Consider an astronomical body of mass

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

M

, and radius

R

(G = 6.67 \times 10^{-11} \text{ Nm}^2\text{kg}^{-2})

(1) Derive an expression, in terms of

M

and

R

, for the escape speed of the body. (2) Now suppose that the escape speed of the body was equal to the speed of light;

c = 3.0 \times 10^8 \text{ ms}^{-1}

. Derive an expression, in terms of

M

and

c

, for the radius of such a body. Astrophysicists have named this radius the Schwartzchild radius. (3) Calculate the Schwartzchild radius for the following astronomical bodies: - i The Sun (

M_{\text{Sun}} = 2 \times 10^{30} \text{ kg}

) - ii The Earth (

M_{\text{Earth}} = 6 \times 10^{24} \text{ kg}

) - iii Cygnus – X1 (

M = 21.2 M_{\text{Sun}}

) (4) What name do we give to an astronomical body whose escape speed is greater than

c

Related theory

Mass-Energy Equivalence
Escape Velocity
Gravitation
Escape speed

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