A binary star system has two stars, each with the same mass as our sun, separated by 1.50×1012 m . A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line that passes through the midpoint between the two stars. What is the speed at the comet's midpoint?

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aristocles aristocles · Answer 1 · 2019-10-25T20:07:25+02:00

Answer:

[tex]v = 2.67 \times 10^4 m/s[/tex]

Explanation:

Given that two stars of same mass as that of sun are separated by the given distance

[tex]d = 1.5 \times 10^{12} m[/tex]

now a comet travels from a distance which is very far away from the stars and reached the mid point of them

so here the change in kinetic energy of comet = loss in its gravitational potential energy

so we will have

[tex]KE_f = U_i - U_f[/tex]

[tex]\frac{1}{2}mv^2 = 0 - (-2\frac{GMm}{r})[/tex]

[tex]v^2 = \frac{4GM}{r}[/tex]

here we know that

[tex]r = \frac{1.50 \times 10^{12}}{2} = 7.5 \times 10^{11} m[/tex]

[tex]v^2 = \frac{4(6.67 \times 10^{-11})(2 \times 10^{30})}{7.5 \times 10^{11}}[/tex]

[tex]v = 2.67 \times 10^4 m/s[/tex]