# Answer to Question #18160 in Astronomy | Astrophysics for Ambre

Question #18160

Calculate the escape velocity from a red giant's atmosphere. Assume that the stars mass is 1 M and its radius is 100 R. How does this compare with the speed at which a planetary nebula shell is ejected?

I already calculate the escape velocity and got 1.34 x 10^-12 I dont know how to go about the second portion of this question.

Thanks for taking the time to help me!

I already calculate the escape velocity and got 1.34 x 10^-12 I dont know how to go about the second portion of this question.

Thanks for taking the time to help me!

Expert's answer

you can find escape velocity as from

v^2/r = GM/r^2

v = sqrt(GM/r)

So for red giant we have

v = sqrt ( 6.67*10^(-11)*1.99*10^(30) / (100*7*10^(8)) ) = 6*10^(4) m/s

For planetary nebula we assume mass to be approximately 1M and radius to be

approximately 10^(15) m. So

v = sqrt(6.67*10^(-11)*1.99*10^(30)/(10^(15) ) = 3.3 * 10^2 m/s

You can see that it is much bigger for red giant

v^2/r = GM/r^2

v = sqrt(GM/r)

So for red giant we have

v = sqrt ( 6.67*10^(-11)*1.99*10^(30) / (100*7*10^(8)) ) = 6*10^(4) m/s

For planetary nebula we assume mass to be approximately 1M and radius to be

approximately 10^(15) m. So

v = sqrt(6.67*10^(-11)*1.99*10^(30)/(10^(15) ) = 3.3 * 10^2 m/s

You can see that it is much bigger for red giant

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