# Tag Info

70

"Accelerate instantly" would imply that a photon takes many different velocities at the same point in time. In fact, it would imply that a photon takes on every velocity between $0$ and $c$ simultaneously, but that clearly makes no sense at all - a particle cannot have many instantaneous velocities simultaneously. When a photon is created, it is ...

21

I am not sure this is a problem of visual communication. My incling would be to think this is a problem of language communication. The equations of relativity tell us that anything with zero rest-mass can only ever exist at the speed of light. So photons don't really accelerate, it is more a fundamental property of their existence to travel at c.

15

If you want just the "shape" you need one number: the eccentricty. The shape of an ellipse is determined by the eccentricty. It is a measure of how "uncircular" an ellipse is. Conventionally this is written as $e$ If the ellipse is centred at the origin, and its long axis ends at (1,0), then the focus of the ellipse is at (e,0) A very ...

14

You are looking for a way to visualize the fact that a photon is created traveling at the speed of light. Remember that a photon is actually a perturbation of the electromagnetic field. That field is everywhere at once. It is part of the fundamental construct of the Universe and it has, essentially, always been so. An approximation of photon propagation ...

12

The half light radius is the radius from within which half the luminosity emerges. "Deprojected" means that the authors must have fitted some model to the 2D distribution of light, which can then be mathematically deprojected to give them a 3D model for luminosity as a function of radius, that they can then integrate to give a number for the half light ...

12

Definition of the velocity dispersion From the title of your question, I'm unsure whether you actually know what "dispersion" means: The dispersion of some numbers is the spread around their mean, usually taken to mean their standard deviation. If you measure the velocity of several light sources (from the Doppler shift of their spectral lines) that are ...

11

The Ca triplet in the near infrared are extremely strong resonance absorption lines. They are by far the strongest features in the near infrared spectra of cool G,K,M type dwarfs and giants, which will be the majority of the stars observed by the Gaia RVS. The Ca triplet lines are so strong that even in low metallicity halo stars, that have little Ca in ...

10

I assume you're asking about central supermassive black holes (SMBHs, one per galaxy), not stellar-mass black holes. The answer is yes, but what actually happens is the two SMBHs have to merge first, and then the resulting combined SMBH can sometimes be ejected from the combined (merged) galaxy. [Edited to add: Since you've updated the question with a ...

10

Take a look at this diagram from Feynman's lectures at Caltech on angular momentum. Here, an atom with angular momentum $m=1$ starts out in an excited state on the left hand side of the diagram. Then it moves to a ground state as it emits a photon, traveling at $c$. Angular momentum is conserved, so the photon now has an angular momentum of 1. As an ...

9

Yes. The velocities you list (X, Y, …) are all velocities with respect to some reference frame. But all reference frames are arbitrary, and you can always define a reference frame where the velocity of some object is exactly zero, as long as it's not accelerating. For instance, Earth's velocity in the Sun's reference frame is X, but in its own reference ...

9

"Peculiar velocity" is a fixed term and describes the velocity of an object relative to a defined rest frame. Astronomy has the problem that you need different methods to measure the 3D motion of an object. Therefor one often only gives the velocity within line-of-sight (from spectrographic data) or the perpendicular velocity as measured from ...

8

Hands down it's Jupiter. It has both the largest radius and faster rotational velocity of the planets, and smaller objects will not be able to compete with that huge radius. Jupiter's rotational velocity is approximately 13.4 km/s (with some variation due to wind currents, as it is a gas), which can be determined both from Doppler shifts of reflected ...

7

The ESA states it pretty clearly (although their figure of 855.2 nm is incorrect; it should be 866.2 nm): The RVS wavelength range, 847-874 nm, has been selected to coincide with the energy-distribution peaks of G- and K-type stars which are the most abundant RVS targets. For these late-type stars, the RVS wavelength interval displays, besides numerous ...

7

Photons are massless. This doesn't depend on their energy, so doesn't depend on their frequency or wavelength. Massless particles travel at the speed of light. Even if we abandon particles and look at classical electrodynamics, we find that the speed of an electromagnetic wave (in vacuum) has a fixed value. It doesn't depend on wavelength. Gravitational ...

