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A dark star, therefore, has a rarefied atmosphere of "visiting particles", and this ghostly halo of matter and light can radiate, albeit weakly. Also as faster-than-light speeds are possible in Newtonian mechanics, it is possible for particles to escape. Radiation effects A dark star may emit indirect radiation as described above.
Dark star (Newtonian mechanics), a star that has a gravitational pull strong enough to trap light under Newtonian gravity Dark star (dark matter), a star heated by annihilation of dark matter particles within it
In April 2023, a study investigated four extremely redshifted objects discovered by the James Webb Space Telescope. [5] Their study suggested that three of these four, namely JADES-GS-z13-0, JADES-GS-z12-0, and JADES-GS-z11-0, are consistent with being point sources, and further suggested that the only point sources which could exist in this time and be bright enough to be observed at these ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Then multiplying the numerator and denominator inside the square root by (1 + cos θ) and using Pythagorean identities leads to: = + . Also, if the numerator and denominator are both multiplied by (1 - cos θ), the result is:
The number of photons per second emitted into the wedge at angle θ is I cos(θ) dΩ dA. Figure 2 represents what an observer sees. The observer directly above the area element will be seeing the scene through an aperture of area dA 0 and the area element dA will subtend a (solid) angle of d Ω 0 , which is a portion of the observer's total ...
In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...