Physics: In a massive-star supernova explosion, a stellar core collapses to form a neutron star roughly 10 kilometers in radius. the gravitational potential energy released in such a collapse is approximately equal to g m2/r, where m is the mass of the neutron star, r is its radius, and g is the gravitational constant. using this formula, estimate the amount of gravitational potential energy released in a massive -star supernova explosion. how does it compare with the amount of energy radiated by the sun

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In a massive-star supernova explosion, a stellar

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Tooey2331

09.01.2022

Physics

The concept used to solve this problem is gravitational potential Energy.

The equation is given by,

$U=\frac{GM^2}{R}$

Where U is the gravitational potential energy

M is the mass of object

R is radius (10000m)

G is the unviersal gravitational constant $(6.67*10^{-11}m^3/kgs^2)$

We know that the mass of neutron star is 1.4 times the mass of the sun.

It is known that the mass of sun is $2*10^{30}Kg$

Replacing the values in our equation we have:

$U= \frac{(6.67*10^{-11})(1.4*(2*10^{30}))}{10000}$

$U= 5.2*10^{46}J$

Therefore the energy released in a massive-star supernova explosion is $5.2*10^{46}J$

To estimate the second point we know that the Total Energy by the Sun is

$E_{sun}=8*10^{35}J$

We can calculate the ratio between a supernova explosion and our entire main-sequence lifetime energy of the sun.

$U' = \frac{U}{E_{sun}}$

$U' = \frac{5.2*10^{46}J}{8*10^{35}J}$

$U' = 6.5*10^{10}$

Therefore the amount of energy radiated by a supernova explosion is around $10^{10}$ times more than the entire main-sequence lifetime energy of the sun.

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