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Physics II workshop_Part_47

# Physics II workshop_Part_47 - Escape velocity The minimum...

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96 Escape velocity The minimum initial velocity needed for an object (such as a rocket) to escape to infinity from the surface of a massive body (such as a planet) is given by v esc = 2 GM R where G = 6.67 × 10 -11 m 3 kg s -2 is the constant of gravitation, M is the mass of the body and R is its radius. Note that v esc only depends on the properties (mass and radius) of the massive body (not the escaping object). Also notice that for a given mass, M , v esc is higher the more compact the body (smaller R ). Lets examine this by imagining we can compress the Sun into a smaller and smaller volume. The mass of the Sun is M ~ = 1.99 × 10 30 kg. Calculate the escape speed in each of the following situations, and compare it with the speed of light (c=3.0 × 10 8 m s -1 ). (a) The normal-size Sun, R ~ =6.95 × 10 5 km. (b) The Sun when it is about the size of the Earth, R=6.95 × 10 3 km (the Sun will actually reach this size when it ends its life as a white dwarf).

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Physics II workshop_Part_47 - Escape velocity The minimum...

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