Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya: Question bank

3.2.37 · D5 · Physics › Orbital Mechanics & Astrodynamics › Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya

Yahan sab kuch usi backbone par tikaa hai jo tum pehle se jaante ho: gravity centripetal force supply karti hai, jisse milta hai $v = μ / r$ aur $T = 2 π r^{3} / μ$ (yahi hai Kepler's 3rd law), aur saath mein $J_{2}$ bulge jo orbit planes aur perigees ko drift karata hai (J2 Perturbation and Nodal Precession).

True or false — justify

"True/false" ka koi matlab tabhi hai jab tum physics bata sako. Har ek padho, decide karo, phir reveal karo.

T/F: Ek higher orbit hamesha tez chalti hai kyunki woh Earth se zyada door hai.

False. Speed hai

v = μ / r

, jo

r

badhne ke saath ghatती hai — GEO sirf ~3.07 km/s par chalti hai jabki LEO ~7.7 km/s par daudta hai. "Zyada door = zyada tez" wali feeling car ki intuition hai, orbit physics ki nahi.

T/F: Sabhі chhe orbit types alag-alag laws of motion follow karti hain.

False. Ye sabhi gravity ke under same two-body ellipse hain; sirf altitude, eccentricity aur inclination alag hoti hai. Dekho Two-Body Problem and the Vis-Viva Equation.

T/F: Ek geosynchronous orbit automatically geostationary hoti hai.

False. Geosynchronous ke liye sirf period = one sidereal day chahiye; agar woh tilted hai (

i \neq = 0

) ya stretched hai (

e \neq = 0

) to woh sky mein figure-8 trace karti hai. Geostationary ke liye uske upar

e = 0

aur

i = 0

bhi chahiye.

T/F: GEO ka period exactly 24 ghante hota hai.

False. Yeh ek sidereal day hota hai, 86 164 s (~23 h 56 min). 86 400 s use karne se altitude ~50 km zyada ho jaati hai kyunki Earth bhi Sun ke around orbit karti hai, jo har solar day mein extra rotation add karta hai.

T/F: Ek Sun-synchronous orbit apna zyaadatar time poles ke upar bitaati hai.

False. SSO near-polar hai, lekin iska purpose nodal precession ke zariye har latitude par constant Sun angle rakhna hai, pole coverage nahi. ~98° inclination Sun ke ~0.9856°/day se match karne ke liye choose ki jaati hai, pole ke upar hover karne ke liye nahi.

T/F: Molniya ki

63. 4^{\circ}

inclination ek convenient-sa round number hai jo designers ne apni pasand se choose kiya.

False. Yeh exactly

5 cos^{2} i - 1 = 0

ka root hai — critical inclination jahan

J_{2}

perigee ko drift karna band kar deta hai. Physics ne force kiya, arbitrary nahi.

T/F: Ek circular LEO aur ek GEO satellite ka orbital energy per unit mass same hota hai.

False. Specific energy hai

E = - μ /2 a

; GEO ka

a

bahut bada hai, to uski

E

kam negative hai (higher). Yahi energy gap hai jo GEO tak pahunchne ko mehenga banata hai (dekho Hohmann Transfer and Delta-v Budgets).

T/F: Do satellites jo same-size circular orbit mein hain lekin alag inclinations par, unka period same hota hai.

True. Period sirf

a

par depend karta hai via

T = 2 π a^{3} / μ

; tilt orbit ka size nahi badalta, to period identical hota hai.

T/F: Equator ke upar ek geostationary satellite North Pole ke paas ke kisi sheher ko acchi coverage de sakta hai.

False. High latitude se GEO sat barely horizon par hota hai; signal atmosphere ko skim karta hai aur buildings block kar deti hain. Yahi failure reason hai ki Molniya ka high northern apogee exist karta hai.

Spot the error

Har line mein ek plausible-sounding statement hai jisme reasoning ka ek hissa toot hua hai. Use dhundho, phir repair reveal karo.

"Molniya north ke upar ruka rehta hai kyunki uska engine wahan use slow karta hai."

Koi engine nahi. Woh apogee par slow hota hai Kepler's 2nd law ki wajah se — equal areas in equal times matlab door hone par crawl karta hai. Stretched ellipse us slow apogee ko northern hemisphere ke upar place karti hai.

"SSO ko Sun track karne ke liye 90° se thodi kam prograde inclination chahiye."

Wrong sign. Precession formula

\dot{Ω} \propto - cos i

ko positive eastward drift deni chahiye, to

cos i

negative hona chahiye ⇒

i > 9 0^{\circ}

(retrograde, ~98°).

"GPS GEO mein hai taki har user ke upar fixed reh sake."

GPS MEO mein hai (~20 200 km, ~12-h period), GEO mein nahi. GPS deliberately sky mein move karta hai; position fix karne ke liye tumhe ek saath kaafi visible satellites chahiye, jo ek single fixed dot kabhi nahi de sakta.

"GEO compute karne ke liye solar day (86 400 s) use karna chahiye kyunki satellites logon ki service karte hain, aur log Sun ke hisaab se jeete hain."

Satellite ko Earth ka rotation stars ke relative (uska inertial frame) match karna hota hai, jo sidereal day 86 164 s hai. Solar day mein Earth ki Sun ke around orbital motion shamil hai aur galat altitude deta hai.

"Apogee par satellite sabse tez hota hai kyunki gravity use poore raaste upar khichti rahi hai."