7

You will always get a "stable" orbit if the stars have less than escape velocity relative to each other. (unless you are modelling the stars as having non-zero radii so they can collide) The stars will enter into elliptical orbits around a barycentre. But I guess you want a circular orbit. For a circular orbit the speed $v$ is given by $$v^2=GM/r$$...

6

No, black holes are not the only cause of HVSs, although it is thought to be the most common mechanism. Hyper velocity stars are believed to be caused when binary stars come close enough to a supermassive black hole for one of the pair to be captured while the other star is ejected at high velocity. This appears to the main mechanism for HVSs. See for ...

6

As Einstein realized and like you correctly state, you indeed can't measure the speed of an object by itself since it has to be measured relative to something else. As a logic result, if you ask the question "How fast is X moving?", you will have to specify that you want the speed with respect to another object because motion cannot be measured without a ...

6

I'd like to know a little more about the geometry of the ship's trajectory. I would be asking for clarification in comments but I don't know how to put images in comments. A good distance away the ship is moving nearly a straight line with regard to the large mass. As the ship gets closer the path gradually bends towards the large mass. If you're still a ...

6

According to Cropper and Katz 2011 part 2.2, the RVS working group considered other bands, but the ~850 nm band is relatively unaffected by absorption in the Earth's atmosphere, facilitating ground-based preparation and follow-up. In addition to the strong Ca II triplet, this band is rich in lines enabling study of astrophysical quantities other than radial ...

6

The vis-viva equation is commonly written like this: $$v^2 = GM\left(\frac{2}{r} - \frac{1}{a}\right)$$. For $r=a(1-e)$: $$v = \sqrt{GM\left(\frac{2}{a(1-e)} - \frac{1}{a}\right)} = \sqrt{GM\frac{1}{a}\left(\frac{2}{1-e}-1\right)} = \sqrt{GM\frac{1}{a}\left(\frac{1+e}{1-e}\right)}$$. The derivation of the vis-viva equation is not at all trivial and ...

6

I think your core misunderstanding is this : In physics, it always takes some time for a particle to move from rest to some speed. If a particle breaks up into two other particles, then the moment those two particles are created they have whatever velocities are required to conserve momentum (i.e. momentum before the break up must equal total momentum ...

5

The reason is detailed in depth in this pdf, which contains the following diagram: Some key quantities: $R_0$: Distance from the observer to the center of the Milky Way $R$: Distance from target gas to the center of the Milky Way $V_0$: Velocity of the observer with respect to a certain reference frame $V$: Velocity of target gas with respect to the same ...

5

In short, the escape velocity from the region we find ourselves in the milky way is 544 Km/s +- 10%. This number, and an extensive explanation of how it was calculated can be found on a paper called The RAVE Survey: Constraining the Local Galactic Escape Speed Also important to consider is the fact that we already are at aproximately 220 Km/s because of ...

5

You can't without assuming something about the overall velocity. The radial velocity is one component of a velocity vector; you are missing the other two components, which could in principle be anything. However, you could assume that as open clusters are mostly quite young and members of the Galactic disc population, that they are moving in the disc on ...

5

"All earth orbiting satellites should have the same velocity" is not true. Kepler's Laws merely state that an object in a circular orbit at a particular altitude must have a particular speed. Not all objects in orbit are in a circular orbit. Non-circular (elliptical) orbital paths can cross one another as the object's altitude varies. Also, speed ...

4

The rest frame for measuring (astronomical) speeds and velocities depends on the context and purpose. A geocentric frame, based on the Earth's centre of mass might be appropriate for objects in orbit around the Earth. A heliocentric reference frame, centred on the Sun, is often used when describing the line of sight velocities of astronomical objects, but ...

4

Before I start, let me just say that this topic is vastly more complicated than you've presented and what I will be showing. The trouble here is that ultimately, everything you've done and I will do (to a lesser extent) uses approximations and assumptions. Because of this, it can sometimes be hard to understand the true underlying physics when looking at ...

4

Chris, you are actually on the verge of understanding how special relativity works. You're very close. You only need to take one extra step. to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer" This is correct. Absolute space, as in newtonian physics, does not exist. Same for ...

4

Hubble velocities The Universe expands and carries galaxies away from each other with a relative velocity proportional to the distance between them. This is Hubble's law, and if the Universe is infinitely large, there is no limit to how fast two galaxies may recede from each other. In our observable Universe, the most distant galaxy observed (GN-z11; Oesch ...

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