Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya: Foundations

3.2.37 · D1 · Physics › Orbital Mechanics & Astrodynamics › Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya

Parent note Orbit types padhne se pehle, tumhe har woh symbol apna banana hoga jo woh throw karta hai. Yeh page har ek ko scratch se build karta hai — pehle plain words mein, phir ek picture, phir yeh kyun zaruri hai. Upar se neeche padho; har block sirf unhi symbols use karta hai jo usse pehle define ho chuke hain. Har figure text mein number se refer hoti hai — "Figure 1", "Figure 2" dekho.

1. Circle aur uske pieces — $r$ , $R_{\oplus}$ , $h$

Ek satellite ko ek dot ki tarah socho jo ek bade ball (Earth) ke around ghoom rahi hai. Teen lengths batati hain ki "woh kitna upar hai". Dekho Figure 1.

Figure — Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya

Figure 1 — teen lengths $R_{\oplus}$ (cyan), $h$ (amber) aur $r$ (white), sab Earth ke centre ko origin maanke.

Teen symbols kyun, ek kyun nahin? Kyunki gravity ko Earth ke centre se measure kiya jaata hai, surface se nahin. Isliye saare physics formulas $r$ chahte hain — lekin engineers $h$ quote karte hain kyunki woh dikhta hai. Bridge simple hai:

2. Path ki roundness — $e$ (eccentricity)

Har orbit perfect circle nahin hoti. Zyaatar ellipses hoti hain — ek circle jo squeeze ho gayi ho. Ek number, $e$ , batata hai ki kitna squeeze hua. Dekho Figure 2.

Figure 2 — jaise $e$ 0 (cyan circle) se 0.7 (amber) tak badhta hai, ellipse stretch hoti hai jabki Earth ek focus par rehti hai.

Topic ko $e$ kyun chahiye: yeh woh single knob hai jo GEO (ko $e = 0$ chahiye, still raho) ko Molniya (bada $e$ chahiye, taaki north ke upar loiter kar sake) se alag karta hai. $e$ nahin, orbit types nahin.

3. Ellipse ka size — $a$ , aur uske do ends $r_{a}$ , $r_{p}$

Ek ellipse mein ek "lamba raasta" aur ek "chota raasta" hota hai. Lambe raaste ka aadha master size number hai. Dekho Figure 3.

Figure 3 — focus par Earth se perigee $r_{p}$ aur apogee $r_{a}$ ; full span $2 a = r_{p} + r_{a}$ hai, jisme $r_{p} = a (1 - e)$ , $r_{a} = a (1 + e)$ .

4. Plane ki tilt — $i$ (inclination)

Ek orbit ek flat plane mein rehti hai jo Earth ke centre se guzarti hai. $i$ measure karta hai ki woh plane equator ke compare mein kitna tilted hai. Dekho Figure 4.

Figure 4 — teen inclinations: equatorial ( $i = 0^{\circ}$ , cyan), Molniya critical angle ( $i = 6 3^{\circ}$ , white), aur retrograde SSO-like ( $i = 9 8^{\circ}$ , amber).

5. Gravity ki strength — $G$ , $M$ , aur shortcut $μ$

Gravity ka pull do cheezein depend karta hai: gravity kitni strong hai generally, aur kheenchne wala kitna bhaari hai.

6. Circle mein motion — $v$ , $T$ , $m$ , aur centripetal force ka idea

Orbit mein rehne ke liye satellite ko move karna hoga. Kuch symbols woh motion describe karte hain.

7. "Din" ke do prakar — sidereal vs solar

Parent note insist karta hai ki GEO $86164$ s use karta hai, $86400$ s nahin. Isliye do din hote hi kyun hain.

8. Woh bulge jo perfection kharab karta hai — $J_{2}$

Earth perfect ball nahin hai; yeh equator par phula hua hai. Maths mein us bulge ka ek naam hai.

Yeh topic ko kaise feed karte hain

Har foundation jo deeper machinery kholti hai: §6 ka balance Two-Body Problem and the Vis-Viva Equation mein poora work kiya gaya hai; timing law $T^{2} \propto a^{3}$ Kepler's Laws of Planetary Motion mein hai; low-orbit ke consequences Atmospheric Drag and Orbital Decay aur Satellite Ground Tracks mein hain; aur $a$ change karna (orbit raise ya lower karna) Hohmann Transfer and Delta-v Budgets mein study ki gayi energy cost karta hai.

Equipment checklist

Cover the right side and test yourself.

Convert altitude 420 km to orbital radius

r

(in SI)

r = 6371 + 420 = 6791

= 6.791 \times 1 0^{6}

What does eccentricity

e = 0

mean geometrically?

A perfect circle.

What is the range of

e

for a bound orbit, and what is

e = 1

0 \leq e < 1

for orbits;

e = 1

is a parabola (escape).

Write

r_{p}

and

r_{a}

in terms of

a

and

e

r_{p} = a (1 - e)

r_{a} = a (1 + e)

Write

a

in terms of apogee and perigee radii

a = (r_{p} + r_{a}) /2

What is inclination

i

the angle between?

The orbit plane and Earth's equator.

cos i

positive or negative for a retrograde (

i > 9 0^{\circ}

) orbit?

Negative.

What does

μ

stand for, its units, and

G

's units?

μ = GM

, units

m^{3} / s^{2}

;

G

m^{3} kg^{- 1} s^{- 2}

Which force supplies the centripetal pull for a satellite?

Gravity,

GM m / r^{2}

What is

m

in the force balance, and why does the orbit not depend on it?

The satellite's own mass; it cancels from both sides.

Which day (sidereal or solar) does GEO use, and its length?

Sidereal,

86164

What does

J_{2}

physically represent?

Earth's equatorial bulge (non-spherical gravity).

Recall Self-test: kya tum core idea ek breath mein bol sakte ho?

Har orbit ek ellipse hai gravity ke under; types sirf uska size $a$ , stretch $e$ , aur tilt $i$ vary karte hain. Ready? ::: Agar tumne checklist ke saare items answer kar liye, toh parent note kholo.