Escape velocity (1 Viewer)

[oompaloompaman]

Hey guys

i was wondering....does the escape velocity increase or decrease for a planet of a larger radius? I was thinking it would increase, cos a larger radius would mean a larger mass, but there are some notes i read which beg to differ. They just all confuzzled me...

 

[xiao1985]

Hey guys

i was wondering....does the escape velocity increase or decrease for a planet of a larger radius? I was thinking it would increase, cos a larger radius would mean a larger mass, but there are some notes i read which beg to differ. They just all confuzzled me...

1/2 m v ^2 = G m1 m / r^2
Ve = sqrt (2 G m1 / r^2)

hence, giving the same mass, greater the radius, smaller the escape velocity...

 

[wogboy]

If you keep the mass of the planet constant, and increase the radius then the escape velocity DECREASES.

since Ve = {sqrt(2*G*M)}/ R
(increase R -> decrease Ve)

On the other hand if you keep the density of the planet the same and increase the radius then the escape velocity INCREASES:

since Ve = {sqrt(2*G*M)}/R
= {sqrt(2*G*p*V)}/R (p is the density & V is the volume, of the planet)
= {sqrt(2*G*p*(4/3)*pi*R^3)}/R
= sqrt(8*pi*G*p*R/3)
(increase R -> increase Ve)

So it all comes down to which variable is kept constant, and which is allowed to vary.