1202.9 m/s
Thats if I got the mass right (200,000,023 kg?)
I found a useful website with a java calculator that does this.
http://www.geocities.com/CapeCanaveral/Lab/8821/telescope.html
'Neath Southern Skies - http://users.mcmedia.com.au/~denian/
Commodore Alfred K Hole - RNS Indy's Folly (CB)
Task Force Admiral Peter Rollins - RNS Waterloo (MKW)
Fleet Admiral Alberto Doyle - NKV Vesuvius (LFI)
[quoted original message omitted]
I'm trying to figure the escape velocity for Alarish. Diameter = 5103km
(.4
Earth), mass is 2.08E+23kg (.034795 Earth), density = 3g/cm^3 .
Applying the formula in Gillett's Worldbuilding, p12 (the simplified form,
k*r*sqrt
rho), I get .208 km/sec ... however, comparing it to Ganymede, Io, etc,
I
suspect it ought to be more like .3km/sec. Help?
> On Thu, 29 Apr 1999, Laserlight wrote:
> I'm trying to figure the escape velocity for Alarish. Diameter =
i'm going to rake over some physics i haven't done for about a year now, so
please don't laugh too hard.
now, lessee. escape velocity is the velocity needed to break out of a planet's
gravity well, so:
v escape velocity m mass of escaping object E gravitational potential energy
of object
E = mv^2/2
v = (2E/m)^(1/2)
now
P gravitational potential of object
E = mP
v = (2P)^(1/2)
and
G = gravitational constant M = mass of body r = radius of body
P = GM/r
v = (2GM/r)^(1/2)
in the case of velikiy alarish,
> I'm trying to figure the escape velocity for Alarish. Diameter =
G = 6.67259 * 10^-11 m^3/s^2kg
M = 2.08 * 10^23 kg
r = 5103 * 10^3 / 2 m
= 2.552 * 10^6 m
v = (2GM/r)^(1/2)
= (2*6.67259e-11*2.08e23/2.552e6)^(1/2)
= 3.298 * 10^3 m/s
> Applying
references i found for ganymede give an escape velocity of 2.74 km/s:
http://galileo.ivv.nasa.gov/ganymede/index.html
http://library.advanced.org/18188/ie_english/planets/jupiter/moons/ganym
ede.htm
and also give ganymede's mass and radius as 1.48e23 kg and 2.633e6 m
respectively, which, plugged into my formula, give an escape velocity of
2.74 km/s, which is reassuring.
this is quite a good match to the 3.30 km/s for alarish, given alarish's
greater mass and smaller radius. anyway, the figure of 0.208 km/s for
alarish is way out.
now,
d density v volume
d = M/v
.PI. erm, pi
v = 4/3.PI.r^3 (for a sphere)
d = 3M/(4.PI.r^3)
3M/d = (4.PI.r^3)
M = 4.PI.dr^3/3
v = (2GM/r)^(1/2)
= (8G.PI.dr^2)^(1/2)
= r(8G.PI.d)^(1/2)
= (8G.PI.)^(1/2)rd^(1/2)
which is your k*r*sqrt(rho) equation, provided that
k = (8G.PI.)^(1/2)
~= 41 * 10^-6
it's possible that the equation in the book is in different units; that would
seem to be a prime contender to me.
Tom
> On Thu, 29 Apr 1999, Robertson, Brendan wrote:
> 1202.9 m/s
perversely enough, this isn't the result i got when i put the data into the
form you mention, and neither your or my result from the form match the
results i calculated, which in turn do not match laserlight's original value.
having looked at the form's code, i have to report a highly suspect value for
the universal gravitational constant there, if i bung in the numbers for
ganymede, i get an escape velocity about 100 times larger than lightspeed. and
yet you seem to have got an answer in the right order of magnitude. weird.
Tom
> 1202.9 m/s
Um, no. The mass is 2.08 * 10^23 kg, not 2*10^8 + 23 kg.