Problem: In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1x103 suns and a radius equal to one-half the radius of our moon.What is the density of the black hole in g/cm3? The radius of our sun is 7.0x105 and it has an average density of 1.4x103 kg/m3. The diameter of the moon is 2.16x103 miles.

FREE Expert Solution

Calculate the volume of the sun:

volume=43πr3volume=43π(7×105 km)3

volume = 1.43675x1018 km3

Calculate the mass of the sun:

mass=1.43675×1018 km3×(103 m1 km)3×1.4×103 kgm3mass=1.43675×1018 km3×109 m31 km3×1.4×103 kgm3

mass = 2.0114x1030 kg

Calculate the mass of the black hole:

mass=(1×103)×(2.0114×1030 kg)mass=2.0114×1033 kg×103 g1 kg

mass = 2.0114x1036 kg

Calculate the radius of the moon in m:

radius=diameter2radius=2.16×103 mi2radius=1080 mi×1.609 km1 mi×103 m1 km

radius = 1737720 m

Calculate the radius of the black hole in m:

radius=(12)(1737720 m)

radius = 868860 m

Calculate the volume of the black hole:

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Problem Details

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1x103 suns and a radius equal to one-half the radius of our moon.

What is the density of the black hole in g/cm3? The radius of our sun is 7.0x105 and it has an average density of 1.4x103 kg/m3. The diameter of the moon is 2.16x103 miles.

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