What is the value of the Hubble constant based upon these values?
Galaxy NGC 2342 has a velocity of 5,690 km/s and is at a distance of 74 Mpc away. Solution: Pop the values into the formulaĢ. How far away is the galaxy according to Hubble's Law? Galaxy NGC 123 has a velocity away from us of 1,320 km/s and the Hubble Constant's value is 70 km/s/Mpc. Technically, this is a very simplified version of the what the Universe is doing, but it is a good first approximation for what we see in the sky.ġ. d = distance of a galaxy, in Mpc (mega-parsecs)Ī rather simple formula for a very important thing, the Universe.H o = Hubble Constant, measured in km/s/Mpc.It shows the expansion of the Universe by showing how distant galaxies are moving away from us. The larger the distance to the system, the longer the emitted photons have travelled through expanding space and the higher the measured cosmological redshift.Hubble's Law - One of the most important formulas of the 20th century. The cosmological redshift would be determined by how far away the system was when the photons were emitted.
The Doppler shift would be determined by the motions of the individual stars in the binary – whether they were approaching or receding at the time the photons were emitted. Cosmological redshift results from the expansion of space itself and not from the motion of an individual body.įor example, in a distant binary system it is theoretically possible to measure both a Doppler shift and a cosmological redshift. In cosmological redshift, the wavelength at which the radiation is originally emitted is lengthened as it travels through (expanding) space. If the object is travelling towards us, the wavelength is shifted towards the blue end of the spectrum, if the object is travelling away from us, the wavelength is shifted towards the red end. In Doppler Shift, the wavelength of the emitted radiation depends on the motion of the object at the instant the photons are emitted. Credit: NASA/JPL-CaltechĪlthough cosmological redshift at first appears to be a similar effect to the more familiar Doppler shift, there is a distinction. This animation’s colour scheme preserves the original colours emitted by the object, while showing the shift that occurs relative to a fixed bandpass window, i.e. Both the absorption lines and the continuum emission experience this stretching and compacting. The object’s entire spectrum is stretched red-ward as the object moves away from us, and the entire spectrum is compacted blue-ward as the objects moves towards us. the emitting light source, at the instant the photons were emitted. This is a complex formula requiring knowledge of the overall expansion history of the universe to calculate correctly but a simple recession velocity is given by multiplying the comoving distance ( D) of the object by the Hubble parameter at that redshift ( H) as:ĭoppler Shift: the wavelength of the observed radiation depends on the motion of the object, i.e. Note this doesn’t break the ultimate speed limit of c in Special Relativity as nothing is actually moving at that speed, rather the entire distance between the receding object and us is increasing. At larger distances (higher redshifts), using the theory of general relativity gives a more accurate relation for recession velocities, which can be greater than the speed of light. For small velocities (much less than the speed of light), cosmological redshift is related to recession velocity ( v ) through: This is known as ‘ cosmological redshift’ (or more commonly just ‘redshift’) and is given by:įor relatively nearby objects, where z is the cosmological redshift, λ obs is the observed wavelength and λ rest is the emitted/absorbed wavelength.Ĭaused solely by the expansion of the Universe, the value of the cosmological redshift indicates the recession velocity of the object, or its distance. However, when astronomers perform this analysis, they note that for most astronomical objects, the observed spectral lines are all shifted to longer (redder) wavelengths. These photons are manifest as either emission or absorption lines in the spectrum of an astronomical object, and by measuring the position of these spectral lines, we can determine which elements are present in the object itself or along the line of sight.
Laboratory experiments here on Earth have determined that each element in the periodic table emits photons only at certain wavelengths (determined by the excitation state of the atoms).
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