Re: [OT] physics help

On Thu, 29 Apr 1999, Laserlight wrote:

> 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  .

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 =
5103km (.4
> Earth), mass is 2.08E+23kg (.034795 Earth), density = 3g/cm^3  .

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
> 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?

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