Solar radiation pressure: Question bank — Hinglish deep dive

3.2.35 · D5 · Physics › Orbital Mechanics & Astrodynamics › Solar radiation pressure

Traps se pehle, aao hum us parent note ke har symbol ko phir se earn karein aur uski derivation chain ki har link ko justify karein — kyunki trap tabhi kuch sikhata hai jab tumhare paas pehle se honest version ho.

Symbols aur chain, zero se re-earned

Definition Har letter, simple words mein

$E$ — ek photon (light ka ek single packet) mein jo energy hoti hai, joules mein maapi jaati hai.
$c$ — speed of light, $\approx 3 \times 1 0^{8} m/s$ .
$p$ — momentum, wo "push-capacity" jo koi bhi chalti cheez apne saath leke chalti hai.
$L_{⊙}$ — Sun ki luminosity: total light power jo wo bahar daalti hai, watts mein.
$r$ — Sun se spacecraft tak ki distance.
$S$ — solar irradiance (intensity bhi kehte hain): distance $r$ par pahunchne wali light ki power per unit area, $W/m^{2}$ mein. 1 AU par ye solar constant $\approx 1361 W/m^{2}$ hota hai.
$P_{rad}$ — radiation pressure: light jo force per unit area exert karti hai.
$A$ — spacecraft ka wo cross-sectional area jo light ke flow ki taraf face kar raha ho.
$η$ — reflectivity coefficient: $0$ (surface poori light nigal leta hai) se $1$ (perfect mirror sab kuch wapas bounce kar deta hai) tak ka dial. Neeche figure dekhein.
$θ$ — surface ke normal (face se seedha bahar nikla hua arrow) aur Sun direction ke beech ka tilt angle.
$m$ — spacecraft ki mass; $a$ — uska acceleration.

Formula Chain, ek honest step at a time

Link 1 — ek photon momentum carry karta hai. $p = E / c$ . KYUN: relativity kehti hai $E^{2} = (p c)^{2} + (m c^{2})^{2}$ ; ek photon ki mass $m = 0$ hoti hai, isliye $E = p c \Rightarrow p = E / c$ . Massless cheez phir bhi momentum carry karti hai.

Link 2 — energy flux se pressure tak. $P_{rad} = S / c$ (perfect absorber). KYUN: $S$ wo energy hai jo per area per second girti hai. Har joule $1/ c$ momentum carry karta hai, isliye per area per second girnewala momentum $S / c$ hai — aur momentum-per-area-per-second hi pressure hai.

Link 3 — plate par force. $F = P_{rad} A (1 + η) cos θ$ . KYUN $cos θ$ : sirf projected area $A cos θ$ actually beam ko intercept karta hai — ek tilted plate ek chota target hoti hai (step figure dekhein). KYUN $(1 + η)$ : absorber momentum $p$ leta hai; mirror photon ko wapas bhej deta hai, uska momentum $2 p$ se change hota hai, yaani $(1 + η)$ $1$ se $2$ tak jaata hai (step figure dekhein). CAUTION: ye single- $cos θ$ form sirf Sun–spacecraft line ke saath wala component hai. Tilted mirror par actual force surface normal ke saath point karti hai aur $cos^{2} θ$ se scale hoti hai — doosra cosine incoming momentum ka normal-projection hai. Dono facts neeche visual mein dikhaye gaye hain aur Spot the error section mein re-test honge.

Link 4 — acceleration. $a = F / m$ . KYUN: orbits acceleration ke response mein chalti hain, aur Newton ka $F = ma$ force ko mass se divide karta hai — isliye design-critical ratio $A / m$ hai.

Upar wali figure Link 3 ki geometry dikhati hai: projected area $cos θ$ se shrink hoti hai (kam photons catch hote hain) aur recoil mirror ke liye momentum change double kar deta hai.

Doosri figure dikhati hai ki ek tilted mirror $cos^{2} θ$ kyun obey karta hai: ek cosine chhote target se aata hai, doosra normal ke saath momentum component rakhne se.

True or false — justify karo

A photon has zero mass, therefore it cannot exert a force.

False. Light ke liye momentum

m v

nahi hota; ye

p = E / c

hota hai jahan

E

photon energy hai. Massless ka matlab momentumless nahi hota, isliye photons ki stream kisi bhi surface par push karti hai jo use hit kare.

1 AU par base radiation pressure roughly sea level ke atmospheric pressure ke same order mein hoti hai.

False.

P_{rad} \approx 4.5 \times 1 0^{- 6} Pa

, jo sea-level air ke

\sim 1 0^{5} Pa

se lagbhag 11 orders of magnitude kamzor hai. Iski power ye hai ki ye continuous aur space mein har jagah hai, strong nahi hai.

Ek perfect mirror same area ke perfect black absorber se exactly double force feel karta hai, dono face-on.

