Quick revision for exams, Summaries of Physics

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Typology: Summaries

2025/2026

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3 •^ F=^ G^ M 8 M 2

E ( in te ns it y ) = G UI ERS E- E 3 NOT E: BOT H ARE VE CT O R S AN D FOL LO W R UL E OF V EC TOR ADD IT ION NO TE: ☐ Mas s'M' b r eaks in to t w o F = m ax → m, = ma = mm^ ,^ S^ mz → M = 2 m 2 ) (^) mW a hs e sn oe f vea r uFnor ifoc r e (^) m duGeo (^) dto dbe o (^) an t o t (^) c ec not nes r i d er ma ss to

U ni for m p: GUE R AM I

  • u se d o c a nd d m m (^) a M, L

a tl

F = GM M

a ca t l)

G= 6 - 6 7 × 10 " Nm ²/ kg²

  1. 6 7 × 10 - 8 d yne on 2 /g. 2
  • Un ive rsa l Gr av ita t ion al c on st: G

g → g ra p h

R

ou ts idg e

  • g s u rf ac e = g e
  • g n = (E n , Je
  • g a = ge ( 1 - ♀)

insi de r= R

✗ CR 8 ) R

g

2 • gn = ge ( 1 - 21 ) ha ck

F = G# (R- d )pm [ at ce nte r = 0

↑^2 )^ fo^ r^ a^ se^ mi^ -^ ci^ r^ cle = 2 GM R R ' I T 3 ) fo r a qu a dra nt m = 21 12 G M m

m

g

g

R

mw ²r / m 8 v² / no v

ma z y

m u zy

e qu ato r

mw ²R

  • O T ATI NG

• R ES T

'g g

pol e -

  • Ma x ef fe c t a t equ at or
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g

  • ng

Fc o so F= mw²r R

Vci ,

G R M C on cep t: C e n Mtr V i p 2 et a=l G=M MGr av it y

R 2

VC XR. pt

R V (^) C=, 09 " R ²P 3

• K E PL ER'S LAW :

maj or axi s

mi nor

a x i s = 2 6

(Ap o gee )

( fu rth est poi nt fro m th e f oc i ) A phe li o n p t. .

I nv- = Gmm (pe r i gee )

✓ =/ E " pe ri ph eli on pt

(n ea re s t pt. fr om

fo c i)

+ a et +^ a^ et

[a - ae y

(a ta e )

E =^ c^ o^ ns^ t

= c onse rv ed (a ng u lar m o me n t um)

A, an d As : Ar ea s w e pt i n th e ti m e p er i o d t i an d tz

V mi n K E m in

Vp = V 1 ) P E m a x

V ma x, KE max ,

PE m in 1 72 7 , V 2

AR EA L LAW:

6 2 a - ( i - ez )]

o Ar ea of se c t or : 1 920

P lan ets d o no t

mov e w it h cons t

v eloc i t y

(e = e cce nt r ici ty ]

A rea l Ve loc i ty = A re a =

t 2

• C O N SERV A TIO N OF A NGU L A R MO ME N TUM :

[ Cons t ant ]

M,V , R, = M 2 V 2 R z

⟂ m² w c an g ul ar

velo cit y)^ =^ A^ s

t , tz

- V , = a t a e

V 2 9 -^ g^ e

• C ON SE RVAT IO N OF E NE RG Y :

- G MM + ⟂ m vp = - GM M + 1 mV

a c te)^2 a^ (^ it^ e^ )

V , =

GE ( r e)

It e V^2 =^ * ( Le )

= Va

f o r earth [ Mas s - 1 7 Ra d ius = R ] ① O uts ide at an hei ght = H :

F = G (R M t Mh) - g = (G RM th) 2

h aa r: gn = ge ( 1 - 2 1 ) On the sur fa c e: F= g = ins ide t he su r f ac e : at d ep th d

G MM

R 2

G RM 2

(i F = GM 'm (R - d ) 2 M ' = # (R - d ) 3

g = G M' ( R - d) 2

g = G # ( R- d) p g e ( 1 - ♀) G MM

f o r H o l l o w S p he re [ Ma ss - M Ra d ius = R] ① O uts id e a t an h eig h t = H :

F= (GRMt Mh) - E = (G R Mt h) 2

h< << ( 2 ) 3 12 I^ R

OR B I T AL V E LOC I T Y:

• G EO ST A T IO N ARY S AT A LIT

HR == 43 62 0 40 00 0 km TVc = = (^23 4) - 1 hKe r m l s

N O TE : R o f E a rth: 6 40 0 Km T = 36 5 - 2 5 d ay W o f E a rth : 7. 2 7 ✗ 1 0 - 5 r a d Is 1 7 ✗ w o f Ea r th: 1 - 23 ✗ 10 - 3 r ad I s : We igh tle s sne ss

E S CAP E V:

VE : ☒^ ×

= 12 Vc

T IM E P E RI OD :

¥ C^ on^ ce^ p^ t:^ KE^ =^ BE

T= Ci rc um V fer en ce

T 2 IR

2 = 4 ¥ 1 1 2 12 3 G M

T ²α R ³

PE = - G MRM

KE = G MM

E NER G Y:

2 R

T E - G MM

2 R

BE = G M M

2 R

TE = - BE =-K E

P O TEN TI AL

V = - GL

V = P E

at sur fa ce

  • ¥ 3 ( 31 2 - 8 2 )

V A-^ - I^ CE NT ER OF S OLI D S P HER E:

☆ V AT A XIS D U E ◦ A R ING :

✓ = - GM

R 2 + 2 2

=/ g ¥

ins id e a h o llo w s ph er e]

Vn =

T i n)

☆ V IN SI DE U NIF O R M SO L I D SPH ERE:

I R

x

WO RK Fo r LA U NCH ING:

W= Ef - E i

GMmh m gh

R C R + h )

1 + hR

- GM M

R th

- GM R M

W O R K FO R C HA NG IN G O RB I T:

W= Ef - E i

G Mmh

RC R + h )

= mg h

1 + hR

- G MM

Rth

- GM M

R

E AR TH

E LOCI TY

Vc at s ur f ace : 7 - 9 Km ls ]

GR AV I TA TI ON: CO N SE R VA TI VE FO R CE:

NO T DE PEN DE NT ON D I ST A NCE :

x

R

ins i de r =R^ o^ ut^ si^ dg^ e

✗ CR 8 )^ R