws of electrodynamics and optics will be valid for all > > > > > > frames of reference for which the equations of mechanics hold good" > > > > > > > with the clarification: > > > > > > > "In order to render our presentation more precise and to distinguish > > > > > > this system of co-ordinates *verbally* from others which will be > > > > > > introduced hereafter, we call it the ``stationary system.'' " > > > > > > And the stationary system is for 1905 Einstein a one in which the > > > > > equations of Newtonian mechanics hold good and a time can be > > > > > determined applying his clock synchronization procedure, i.e., > > > > > according to our previous considerations, a centre of mass inertial > > > > > frame corresponding to a body set with at least two bodies.> That is at odds with your statement that: > > > > > > > > > > "the moving system must be always part > > > > > > > > > of the stationary system, and a stationary system moving with > > > > > > > > > respect to a moving system at rest is nothing more that a huge > > > > > > > > > absurd [..]. > > > > > > What contradiction do you find between that statement and 1905 > > > > > Einstein? > > > > > In SRT we are free to choose which Newtonian coordinate system we call > > > > "moving" and which one "stationary"; as they are equally valid for the > > > > laws of physics, not one of the two is preferred. The only way in > > > > which "mass" is relevant is that it is convenient to choose a high > > > > mass object as approximation for a Newtonian reference system. That is > > > > at odds with your introduction of "body sets" and your preference for > > > > calling certain "centre of mass" systems "stationary" and not > > > > "moving". And here below you do it again... > > > > We are not addressing here SR theory, but 1905R one. That they are > > > different theories can be checked very easily. > > > No, they are not. They are different presentations of growing > > sophistication of the SAME theory. > > Comment then my arguments showing why they are different theories. > Explain to me then why being Gravity out of the scope of SR, in the > 1905R we find as an example the rotating Earth as the stationary > system and a clock at the equator as the moving system gravitational > centripetal accelereted with a CIRCULAR trajectory! Being the Earth > also gravitational centripetal accelerated by the Sun, explain to me > what kind of inertial systems are managing 1905 Einstein with Gravity > present. Where are the movements with uniform linear velocities > characteristic of inertial frames in SR? > Can you consider the (moving) clock at the equator at rest, with the > clock (at rest in the pole) moving with respect to it? Are not all > inertial frames equivalent ones? Are not all of them equivalent to > describe our Universe? Try to describe the Sun's trajectory in the GPS > ECI frame, the same one that is the stationary system in the 1905R > example. When you showed me the Sun's trajectory in the ECI I will > trust in you when saying that SR and 1905R are the same theory. If you > can't do it, you must explain me in detail why it is imposible to > describe the Sun's trajectory in the ECI without violating the > Newton's laws that define an stationary system in 1905R. > > RVHG (Rafael Valls Hidalgo-Gato) Indeed, and again this points to the problem of reading papers in isolation, and also considering a seminal paper to be the complete presentation of a theory. The "1905R" paper you mention is NOT a complete explication of special relativity, let alone relativity. It is the FIRST explication of special relativity, and as such it has a number of hanging threads, unfinished business, only partly explicated answers, superficially understood and explained concepts, and so on. For example, the 1905R paper makes a statement about the laws of physics in *inertial* reference frames, which had a very well understood meaning in physics well before this paper, and was not replaced in meaning by this paper. However, as you noted, Einstein attempted to bend this statement to apply the principle to a NONinertial frame, that inhabited by a clock at the Earth's equator. This iffy application was noted by people working on relativity after this paper, including Einstein himself, and there were a couple of outcomes from this specific example. One was the more complete calculation of the effect per general relativity. Another was the discovery that accelerating reference frames could be analyzed with care using special relativity. Both these results came well after the 1905R paper, but are both part of relativity -- or, more appropriately, part of the relativistic aspects of nature that were being discovered by physicists in this time period. PD
From: Darwin123 on 28 May 2010 15:57 On May 28, 12:48 pm, va...(a)icmf.inf.cu wrote: > On 27 mayo, 14:56, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 27, 10:08 am, va...(a)icmf.inf.cu wrote:> On 25 mayo, 19:16, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 25, 5:42 pm, va...(a)icmf.inf.cu wrote: > > > > > > On 21 mayo, 15:00, Darwin123 <drosen0...(a)yahoo.com> wrote:> On May 20, 6:17 pm, va...(a)icmf.inf.cu wrote:> On 20 mayo, 11:57, Darwin123 <drosen0...(a)yahoo.com> wrote:> On May 20, 12:28 pm, va...(a)icmf.inf.cu wrote:> On 20 mayo, 08:50, harald <h...(a)swissonline.ch> wrote:> On May 20, 3:19 pm, va...