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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 ...
Dark stars and black holes both have a surface escape velocity equal or greater than lightspeed, and a critical radius of r ≤ 2M. However, the dark star is capable of emitting indirect radiation – outward-aimed light and matter can leave the r = 2M surface briefly before being recaptured, and while outside the critical surface, can interact ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The Dark Star, a 1917 novel by Robert W. Chambers; Dark Star, a 1929 novel by Lorna Moon; The Dark Star, a 1939 novel by Margaret Mackie Morrison, writing as March Cost; Dark Star, a 1969 novel by Norma K. Hemming, writing as Nerina Hilliard
This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...
For example, for a Lambertian radiator (no limb darkening) we will have all a k = 0 except a 1 = 1. As another example, for the Sun at 550 nanometres (5.5 × 10 −7 m), the limb darkening is well expressed [ 2 ] by N = 2 and a 0 = 1 − a 1 − a 2 = 0.3 , a 1 = 0.93 , a 2 = − 0.23 {\displaystyle {\begin{aligned}a_{0}&=1-a_{1}-a_{2}=0.3,\\a ...
If vectors u and v have direction cosines (α u, β u, γ u) and (α v, β v, γ v) respectively, with an angle θ between them, their units vectors are ^ = + + (+ +) = + + ^ = + + (+ +) = + +. Taking the dot product of these two unit vectors yield, ^ ^ = + + = , where θ is the angle between the two unit vectors, and is also the angle between u and v.
Thus, for example, / = is a constructible angle because 15 is the product of the Fermat primes 3 and 5. Similarly π / 12 = 15 ∘ {\displaystyle \pi /12=15^{\circ }} is a constructible angle because 12 is a power of two (4) times a Fermat prime (3).