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HW4-SOL - Astronomy 1F03 Problem Set 4 Solution Friday Nov...

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Astronomy 1F03 Problem Set 4 Solution Friday Nov 26th, 2010 Please write your answers on a separate sheet including your working. 1. Escape velocity can be calculated by equating the kinetic energy 1 2 m v 2 esc to the gravitational energy G M m/R and solving for v esc . The m’s cancel: 1 2 v 2 esc = G M/R so v esc = radicalbig 2 G M /R . a) What would be the escape velocity from a 1.6 solar mass Neutron star with a radius of 10 km? Note that you should convert everything to SI (kg, m, s) because G is given in SI units. v esc = radicalbig 2 G M /R = radicalbig 2 × 6 . 67 × 10 - 11 × 1 . 6 × 2 × 10 30 / 10000 = 2 . 1 × 10 8 m/s b) Calculate the escape velocity from an object that weighs 1 solar mass with a radius of 3 km. Comment on your answer – what does it imply? v esc = radicalbig 2 G M /R = radicalbig 2 × 6 . 67 × 10 - 11 × 2 × 10 30 / 3000 = 3 . 0 × 10 8 m/s. This is the speed of light so even light could not escape. This would make the object a black hole.
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