What force provides the centripetal force for an orbiting satellite?
Gravity: GMm/r2=mv2/r.
Formula for circular orbital speed?
v=μ/r (decreases with altitude).
Formula for orbital period (circular)?
T=2πr3/μ (Kepler's 3rd law).
GEO altitude and why?
~35 786 km, because period must equal one sidereal day (86 164 s).
Sidereal vs solar day for GEO?
Use sidereal (86 164 s); Earth also orbits the Sun so a solar day is longer.
Difference: geostationary vs geosynchronous?
Both period = sidereal day; geostationary also has e=0,i=0 so it stays fixed over one equatorial point.
What makes an orbit Sun-synchronous?
Its J2 nodal precession equals Earth's ~0.9856°/day around the Sun, keeping constant local Sun time.
Why must SSO be retrograde (~98°)?
cosi must be negative to get eastward precession matching the Sun.
Molniya inclination and why?
63.4°, the critical inclination where 5cos2i−1=0 so perigee doesn't drift.
Molniya period?
Half a sidereal day (~12 h) with high northern apogee for long loiter.
Which orbit hosts GPS and at what altitude?
MEO, ~20 200 km, ~12-h period.
Semi-major axis in terms of apogee & perigee radii?
a=(ra+rp)/2.
Why does the satellite move slowest at apogee?
Kepler's 2nd law: equal areas in equal times → slow when far.
Recall Feynman: explain to a 12-year-old
Imagine swinging a ball on a string in a circle. Gravity is the string. If you're close to Earth, gravity pulls hard, so you must swing FAST — that's a low satellite doing a lap in 90 minutes. Way up high, gravity is a weak string, so the ball drifts slowly — GEO takes a whole day, which is why a TV dish can point at one spot forever and never move. Some satellites are lazy on one side of a squished loop: they zoom past the bottom and then loaf way out at the top for hours, so they can watch cold northern countries — that's a Molniya. And Earth's slightly-fat middle gives a gentle push that we cleverly use so one kind of satellite always sees the ground at the same time of day, perfect for comparing photos.
Dekho, saare orbits basically ek hi physics hain — gravity aur centripetal force ka balance. Jab tum gravity ko centripetal force ke barabar rakhte ho (GMm/r2=mv2/r), tumhe milta hai v=μ/r. Iska matlab: jitna upar jaoge, utna slow chaloge. Isiliye LEO (~420 km, ISS) sirf 90 minute me ek chakkar maar leta hai, jabki GEO (35 786 km) ko poora ek sidereal din lagta hai — aur wahi trick se woh aakash me ek jagah "fixed" dikhta hai, perfect for TV/weather satellites.
Types sirf mission ke hisaab se choose kiye jaate hain. LEO = high resolution imaging par choti footprint aur drag. MEO = GPS jaisa navigation (~20 200 km). GEO = communications, kyunki ground se dish hilana nahi padta. SSO ek clever chaal hai: Earth ke bulge (J2) ki wajah se orbit ka plane slowly ghoomta hai, aur agar inclination ~98° (retrograde) rakho to yeh ghoomna Sun ke saath match kar jaata hai — matlab satellite har jagah same local time pe pahunchta hai, shadows same rehti hain, imaging comparison easy.
Molniya sabse mazedaar hai. Russia ko high-latitude (Moscow type) coverage chahiye tha, par wahaan GEO horizon ke bilkul neeche dikhta hai — useless. To unhone ek lambi squished ellipse banayi: apogee north ke upar bahut ऊँचा, jahan Kepler ke second law se satellite bahut dheere chalta hai — matlab 12 ghante me se ~8 ghante wahin "loiter" karta hai. Aur inclination 63.4° isliye kyunki wahi woh critical angle hai (5cos2i−1=0) jahan perigee drift band ho jaata hai. Yaani nature ka ek "bug" ko feature bana diya. Yahi orbital mechanics ki khoobsurti hai — trade-offs samajh lo, baaki sab derive ho jaata hai.