True. Absorber ek photon-momentum

p

gain karta hai; mirror use reverse karta hai,

2 p

gain karta hai (recoil). Ye hi

(1 + η)

factor hai jo

η = 0

η = 1

tak jaata hai.

SRP aur Sun ki gravity dono

1/ r^{2}

se fall off karte hain, isliye unka ratio har object ke liye same hota hai.

False. Dono accelerations

1/ r^{2}

se fall karti hain isliye ratio distance-independent hai, lekin phir bhi

\propto A / m

hai. Ek solar sail ka ratio bahut bada hota hai; ek dense probe ka bahut chota. Ye Orbital perturbations by SRP ka central idea hai.

Sun se distance double karne par SRP force half ho jaati hai.

False. Irradiance

S \propto 1/ r^{2}

(Inverse-square law), isliye

r

double karne par force quarter ho jaati hai, half nahi.

Ek spacecraft jo twice as massive ho lekin same cross-section ho, half SRP acceleration feel karta hai.

True.

a_{SRP} \propto A / m

; fixed

A

par double

m

acceleration half kar deta hai, bhale hi force

F

unchanged ho.

SRP hamesha spacecraft ko directly Sun se door dhakelta hai.

False. Ek flat plate jo face-on nahi hai ke liye, reflected photons surface normal ke saath nikalte hain, isliye reaction force partly sideways point karti hai — exactly isi tarah Solar sails orbit raise ya lower karne ke liye tack karte hain.

Ek transparent (fully transmitting) object 1 AU par essentially koi SRP feel nahi karta.

True. Agar photons seedhe pass ho jaate hain, toh koi momentum transfer nahi hota, isliye

F \to 0

. SRP ko act karne ke liye absorption ya reflection chahiye.

Spot the error

"Reflection ek single factor of

cos θ

deta hai kyunki sirf projected area

A cos θ

hi light intercept karti hai."

Projection ek cosine hai, lekin perfect mirror ki normal-force bhi ek doosra cosine carry karti hai (sirf momentum ka normal component reverse hota hai), jo

\propto cos^{2} θ

deta hai normal ke saath — exactly wahi jo figure s02 dikhata hai. Simple

(1 + η) cos θ

sirf along-Sun component approximation hai.

P_{rad} = S / c

kisi bhi surface ke liye kaam karta hai, isliye 1 AU par ek mirror

4.5 \times 1 0^{- 6} Pa

feel karta hai."

P_{rad} = S / c

absorber ki base value hai. Ek face-on mirror ko

(1 + η) P_{rad} = 2 P_{rad} \approx 9 \times 1 0^{- 6} Pa

milta hai; reflection factor

(1 + η)

drop kar diya gaya tha.

"Kyunki

p = E / c

hai, ek brighter (higher-frequency) photon ek dim wale ke same momentum carry karta hai."

Momentum energy ke saath scale karta hai,

p = E / c

. Ek higher-energy photon zyada momentum carry karta hai; sirf equal-energy photons equal momentum carry karte hain. (Photon momentum and relativity ki foundation.)

"SRP real missions ke liye negligible hai — ye ek textbook curiosity hai."

High-

A / m

objects (sails, balloons, defunct panels) ke liye SRP Atmospheric drag ko rival ya beat karta hai aur months tak orbits ko perturb karta hai. Ise ignore karne se long-term ephemerides kharab ho jaati hain.

"Irradiance paane ke liye hum Sun ki power ko Sun ki surface area se divide karte hain."

Hum

L_{⊙}

4 π r^{2}

se divide karte hain, jo spacecraft ki distance

r

par sphere ki area hai, Sun ki apni surface ki nahi — yahi

S

ko distance ke saath fall karata hai.

"Kyunki per photon momentum change tiny hai, total force wildly fluctuate karta hai."

Photon flux astronomically large aur steady hai, isliye law of large numbers se force smooth aur constant hai — wahi steadiness exactly wajah hai ki ye lambe time par matter karta hai.

"Satellite ko black paint karna SRP minimize karta hai kyunki black reflect karne ki jagah absorb karta hai."

Absorbing (

η = 0

) minimum factor

(1 + η) = 1

deta hai, isliye black mirror se kam feel karta hai — lekin phir bhi poori absorbing pressure feel karta hai. Zero SRP ke liye transparency chahiye, blackness nahi.

Why questions

Same power Sun ke center par har sphere se kyun pass hoti hai?

Energy conserved hoti hai aur Sun aur spacecraft ke beech ki space na light create karti hai na absorb, isliye har concentric sphere se cross karne wali total power

L_{⊙}

fixed rehti hai — sirf area

4 π r^{2}

badhta hai jiske upar ye spread hoti hai, isliye

S = L_{⊙} /4 π r^{2}

Hum energy flux ko momentum flux mein

1/ c

factor ke saath kyun convert karte hain?

