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Re: escape velocity question



On Mon, 15 Mar 1999, William J. Larson wrote:

A great question Jonathan. May I put it on my physics final exam (on
Thursday)?

I was doing some research on 40 Eridani B (a white dwarf). I read that
it has 37,000 times the surface gravity of the Earth. Since Earth's
escape velocity is 11.2 kilometers per second, the white dwarf's escape
velocity should be 414,400 kilometers per second, exceeding the speed of
light.

Shouldn't this make the star invisible? Perhaps the data is wrong. Or
perhaps the light is just deflected. ...

To which Jack wrote:

Try calculating the escape kinetic energy (relativistically) so
you don't get an absurd result.

No relativity required here. Escape velocity is given classically by

v_esc = (2 g R)^(1/2)

For an escape velocity equal to the speed of light with g = 37,000 g_earth
we would find R = 120 million km (the size of a red giant) and
M = 42 million solar masses. A white dwarf has (I think) a radius closer
to that of Earth so the escape velocity would be "only"
37000^(1/2) x 11.2 km/s = 2.2 x 10^6 m/s, less than 1/100 the speed of
light.

John
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A. John Mallinckrodt http://www.csupomona.edu/~ajm
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