(a)icmf.inf.cu wrote: > > > He simply denotes stationary frame a reference one> in which the equations of Newtonian mechanics hold good (the first > > > By the way, the presence of an external force accelerating > > > the centre of mass of some inertial system doesnt affect at all the > > > holding of Newtons laws in it when the same acceleration is shared by > > > all the bodies composing the system. > > > By the way, this statement is not true. > > If we have a set of measuring instruments (clocks and rulers) that > > accelerate in the exact same way relative to the stationary frame, as > > defined by Einstein, then each is acted on by an outside "force". Each > > an every instrument in this frame has to be subject to a force equal > > to the mass of this instrument times this acceleration. If there is no > > such force, then the instruments are not obeying the first and second > > laws. > > If these instruments are used to examine another body to which no > > force is applied, then these instruments will determine that this new > > body is accelerating in a direction equal and opposite the > > acceleration of the frame. > > The acceleration of this new body, isolated from forces, violates > > Newton's first law. A body in motion without any outside force > > accelerated. > > Thus, the acceleration of the instruments relative to the > > stationary frame can be measured using an accelerometer. The > > accelerometer is a device that uses a body that is isolated from the > > forces that accelerate the instruments in the accelerated frame. > > For instance, suppose we have a set of positively charged clocks > > and rulers accelerated by a homogeneous and stationary electric field. > > Now, it is impossible to measure the acceleration using any of these > > positively charge instruments. However, we can take another body and > > place it in an enclosed metal container. Then, this body won't be > > accelerated by the electric field. It hits the side of the metal > > container. The impact tells us the acceleration of the frame. > > 1) A body in motion tends to remain in motion, unless acted on by some > > outside force. > > Ever > > Consider the Solar System (SS) motion in the Galaxy. Taking into > account the great distance between SS and the rest of the Galaxy, the > gravitational acceleration the Galaxy provokes in all bodies composing > the SS is with an extraordinary accuracy practically the same. I agree. The galaxy rotates as though it were a rigid body. This observation is often attributed to Dark matter. A rigid pie plate would also rotate the same way due to elastic-like forces between its atoms. These objects, even by your definition, can not be considered inertial frames. The centripetal acceleration of an atom in these rigid bodies increases with distance from the center. Therefore, the acceleration of bodies in the galaxy, and in a rotating pie plate, varies across the entire object. At the center of the pie plate, the centripetal acceleration is zero. At the edges of the pie plate, the acceleration is huge. You are thinking thinking of the angular velocity. The number of revolutions per unit time is constant in a rigid body. The number of times per megayear that an object orbits in the galaxy is almost the same, from center to edges. The suns orbit around the galaxy in principle could be measured by an accelerometer. This is the reason that I say the SS is not a precise inertial frame. This has nothing to do with the rigidity of the galaxy. Some accelerometers on the earths surface have the sensitivity necessary to measure the centripetal acceleration of the earths surface. The centripetal acceleration caused by galactic motion is fare less than that of the earths surface. The centripetal acceleration of the earths surface is too large a background to even consider measuring the acceleration due to the galaxy. It is the difference between acceleration components that determines what is approximately an inertial frame, not the "rigidity" of the frame. On the equator surface, a tree is moving on or about 1000 miles per hour due to the earths spin (rotation of the earth around its pole). The centripetal acceleration due to this motion is 120 miles per hour squared. The Foucault pendulum, and the Sagnac interferometer, are sensitive enough to pick up this centripetal acceleration. Notice that the Foucault pendulum is fixed on a fairly rigid earth and on a fairly rigid frame. By your logic, the Foucault pendulum shouldn't work. After all, the earth also rotates like a rigid body on time scales shorter than centuries. The rigidity of rock doesn't make the surface of the earth an inertial frame. A Foucault pendulum is a great counter example of what Einstein meant by stationary frame. According to the Laws of Newton, the Foucault pendulum can not precess if its frame was stationary. The torque that causes the Foucault pendulum to precess does not seem to come from another body. Thus, the Foucault pendulum seems to violate Newton's Laws of motion, at least if you didn't know about the earths spin. In the frame of the rotating earth, a rigid object, the Foucault pendulum is experience a torque that seems to come from nowhere. However, the torque is proportional to the centripetal acceleration of the frame in a real inertial frame. The annual orbit motion and the galactic motion aren't detected by the Foucault pendulum because the corresponding centripetal accelerations are too small. > why the SS is the more accurate inertial frame known by men. This is incorrect. The reason that the center of the earth is close to being an inertia frame is because the other components of acceleration are extremely small. > I write > when the SAME acceleration is shared by all the bodies composing the > system. That is the condition for any accelerated system to be > internally an inertial frame. > My statement is true. The unique not true is the existence of a system > in the real world with a mathematically exact same acceleration in all > its bodies provoked by the rest of the Universe in it. > Explain to us, in your words, why a Foucault pendulum has a precessing period between 0 and 24 hours. Explain to us why the precess period at the equator is 24 hours, and at the north or south poles is zero. Explain why the precessing period is not one year because of the orbiting motion of the earth around the sun, or thousands of years because of the orbiting motion of sun about the galaxy.
