Apparent equality between Jovian esc. velocities and Sol's esc. vel.

[stargene]

Okay, I've never heard anything about this before=E2=80=A6Somebody =
please
explain this:

In scanning the wikipedia entry on "Escape Velocity", at
https://en.wikipedia.org/wiki/Escape_velocity , I noticed in its list
of escape velocities that for the Jovian planets alone (but not for smaller
planets) the tabulated escape velocities for each Jovian was almost exactly
identical to the escape velocity for the sun itself AT that planet's orbit.

IE:
(1) Jupiter's esc. vel. = 60.2 km/s Sol's esc. vel. =
at J's orbit = 60.4 km/s
(2) Saturn's esc. vel. = 36.09 km Sol's esc. vel. a=
t S's orbit = 36.3 km/s
(3) Uranus's esc. vel. = 21.38 km/s Sol's esc. vel. =
at U's orbit = 23.7 km/s
(4) Neptune's esc. vel. = 23.56 km/s Sol's esc. vel. =
at N's orbit = 23.7 km/s
i.e.: Sol/planet ratios very close to unity.

On the other hand, the analogous values for the smaller terrestrial
planets are in a ~Sol/planet ratio very roughly equal to ~1.5 to ~2
or so

Am I the victim of a vast astronomical hoax, or just some blitheringly
obvious well known phenomenon, or can I get a door prize at the Nobel's
shindig next year? :-)

[[Mod. note -- You're very likely just seeing approximate coincidences.

If I've done my algebra correctly the escape velocity at a distance r
from a mass M is given by sqrt(2GM/r) where G is the Newtonian
gravitational constant, so you're essentially asking where there's
any special relationship between the ratios
M_sun / planet_orbit_radius_about_sun
and
M_planet / planet_radius
There no reason to expect any such relationship, since these ratios
are set by quite different physical phenomena, and the first ratio
may change over time if the planet migrates in the solar disk during
the early formation of the solar system.
-- jt]]

[stargene]

Post by stargene
Okay, I've never heard anything about this before=E2=80=A6Somebody =
please
In scanning the wikipedia entry on "Escape Velocity", at
https://en.wikipedia.org/wiki/Escape_velocity , I noticed in its list
of escape velocities....
[[Mod. note -- You're very likely just seeing approximate coincidences.
If I've done my algebra correctly the escape velocity at a distance r
from a mass M is given by sqrt(2GM/r) where G is the Newtonian
gravitational constant, so you're essentially asking where there's
any special relationship between the ratios
M_sun / planet_orbit_radius_about_sun
and
M_planet / planet_radius
There no reason to expect any such relationship, since these ratios
are set by quite different physical phenomena, and the first ratio
may change over time if the planet migrates in the solar disk during
the early formation of the solar system.
-- jt]]

Thanks, JT. You're not only right, but when I bothered to actually
check wiki's data on the Jupiter and Sol values, their "60.2 km/s" for
Jupiter's esc. vel. is correct but the esc. vel. for Sol at Jupiter's orbit
is 18.46 km/s, NOT their "60.4 km/s". Catch me trusting wikipedia as
an authority again. Embarrassing. We can cancel that door prize.
stargene

[Libor 'Poutnik' Stříž]

Post by stargene
Thanks, JT. You're not only right, but when I bothered to actually
check wiki's data on the Jupiter and Sol values, their "60.2 km/s" for
Jupiter's esc. vel. is correct but the esc. vel. for Sol at Jupiter's orbit
is 18.46 km/s, NOT their "60.4 km/s". Catch me trusting wikipedia as
an authority again. Embarrassing. We can cancel that door prize.
stargene

It is not their, but of the OP info he provided.
There are 2 columns in Wikipedia and he confused them.
60.4 is Sun-Jupiter system escape speed ( velocity is vector).
Sun escape speed at Jupiter orbit is displayed there correctly.

[Libor 'Poutnik' Stříž]

Post by stargene
[...]
In scanning the wikipedia entry on "Escape Velocity", at
https://en.wikipedia.org/wiki/Escape_velocity , I noticed in its list
of escape velocities that for the Jovian planets alone (but not for smaller
planets) the tabulated escape velocities for each Jovian was almost exactly
identical to the escape velocity for the sun itself AT that planet's orbit.
(1) Jupiter's esc. vel. = 60.2 km/s Sol's esc. vel. =
at J's orbit = 60.4 km/s
[...]

You confuse Sun escape speed at Jupiter orbit
with Sun-Jupiter system escape speed 60,4 km/s

V = sqrt ( ((v_S . k )^2 + (v_J)^2 )

where
k = 1-1/sqrt(2) = cca 0.2929 for circular orbits
v_S is Sun escape speed at Jupiter orbit
v_J is Jupiter escape speed
v_Sys is Sun-Jupiter system escape speed
to escape both Jupiter and Sun gravity.

Read the section Multiple bodies.

https://en.wikipedia.org/wiki/Escape_velocity#Multiple_bodies