4. What is the formula for the escape velocity from the surface of an object of

Question

4. What is the formula for the escape velocity from the surface of an object of radius R and mass
M? What is the surface gravity of such an object (i.e. the surface gravitational acceleration)?
What is the escape velocity and surface gravity of (i) the Earth, (ii) the Sun, (iii) Betelgeuse
(radius 1200radius of sun, mass 20mas of sum) and (iv) a white dwarf with mass 1mass of sun and radius 0.01radius of sun and
(v) the Milky way galaxy, mass 10^1 2mass of sun and `surface' radius 30,000pc. Express your answers
for the escape velocity in km/s and also as a fraction of the speed of light, and your answer for
the surface gravity in both ms^-2 and relative to the Earth's gravitational acceleration.

Explanation / Answer

1 /2 m v^2 = GMm / R ;

v^2 = ( 2GM / R ) ;

v = ( 2GM / R ) ;

( i ) V = ( 2GM / R ) ;putting in the values , M = 6e24 , R = 6e6

earth , v = 11552 m /s

( ii ) sun , M = 1.98e30 , R = 695500e3

v = 6.1639 e 5 m /s

( iii) Betelguse

v = 7.957 e 4 m /s

( iv ) v = 6.163 e 6 ms/

( v ) R = 30 000 pc = 30 000 * 31 e 15 m ; M = 1 e 12 * 1.98 e 30

v = 2.503 e -16 m /s

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