Geostationary satellite height fixed kyun hai, only over equator, and are astronauts really at zero gravity?

7 answers & replies

• [+][–]Zoya Khan12thSample· 6d ago

  For a circular orbit, the period depends only on the radius, because $T^2 = \dfrac{4\pi^2}{GM}r^3$. So if the period has to be exactly one day, there is only one possible radius. Put in $T = 86400$ s and $GM_E \approx 4\times10^{14}\ \text{m}^3\text{s}^{-2}$, and you get $r \approx 4.2\times10^7$ m, which is 42,000 km from the centre of the Earth. Subtract Earth's radius, about 6,400 km, and you get roughly 36,000 km above the surface. That's the number in NCERT.

  A satellite at 20,000 km would go around faster than once a day, so it would drift across the sky.

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• [+][–]Riya Singh12thSample· 6d ago

  About Delhi, think about where the centre of the orbit has to be. The only force on the satellite is gravity, and it points to the centre of the Earth, so the orbit's plane has to pass through the Earth's centre. Any circle in such a plane that stays above one point must be above the equator, because the equator is the only latitude circle whose plane passes through the Earth's centre. A satellite parked over Delhi would need a force toward the Earth's axis, not toward the centre, and nobody is providing that.

  So no geostationary over Delhi, but the equatorial one can still "see" India, that's how the TV dish works.

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• [+][–]Ishaan Bose11thSample· 6d ago

  A thing which helped me, geostationary isn't the only kind. NCERT also talks about polar satellites: they go around at a few hundred km height (low, so fast) in an orbit passing near the poles, with a period of about 100 minutes, and as the Earth turns beneath them they scan the whole surface. Used for remote sensing and weather pictures. Geostationary ones, being very high and fixed over one spot, are used for communication and TV. Same gravity, different radius, so different period. Yash if you remember only one line, remember that period is decided by the radius.

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• [+][–]Siddharth RaoDropperSample· 6d ago

  Yash, your third question first. "No gravity up there" is the most common myth, and it's wrong. At a height h the value of g is

  $g' = g\left(\frac{R}{R+h}\right)^2 \approx 9.8\times\left(\frac{6400}{6800}\right)^2 \approx 8.7\ \text{m s}^{-2}$

  so at 400 km up gravity is still about 90% of what we feel. The astronauts float because they and the station are both in free fall, falling around the Earth with the same acceleration. The floor doesn't push on them, so they feel no normal reaction. That's apparent weightlessness: weight (the force of gravity) is still there; what's missing is the contact force that we feel as weight.

  Same thing in a falling lift. Moon has gravity too (about 1/6 of Earth's).

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  • [+][–]Yash Tiwari11thSample· 6d agoAuthor

    oh bhai, so free fall wala logic. lift ke cut jaane wala example kaafi clear hai. thanks Siddharth bhaiya, ab cousin ko galat sabit karunga 😂

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  • [+][–]Ishaan Bose11thSample· 6d ago

    ok that blew my mind, still 90% of g and they float anyway. free fall is such a good explanation. and good to know about polar satellites too, i said "space has no gravity" for years lol

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• [+][–]Lakshmi TripathiDropperSample· 6d ago

  Speed for completeness. In one day the satellite covers a circle of circumference $2\pi r = 2\pi\times4.2\times10^7$ m. Divide by 86400 s:

  $v = \frac{2\pi r}{T} \approx 3.1\times10^3\ \text{m s}^{-1}$

  about 3 km/s, much slower than a low orbit satellite (about 8 km/s). The farther you go, the slower you orbit. NCERT also notes that the geostationary satellite turns west to east with the same angular speed as Earth's rotation, which is why it looks stationary from the ground.

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