The speed of light is 3 × 108m/s. The Sun has a mass of 2 × 1030kg. a). If all of the Sun’s mass were concentrated at a single point, at what distance would the orbital velocity of an object be the speed of light? The universal gravitational constant is G=6.67×10−11[m3/(s2 · kg)] (Schwarzchild radius). b). Suppose the Sun were to actually collapse into such a black hole meaning that its radius shrinks to the size in part (a), and the mass remains the same. How would the orbit of the Earth change (if at all?) In other words, would the orbital radius or velocity change, and if so, by how much? Explain. c). The sun rotates once every 24 days and has a radius of 6.96×108m. What would the rotational period of the sun be if it collapsed to a radius equal to the radius in part (a)?
9)
The speed of light is 3 × 108m/s. The Sun has a mass of 2 × 1030kg.
a). If all of the Sun’s mass were concentrated at a single point, at what distance would the orbital velocity of an object be the speed of light? The universal gravitational constant is G=6.67×10−11[m3/(s2 · kg)] (Schwarzchild radius).
b). Suppose the Sun were to actually collapse into such a black hole meaning that its radius shrinks to the size in part (a), and the mass remains the same. How would the orbit of the Earth change (if at all?) In other words, would the orbital radius or velocity change, and if so, by how much? Explain.
c). The sun rotates once every 24 days and has a radius of 6.96×108m. What would the rotational period of the sun be if it collapsed to a radius equal to the radius in part (a)?
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