From: Androcles on 28 May 2010 16:21 "Darwin123" <drosen0000(a)yahoo.com> wrote in message news:600bbce2-1f49-4623-9b39-4d168414750f(a)q23g2000vba.googlegroups.com... On May 28, 12:48 pm, va...(a)icmf.inf.cu wrote: > On 27 mayo, 14:56, Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 27, 10:08 am, va...(a)icmf.inf.cu wrote:> On 25 mayo, 19:16, > > Darwin123 <drosen0...(a)yahoo.com> wrote: > > > > > On May 25, 5:42 pm, va...(a)icmf.inf.cu wrote: > > > > > > On 21 mayo, 15:00, Darwin123 <drosen0...(a)yahoo.com> wrote:> On May > > > > > 20, 6:17 pm, va...(a)icmf.inf.cu wrote:> On 20 mayo, 11:57, > > > > > Darwin123 <drosen0...(a)yahoo.com> wrote:> On May 20, 12:28 pm, > > > > > va...(a)icmf.inf.cu wrote:> On 20 mayo, 08:50, harald > > > > > <h...(a)swissonline.ch> wrote:> On May 20, 3:19 pm, > > > > > va...(a)icmf.inf.cu wrote: > > > He simply denotes �stationary frame� a reference one> �in which the > > equations of Newtonian mechanics hold good� (the �first > > > By the way, the presence of an external force accelerating > > > the centre of mass of some inertial system doesn�t affect at all the > > > holding of Newton�s laws in it when the same acceleration is shared by > > > all the bodies composing the system. > > > By the way, this statement is not true. > > If we have a set of measuring instruments (clocks and rulers) that > > accelerate in the exact same way relative to the stationary frame, as > > defined by Einstein, then each is acted on by an outside "force". Each > > an every instrument in this frame has to be subject to a force equal > > to the mass of this instrument times this acceleration. If there is no > > such force, then the instruments are not obeying the first and second > > laws. > > If these instruments are used to examine another body to which no > > force is applied, then these instruments will determine that this new > > body is accelerating in a direction equal and opposite the > > acceleration of the frame. > > The acceleration of this new body, isolated from forces, violates > > Newton's first law. A body in motion without any outside force > > accelerated. > > Thus, the acceleration of the instruments relative to the > > stationary frame can be measured using an accelerometer. The > > accelerometer is a device that uses a body that is isolated from the > > forces that accelerate the instruments in the accelerated frame. > > For instance, suppose we have a set of positively charged clocks > > and rulers accelerated by a homogeneous and stationary electric field. > > Now, it is impossible to measure the acceleration using any of these > > positively charge instruments. However, we can take another body and > > place it in an enclosed metal container. Then, this body won't be > > accelerated by the electric field. It hits the side of the metal > > container. The impact tells us the acceleration of the frame. > > 1) A body in motion tends to remain in motion, unless acted on by some > > outside force. > > Ever > > Consider the Solar System (SS) motion in the Galaxy. Taking into > account the great distance between SS and the rest of the Galaxy, the > gravitational acceleration the Galaxy provokes in all bodies composing > the SS is with an extraordinary accuracy practically the same. I agree. The galaxy rotates as though it were a rigid body. This observation is often attributed to Dark matter. A rigid pie plate would also rotate the same way due to elastic-like forces between its atoms. These objects, even by your definition, can not be considered inertial frames. The centripetal acceleration of an atom in these rigid bodies increases with distance from the center. Therefore, the acceleration of bodies in the galaxy, and in a rotating pie plate, varies across the entire object. At the center of the pie plate, the centripetal acceleration is zero. At the edges of the pie plate, the acceleration is huge. You are thinking thinking of the angular velocity. The