Kyunki pressure momentum hai jo per area per second deliver hota hai, aur light ka har joule

1/ c

momentum carry karta hai (

p = E / c

S

(energy flux) ko

1/ c

se multiply karne par ye momentum flux = pressure

P_{rad}

ban jaata hai.

Area-to-mass ratio

A / m

kyun key design number hai, area ya mass akele nahi?

Orbits acceleration ke response mein chalti hain

a = F / m

, aur

F \propto A

, isliye

a \propto A / m

. Sirf combination bachta hai — ek bada light sail aur ek chota dense probe equal

A / m

ke saath same accelerate karte hain.

Solar sail badi aur patli kyun banayi jaati hai, choti aur massive kyun nahi?

A / m

maximize karne ke liye: bada area zyada photons catch karta hai jabki kam mass ka matlab hai ki force ki har unit zyada acceleration produce kare, jo sabse bada useful thrust deta hai.

Ek tiny

\sim 9 mN

force phir bhi ek bada

Δ v

kyun produce kar sakti hai?

Kyunki ye space ke frictionless vacuum mein continuously months ya years tak act karti hai; impulse

= F \times t

bina kisi air ke accumulate hota hai jo ise cancel kare.

E = p c

relation Newtonian mechanics se nahi, relativity se kyun aata hai?

Newton ka

p = m v

massless particle ke liye zero deta hai. Relativistic

E^{2} = (p c)^{2} + (m c^{2})^{2}

with

m = 0

E = p c

milta hai, jo akela self-consistent statement hai (dekhein Photon momentum and relativity).

Edge cases

Jab

θ \to 9 0^{\circ}

ho (sunlight plate edge-on par graze kare) toh SRP force ka kya hoga?

cos θ \to 0

, isliye intercepted light — aur hence force — zero ho jaati hai: ek edge-on plate essentially koi photon catch nahi karti.

Earth ke shadow (umbra) mein spacecraft par SRP force kya hogi?

Direct sunlight nahi hai toh wahan

S \to 0

, isliye SRP khatam ho jaati hai — ye per-orbit on/off cycling khud ek perturbation hai (dekhein Orbital perturbations) jo mission planners ko model karni padti hai.

Jab

r \to \infty

ho (deep space, Sun se bahut door), SRP ka kya hoga?

S \propto 1/ r^{2} \to 0

, isliye SRP fade ho jaati hai; kisi bhi star se bahut door, radiation pressure negligible ho jaata hai.

Ek perfectly reflecting surface

θ

par tilt ho, toh force simply kyun vanish nahi hoti jaise mirror "light ko slide off" karne deta hai?

Incoming momentum ka normal component reflection par reverse hota hai, jo normal ke saath

\propto cos^{2} θ

force deta hai — ye tilt ke saath weak hoti hai lekin sirf true edge-on par zero hoti hai (

θ = 9 0^{\circ}

Limiting reflectivity behaviour kya hai:

η = 0

η = 1

tak force kaise change hoti hai?

Factor

(1 + η)

1

(pure absorber) se

2

(perfect mirror) tak jaata hai, isliye force at most double hoti hai; ek passive flat surface se

2 P_{rad} A cos θ

exceed karna possible nahi hai.

Agar ek surface absorbed light ko heat ke roop mein unevenly re-emit kare (thermal recoil) toh kya hoga?

Tum anisotropic thermal photons se extra thrust paate ho — ye Yarkovsky effect hai, SRP ka cousin, isliye absorbing bodies sunlight khatam hone ke baad bhi ek directional push feel kar sakti hain.

Recall One-line self-audit (answers hide karein)

Massless ⇒ koi push nahi? ::: Nahi — $p = E / c$ , mass ke bina momentum.
Mirror vs black force ratio, face-on? ::: 2 to 1 (recoil, $(1 + η)$ factor).
SRP/gravity ratio depend karta hai? ::: $A / m$ par, distance par nahi.
Shadow mein ya edge-on force? ::: Dono cases mein Zero.
$S$ kya hai? ::: Solar irradiance, power per area $= L_{⊙} /4 π r^{2}$ .

8. Connections

Solar radiation pressure — parent note jiske symbols ( $E, S, η, P_{rad}$ ) aur chain ko ye traps drill karti hain.
Solar sails — tilt/reflection subtleties (Links 3) jo SRP ko steerable propulsion banne deti hain.
Atmospheric drag — competing non-conservative force jiske saath true/false items contrast karte hain.
Orbital perturbations — jahan $A / m$ dependence aur shadow cycling long-term matter karte hain.
Inverse-square law — $S \propto 1/ r^{2}$ distance edge cases ke peeche.
Photon momentum and relativity — Link 1 mein use hone wale $E = p c$ ka source.
Yarkovsky effect — thermal-recoil edge case, SRP ka absorbing-body cousin.