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From this measurement and the apparent magnitudes of both stars, the luminosities can be found, and by using the mass–luminosity relationship, the masses of each star. These masses are used to re-calculate the separation distance, and the process is repeated. The process is iterated many times, and accuracies as high as 5% can be achieved. [8]
= molar mass of Earth's air: 0.0289644 kg/mol The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. The reference value for ρ b for b = 0 is the defined sea level value, ρ 0 = 1.2250 kg/m 3 or 0.0023768908 slug/ft 3 .
The minimum brightness is about magnitude +1.6 [14] when Mars is on the opposite site of the Sun from the Earth. Rotational variations can elevate or suppress the brightness of Mars by 5% and global dust storms can increase its luminosity by 25%. [14] [18]
Ned Wright's cosmology calculator calculates a luminosity distance for a redshift of 1 to be 6701 Mpc = 2×10 26 m giving a radio luminosity of 10 −26 × 4 π (2×10 26) 2 / (1 + 1) (1 + 2) = 6×10 26 W Hz −1. To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission.
Nonthermal sources can have very high brightness temperatures. In pulsars the brightness temperature can reach 10 30 K. [9] For the radiation of a helium–neon laser with a power of 1 mW, a frequency spread Δf = 1 GHz, an output aperture of 1 mm 2, and a beam dispersion half-angle of 0.56 mrad, the brightness temperature would be 1.5 × 10 10 ...
Earth's albedo varies by a factor of 6, from 0.12 in the cloud-free case to 0.76 in the case of altostratus cloud. The absolute magnitude in the table corresponds to an albedo of 0.434. Due to the variability of the weather, Earth's apparent magnitude cannot be predicted as accurately as that of most other planets. [20]
The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, = where F is flux (W·m −2), and L is luminosity (W). From this the luminosity distance (in meters ...
A truly dark sky has a surface brightness of 2 × 10 −4 cd m −2 or 21.8 mag arcsec −2. [9] [clarification needed] The peak surface brightness of the central region of the Orion Nebula is about 17 Mag/arcsec 2 (about 14 milli nits) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec 2 (about 0.27 millinits). [10]