number of revolutions per unit time is constant in a rigid body. The number of times per megayear that an object orbits in the galaxy is almost the same, from center to edges. The suns orbit around the galaxy in principle could be measured by an accelerometer. This is the reason that I say the SS is not a precise inertial frame. This has nothing to do with the rigidity of the galaxy. Some accelerometers on the earths surface have the sensitivity necessary to measure the centripetal acceleration of the earths surface. The centripetal acceleration caused by galactic motion is fare less than that of the earths surface. The centripetal acceleration of the earths surface is too large a background to even consider measuring the acceleration due to the galaxy. It is the difference between acceleration components that determines what is approximately an inertial frame, not the "rigidity" of the frame. On the equator surface, a tree is moving on or about 1000 miles per hour due to the earths spin (rotation of the earth around its pole). The centripetal acceleration due to this motion is 120 miles per hour squared. The Foucault pendulum, and the Sagnac interferometer, are sensitive enough to pick up this centripetal acceleration. Notice that the Foucault pendulum is fixed on a fairly rigid earth and on a fairly rigid frame. By your logic, the Foucault pendulum shouldn't work. After all, the earth also rotates like a rigid body on time scales shorter than centuries. The rigidity of rock doesn't make the surface of the earth an inertial frame. A Foucault pendulum is a great counter example of what Einstein meant by stationary frame. According to the Laws of Newton, the Foucault pendulum can not precess if its frame was stationary. The torque that causes the Foucault pendulum to precess does not seem to come from another body. Thus, the Foucault pendulum seems to violate Newton's Laws of motion, at least if you didn't know about the earths spin. In the frame of the rotating earth, a rigid object, the Foucault pendulum is experience a torque that seems to come from nowhere. However, the torque is proportional to the centripetal acceleration of the frame in a real inertial frame. The annual orbit motion and the galactic motion aren't detected by the Foucault pendulum because the corresponding centripetal accelerations are too small. > why the SS is the more accurate inertial frame known by men. This is incorrect. The reason that the center of the earth is close to being an inertia frame is because the other components of acceleration are extremely small. > I write > �when the SAME acceleration is shared by all the bodies composing the > system�. That is the condition for any accelerated system to be > internally an inertial frame. > My statement is true. The unique not true is the existence of a system > in the real world with a mathematically exact same acceleration in all > its bodies provoked by the rest of the Universe in it. > Explain to us, in your words, why a Foucault pendulum has a precessing period between 0 and 24 hours. Explain to us why the precess period at the equator is 24 hours, and at the north or south poles is zero. ======================================================== The sidereal day is 23 hours 56 minutes. It doesn't change between equator and pole. If you set the pendulum swinging E-W at the equator it will continue swinging E-W. If you set the pendulum swinging N-S at the pole it will continue swinging N-N, you cannot set it swinging E-W. A very slowly swinging pendulum at the pole will do this: http://www.androcles01.pwp.blueyonder.co.uk/FrameB.gif or as seen from the Moon, http://www.androcles01.pwp.blueyonder.co.uk/FrameA.gif ======================================================== Explain why the precessing period is not one year because of the orbiting motion of the earth around the sun, or thousands of years because of the orbiting motion of sun about the galaxy.
