1. The star Betelgeuse, αOri, has a bolometric apparent magnitude, mbol = -1.29, a bolometric ab

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1. The star Betelgeuse, \alpha Ori, has a bolometric apparent magnitude, $m_{bol} = -1.29$, a bolometric absolute magnitude, $M_{bol} = -7.76$, and a surface temperature, $T_e = 3950$ K. A) Find the distance to Betelgeuse in parsecs. B) Using the bolometric absolute magnitude of the Sun, $M_{bol} = +4.74$, and the Sun's luminosity, $L_\odot = 3.84 \times 10^{26}$ W, find the radius of Betelgeuse in meters, assuming it radiates as a spherical blackbody. C) Determine whether a single 10-meter telescope (i.e., with an aperture of 10 meters) at the W.M. Keck Observatory can spatially resolve, theoretically, the full extent of Betelgeuse's diameter by observing it in blue light with $\lambda = 440$ nm?

          1. The star Betelgeuse, \alpha Ori, has a bolometric apparent magnitude, $m_{bol} = -1.29$, a bolometric absolute magnitude, $M_{bol} = -7.76$, and a surface temperature, $T_e = 3950$ K.

A) Find the distance to Betelgeuse in parsecs.

B) Using the bolometric absolute magnitude of the Sun, $M_{bol} = +4.74$, and the Sun's luminosity, $L_\odot = 3.84 \times 10^{26}$ W, find the radius of Betelgeuse in meters, assuming it radiates as a spherical blackbody.

C) Determine whether a single 10-meter telescope (i.e., with an aperture of 10 meters) at the W.M. Keck Observatory can spatially resolve, theoretically, the full extent of Betelgeuse's diameter by observing it in blue light with $\lambda = 440$ nm?

1. The star Betelgeuse, αOri, has a bolometric apparent magnitude, mbol = -1.29, a bolometric absolute magnitude, Mbol = -7.76, and a surface temperature, Te = 3950 K.

A) Find the distance to Betelgeuse in parsecs.

B) Using the bolometric absolute magnitude of the Sun, Mbol = +4.74, and the Sun's luminosity, L⊙ = 3.84 × 10^26 W, find the radius of Betelgeuse in meters, assuming it radiates as a spherical blackbody.

C) Determine whether a single 10-meter telescope (i.e., with an aperture of 10 meters) at the W.M. Keck Observatory can spatially resolve, theoretically, the full extent of Betelgeuse's diameter by observing it in blue light with λ = 440 nm?

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