Planetary Sciences Class #2

STA → # 13

Tides-

Fm : GMM.

r

:r#.

Mn Mz

DF = F- Fz =off

. dr = -

26Mr#dr

Center : Fe=

6Y÷nEt 05

> FxF

↳R ?it'

*--5in- - - . - . -. -

.?:

C

r

Fpm- GMT asp

SZ

Fpy = - GMT sin $52

Differentialforce between center and

surface is

DF = Fp - Fc

= 6mm (age - de ) ie .

6sM÷n s in ffS

Kodiak 5¥;Ioriotitration: r

' [ I + Id-

2R= oso ]s2= ryn - 2 ; oso )DF= 6=Mqfood (t +2¥ Gso ) -

1 ) si

-

6nn= [ l +

2yd oso] Sino jFor cost a I

,sin + = Rsi¥t

DF =

6M=3R ( Zoso I -sino 5 )

Europe ; en deuce for non - synchronous rotation

Roche limit

÷del

force

supplants internal forces holdingbody

together

we < 26 Mprm.

r3grainy oh tidal fee

surface from planet3

Mr3< ZMI Rm

P Mm

Mn .Rx r3< 2fjR÷n*#÷z

"3#g)"3Rp-

.

Osefl because we an mecuse pj and RJ( and estimate f. better Hren Nl Can mm end Rm )

.

True value not 2113=1 ] but ~ 2.456.

For saturn;

r - 1.23×10 8m

Planets imaltrueSelf - gravity of

dust to overcome the solartide

gyp>2¥34p¥r±kzn÷K.

pp > 2Mg

. ¥- 05my

Boosting ) no ftp..to ,

neo 's Mao )#P ME

a±v→§uf÷o)nf±€

.

M xp . ✓ = pn .

.

4§ rp

=p .4

Izrp'

R = RH = a ¢±*Tb 3

kafyhz )N =p .

¥ " FHER,!p .

pre /4IzR+3

p. ) "I=p. r,?

Mdb

Pra # " Hhs,,=p%p←RP = piney,

# "' ¥"

Rt=fII#nni"H÷M3mi2" ¥43

axv→§uf÷o)nf±€

Suppose that the collapse happens vertically ,so

that p changes but E stays the same

3 3MNEDna⇐notp

Mn no't :4Ceres Mass ~ 10 g

Very low density. Asteroids here densities

q the order of no"

gkm ?

Pr Rr →p.

R.

The mass that collapses rmouidtg ,compared to Ceres Mass ~ Mae , -1024g

MaEKED not

Mo.reakhzep - not

so Rc ~ ( lost ) 'sRanes should be the typical

radius of a dust ball produced by

gravitationalinstability . Ceres radius being roughly 500 km

,we he

:( ix 163.pe ~ 2.5km

so,

plateletsshould se -5kmin size

.