اردو: H–R Diagram & Star Cluster

اردو: H–R Diagram & Star Cluster brings the Hertzsprung–Russell diagram to life in 3D. The horizontal axis plots surface temperature backwards from hot blue O-type stars (40,000 K) on the left to cool red M-type stars (2,500 K) on the right, while the vertical axis plots logarithmic luminosity log(L/L_sun). Students can drag a glowing test star anywhere across the H–R plane or adjust its mass slider to compute its exact radius in solar radii via the Stefan–Boltzmann law. Evolving the Cluster Age slider from 0.01 to 12 Gyr demonstrates why high-mass stars burn through their fuel rapidly and peel off the Main Sequence turnoff point into Red Giants, Supergiants, and White Dwarfs.

• اردو: Drag the Test Star from the lower-right (cool, dim M-dwarf) to the upper-left (hot, luminous O-star) along the Main Sequence diagonal.
• اردو: Move the Test Star to the upper-right corner (cool temperature ~3,500 K but high luminosity) and verify on the Radius readout that it must be a huge Red Supergiant.
• اردو: Drag the Test Star to the lower-left (hot temperature above 15,000 K but tiny luminosity) to see it shrink into an Earth-sized White Dwarf.
• اردو: Slowly increase the Cluster age slider from 0.1 Gyr to 10 Gyr and watch heavy blue stars peel off the Main Sequence turnoff point before lighter yellow and red stars.

1. 1اردو: Locate the Main Sequence, Red Giants, Supergiants, and White Dwarfs on a Hertzsprung–Russell diagram.
2. 2اردو: Relate a star's surface temperature (spectral class OBAFGKM) and luminosity to its physical radius using the Stefan–Boltzmann law.
3. 3اردو: Explain how a star's initial mass determines both its Main Sequence luminosity (L ∝ M^3.5) and its hydrogen-burning lifetime.
4. 4اردو: Use the Main Sequence turnoff point on a cluster H–R diagram to estimate the age of a star cluster.

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