From: Darwin123 on 28 May 2010 17:20
On May 28, 9:55 am, va...(a)icmf.inf.cu wrote: > On 27 mayo, 10:52, harald <h...(a)swissonline.ch> wrote: > > > On May 24, 12:47 pm, va...(a)icmf.inf.cu wrote:> On 21 mayo, 04:35, harald <h...(a)swissonline.ch> wrote: > > > [..] > > > > > > By the way, we are considering here only 1905 Relativity (and > > > > > I was born long after that epoch). 1905 Einstein can support only 1905 > > > > > Relativity. > > > > > Exactly, that is what I referred to. His purpose was to show how: > > > > > "the same laws of electrodynamics and optics will be valid for all > > > > frames of reference for which the equations of mechanics hold good" > > > > > with the clarification: > > > > > "In order to render our presentation more precise and to distinguish > > > > this system of co-ordinates *verbally* from others which will be > > > > introduced hereafter, we call it the ``stationary system.'' " > > > > And the stationary system is for 1905 Einstein a one in which the > > > equations of Newtonian mechanics hold good and a time can be > > > determined applying his clock synchronization procedure, i.e., > > > according to our previous considerations, a centre of mass inertial > > > frame corresponding to a body set with at least two bodies.> That is at odds with your statement that: > > > > > > > > "the moving system must be always part > > > > > > > of the stationary system, and a stationary system moving with > > > > > > > respect to a moving system at rest is nothing more that a huge > > > > > > > absurd [..]. > > > > What contradiction do you find between that statement and 1905 > > > Einstein? > > > In SRT we are free to choose which Newtonian coordinate system we call > > "moving" and which one "stationary"; as they are equally valid for the > > laws of physics, not one of the two is preferred. The only way in > > which "mass" is relevant is that it is convenient to choose a high > > mass object as approximation for a Newtonian reference system. That is > > at odds with your introduction of "body sets" and your preference for > > calling certain "centre of mass" systems "stationary" and not > > "moving". And here below you do it again... > > We are not addressing here SR theory, but 1905R one. That they are > different theories can be checked very easily. 1916 Einstein is the > one introducing by first time the word Special, transforming the > previous Relativity in SR according to the needs of his new GR. > Gravity is eliminated then, declaring it out of the scope of SR. But > Einstein (or any other) cant change history, and the presence of > Gravity in 1905R is out of any doubt. Gravity cant be separated from > Newtonian mechanics, and the stationary system of 1905R is defined > as one in which the equation of Newtonian mechanics hold good. We > can identify then stationary system with Newtonian > system (following 1905 Einstein). > > I dont understand why you say that a high mass object approximates > a Newtonian system. The centre of mass system corresponding to ANY > body set composed by bodies with ANY mass can be already a Newtonian > system long before 1905 Einstein. I am NOT the one introducing body > sets that determine Newtonian systems, and I am also NOT the one > calling a Newtonian system stationary. It is 1905 Einstein who > define stationary system as a Newtonian one! And having put out 1905 > Einstein all empty reference frames without massive bodies (the > Newtons absolute one and with it all the derived ones moving with > respect to it with all possible uniform velocities), only remain de > centre of mass Newtonian systems as the stationary systems. And > exists a different one for every possible different body set. > > In 1905R, having you any two different Newtonian systems A and B, you > are NOT free to choose which one is moving and which one is > stationary. Let us explain why with a simple example. Suppose de > body set of A is the single Sun, and the one of B the system Earth- > Moon. You cant consider B (Earth-Moon) stationary and A (Sun) > moving!(remember Galileo). The unique possible stationary system > here is the one having as its body set ALL the bodies involved (Sun , > Earth and Moon) with a new CM stationary and all its components > moving, the Earth-Moon and the Sun, having the first a greater > velocity. The Earth and the Moon are both moving with respect to the > stationary Earth-Moon system (the same Earth-Moon that is moving in > the other system!). See how the mass of the bodies decides all in > 1905R (the clock at the pole is the unique at rest, the one at the > equator is the unique moving). I suppose you already understand why in > 1905R the moving system must be always a part of the stationary > system, without any contradiction at all. By the way, Physics laws > remain being the same in all Newtonian systems. > (I have avoided here the word hierarchy for the benefit of other > readers not knowing its meaning for us). > > > Regards, > > Harald > > RVHG (Rafael Valls Hidalgo-Gato) I made a mistake. The maximum precession is at the poles, not the equator. So here are my corrected questions. Explain to us, in your words, why a Foucault pendulum has a precessing period between 0 and 24 hours. Explain to us why the precess period at the equator is 0 hours, and at the north or south poles is 24 hours. Explain why the precessing period is not one year because of the orbiting motion of the earth around the sun, or thousands of years because of the orbiting motion of sun about the galaxy. |