F Satllt Moton 10a-0 U () - U ( ) 0 f ow g dos t go? scap locty Kpl s nd Law ::= Aas Angula Mo. Consaton!!!!
Nwton s Unsal Law of Gaty 10a-1 M F F 1) F acts along t ln connctng t cnts of objcts Cntal Foc (fo spcal objcts) ) F ponts towad M (attact foc) 3) Nwton says: F= foc of gaty on (M) du to M () F = G=6.67x10-11 [ 3 /Kg s ] fo spcal cas on t at s sufac, ts acclaton s: g = 9.81 /s G s a y sall nub!
call 10a-1a
10a-1b
Popts of Gaty Gataton fo a Sp 10a- Gatatonal foc btwn an objct and a sp s t sa as f all t ass of t sp was concntatd at ts cnt.
Calculat a oon-n-obt fo lat (ccula obt) Wat s a oon n obt? 10a-3 a ( ) ([3.14]) 3.84(10) 6 [.3(10) s] 8 8 (10) 8.6 (10) 1 s a Moon 0.0086 s 8 3.84(10)
cannon fd ozontally low locty- ~paabolc pat g locty - at cus away und fallng objct Fo spcal obtal locty t ball falls at t sa at tat t at cus away a of objct n obt (at sufac) s sa as doppd objct Nwton s conncton a fallng-appl =a obtng-appl =g!!!!!! 6 6.378(10) 8 3.84(10) Moondst 1.0166 60. Moondst Sa da fo oon n obt- oon fallng towad at a a F a a oon oon appl 10a-4 at oon a oon aappl a appl g a a a Moon Moon Moon Moondst 1 60. a 9.8 s 0.007 appl s aoon g dad gt Nwt. nald t!!! appls-oon ytng uld by 1/ gaty ttp://gallo.pys.gna.du/classs/109n/o_stuff/applts/nwt/nwttn.tl
call ngy consaton na at's sufac y= ow an objct up (y slow) ow g dos t go? f 1 top = 0 : know f 0 g g g 100 (9.8) 510 s ( ) s 10a-5 U = 0 y = 0 = 100 /s 1 0
Unsal Gatatonal Potntal ngy U ()=- :::: U ( = )= 0 10a-6 top = 0 : know f at f - 1-1 - - 3 cass < 0 can fnd ax and objct falls back = 0 can just gt to and stops > 0 gts to And kps gong
Unsal Gatatonal Potntal ngy U () - :::: U ( ) 0 ow an objct up (y fast) ow g dos t go? f top = 0 : know f at - 1 1 - - < 0 can fnd ax and objct falls back - not g= g = 10a-6a - 1-1 call so ax {1- } g g ax {1- } 0
Unsal Gatatonal Potntal ngy U () - :::: U ( ) 0 scap locty : f =0 and ax = =0 f top = 0 : know f - 0(at ) 1 at 1 - =0-10a-6b so call g= g = 1-0 sc scap locty sc sc g
scap locty : f =0 and ax = =0 f 0 top = 0 : know and U(=)=0 =0 ctcal scap condton f 0 1-0 scap locty 10a-6c = sc sc = = g call g = 1 at - s 6 sc = (9.8 )(6.378(10) ) =11.1(10) sc 3 s
Kpl s 1 st Law 10a-7 (all objcts bound to sun- Kpl fgud out wt Mas) 1. obtal oton of t plants about t sun s an llps wt t sun at on focus. s-no axs n ot pty focus. llps = squasd ccl ccntcty ~ n / aj n aj gt ccl Not n alty bot M sun and plants-tc obt coon CM Nwton!! - all oton n 1/ foc law (lk gaty) follows conc sctons (slcs of a con) - bound oton llpss unbound oton paanoa o ypbola - not on assus fo ts M sun >>> plants-tc. -Hally s Cot cong back y 76 yas nald ts (Hally ddn t l to s t tun but usd Nwton s Laws to pdct xactly t tun) aj s-ajo axs You canc to s Hally s Cot 1986+76= 06 (y fat saw n 1910 wt s gandfat) ( I sowd y cldn, n 1986)
Kpl s nd Law 10a-8 (all objcts bound to sun- Kpl fgud out wt Mas). As t plant os n ts obts t swps out qual aas n an qual ts plant os fast (slow) wn clos to (fat fo) to t sun M sun >>> plants-tc. plant cot Nwton!! -Gaty = a cntal foc (acts btwn cnts of ~spcal objcts) no toqu on plant (cot tc.) angula ontu consd 1 1 ΔA= (Δl) = (Δt) ΔA 1 1 1 = [ ] ( ) =[ ] (L) Δt Aa tangl= A call!!! Ang. Mo. L l= t Kpl s nd Law ::= Aas Angula Mo. Consaton!!!!
10a-9
Kpl s 3 d Law P sc k 3 sc 3 P 3 yas AU= (at) =1 AU 10a-9a Kpl pobably td P n P n/ n/=1/ NO cus down n=: =3 YS lna!! n==1 NO cus up
Kpl s 3 d Law ( ~ 3 ) Nwton's Law conncton ow Nwton knw d nald t 10a-10 Mass of Sun!!!
M G Satllt Moton Fa M =5.97(10) 4 M Satllt at sufac (of at) = =6378(10) 3 g 9.8(6.378)(10) 6 s g g =7.906(10) 3 /s 6 (3.14159)6.378(10) 3 7.906(10) 3 5.07(10) s 84.5n 10a-11
Satllt Moton G M ( ) 3 Gocntc Satllt 3 3 ( ) ( ) Fa M 4 8.6410 =9598 (10) 3 4 s M =5.97(10) 4 g 10a-1
Fnd t gt (alttud) of a satllt abo t at sufac so tat t s always abo t sa pont on t at s sufac. Notc, n od fo t satllt to ang abo t sa spot on t at t as to a = 4 ous Gocntc satllts ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 4 M G M G S S S S ( ) s 6 4 3 10 3.58 10 8.64 4 4 10a-1a