Ulta hai. Apogee tak chadna kinetic energy ko potential energy mein convert karta hai, to woh apogee par sabse slow hota hai aur perigee par sabse tez.

"Orbit ko Sun-synchronous banane ke liye bas altitude badha do; higher orbits tezi se precess karti hain."

Iska ulta:

\dot{Ω} \propto n (R_{\oplus} / p)^{2} \propto a^{- 7/2}

, to higher orbits slower precess karti hain. SSO ko inclination (aur altitude) milaakar tune kiya jaata hai, sirf zyada upar jaane se nahi.

"Molniya aur GEO ek period share nahi kar sakte kyunki unki shapes alag hain."

Period sirf

a

par depend karta hai, shape par nahi. Ek Molniya orbit ek 12-h orbit hai jiska

a

same hai circular 12-h MEO jitna; woh sirf circle ki jagah stretched ellipse mein woh time spend karta hai.

"LEO mein atmospheric drag negligible hai kyunki space vacuum hai."

400–600 km par residual atmosphere thin hai lekin zero nahi, aur satellite usme se ~7.7 km/s par guzarta hai, to drag steadily orbit ko neeche laata hai. Dekho Atmospheric Drag and Orbital Decay.

Why questions

Mechanism ka ek sentence mein jawab do, definition nahi.

Lower orbit ka period shorter kyun hota hai jabki woh ek chhota loop bhi hai aur tez bhi?

Dono effects ek hi direction mein push karti hain: path chhota bhi hai aur

v = μ / r

bada bhi hai, to

T = 2 π r / v

doubly collapse hota hai — yahi hai

T^{2} \propto r^{3}

J_{2}

perigee drift ka bug

63. 4^{\circ}

par feature kyun ban jaata hai?

Us critical inclination par

5 cos^{2} i - 1 = 0

, to drift term vanish ho jaata hai aur perigee/apogee frozen rehte hain — Molniya apna apogee permanently north ke upar park kar leta hai.

Molniya ka ground track Russia ke upar ghanton tak "hang" kyun karta dikhta hai?

Apogee ke paas satellite sabse slow move karta hai (Kepler's 2nd law) aur apogee north ke upar place hota hai, to woh us region ke upar apne 12 ghanton mein se ~8 ghante ruka rehta hai — Satellite Ground Tracks par visible.

GEO tak pahunchne mein LEO se zyada energy kyun lagti hai jabki GEO slow move karta hai?

Tumhe gravity well se bahut door tak climb karna padta hai; specific orbital energy

E = - μ /2 a

a

ke saath badhti hai, aur woh potential-energy gain GEO par kam kinetic energy ko dominate karta hai.

SSO har latitude par same Sun angle (constant shadows) kyun maintain karta hai?

Uska orbit plane eastward ~0.9856°/day precess karta hai, exactly Earth ki Sun ke around motion se match karta hai, to Sun-to-plane geometry poore saal fixed rehti hai.

Imaging usually GEO ki jagah LEO se kyun ki jaati hai?

LEO ki chhoti distance fine ground resolution aur tight footprint deti hai; GEO ki huge range detail blur kar deti hai bhaले hi woh ek saath poora hemisphere dekh sake.

Edge cases

Boundaries aur degenerate inputs — woh scenarios jo naive rules ko tod dete hain.

Fixed semi-major axis

a

par eccentricity

e \to 0

hone par period ka kya hota hai?

Kuch nahi — period sirf

a

par depend karta hai, to same

a

wale ek circle aur ek thin ellipse ka period identical hota hai; sirf loop ke around speed variation badlati hai.

Altitude

h \to \infty

par orbital speed ka limiting behaviour kya hai?

v = μ / r \to 0

; infinitely distant orbit ko essentially koi speed nahi chahiye kyunki wahan gravity vanishingly weak hai.

Degenerate case: inclination

i = 0

aur

e = 0

wali orbit GEO altitude par — kya milta hai?

Ek true geostationary orbit: woh ek equatorial longitude ke upar motionless hang karta hai, poore GEO family ka special (non-degenerate-purpose) point.

Edge case: exactly

i = 9 0^{\circ}

(pure polar) par,

J_{2}

nodal precession kya karta hai?

\dot{Ω} \propto cos i

zero ho jaata hai, to plane bilkul precess nahi karta — yahi reason hai ki ek pure polar orbit Sun-synchronous nahi ho sakti aur SSO ko thoda 90° se aage tilt karna padta hai.

Boundary: ek satellite itna neeche ki uska perigee har pass mein dense atmosphere mein dip kare — uska kya hoga?

Drag perigee par energy leeta hai, apogee neeche aata hai, orbit circularise aur shrink hoti hai jab tak re-entry nahi ho jaati; orbit stabilise hone ki jagah decay hoti hai (Atmospheric Drag and Orbital Decay).

Limiting case: agar ek "geosynchronous" orbit ka

e = 0

ho lekin

i

0

se badhne lage, to ground track kya banta hai?

Woh ek fixed dot se north-south figure-8 (analemma) mein khul jaata hai; period abhi bhi sidereal day ke barabar hai lekin woh stationary nahi rehta.

Recall Ek-line self-test

Zor se bolo ki "higher = faster" kyun galat hai. ::: Kyunki $v = μ / r$ $r$ ke saath decrease karta hai — zyada door, gravity kamzor, to ek slower orbit use balance karti hai.