JEE/NEET Physics · Gravitation series · Part 9 of 9 · All parts →
- Field = gravity felt per kilogram (E = GM/r²) — exists even in empty space
- Inside a hollow planet shell: gravity is exactly ZERO everywhere
- At a planet’s centre: no pull, but the deepest gravity trap
- Weightlessness = falling together, NOT zero gravity
- TV satellites sit at exactly 36,000 km — here’s why
Eight cards covered the main roads. This bonus card completes the chapter’s side streets — gravity ‘field’, the hollow-shell surprise, true weightlessness, and why your TV satellite sits at exactly 36,000 km. All simple, all exam-tested. Part 9 (bonus) of the Gravitation series.
- Gravity field: the ‘pull per kilogram’
- The hollow-planet surprise
- At the centre of a planet
- Weightlessness, properly understood
- TV satellites: the 36,000 km story
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Gravity Field: The ‘Pull Per Kilogram’
You know g = 9.8 m/s². Generalise: the field at any point is the pull a 1-kg test mass would feel there: E = GM/r², direction: toward the planet. The subtle point: the field exists whether or not anything is there to feel it — it’s a property of space around a mass, an invisible arrow at every point. (E and g are the same number; exams swap the names.)
The Hollow-Planet Surprise
Stand anywhere inside a hollow spherical shell of rock. Which way do you fall? Nowhere — gravity is exactly zero, everywhere inside. Not approximately — exactly.
Why? Look at a patch of shell on your right: close, so it pulls hard, but a cone of vision catches only a small patch. The same cone extended left catches a bigger but farther patch that pulls weakly. Small-near-strong exactly cancels big-far-weak. Every direction cancels. This is why, when you dig into the Earth (Part 7), only the rock BENEATH you counts — the shell above you cancels itself out.
At the Centre of a Planet
Combine the ideas: at the centre, pulls cancel from all sides (field = 0, you’d float) — but the gravity trap is at its deepest (energy −1.5GMm/R). No pull ≠ shallow trap. A favourite conceptual MCQ: zero field, deepest well — both at once.
Weightlessness, Properly Understood
Astronauts float not because gravity is absent (at ISS height it’s 89% of surface value) but because they and their spacecraft fall together — nothing presses against anything. Same as a lift with a snapped cable: you’d float inside it, in full gravity. Weight is a contact force; weightlessness is absence of contact.
TV Satellites: The 36,000 km Story
For a satellite to hover over one fixed spot (so your dish never moves), it must circle exactly once per day. Part 3’s rule then FIXES its distance — no choice: r³ = GMT²/4π² gives r ≈ 42,300 km from Earth’s centre, i.e. 36,000 km up. Plus two more conditions: circle directly above the equator, moving eastward. All three together = ‘geostationary’.
Solved Examples
Direct: E = GM/(2R)² = GM/4R².
Check: double the distance, quarter the field — the same inverse-square as gravity always. ✔
Answer: GM/4R², pointing at the planet
Step 1 — Kepler solved for r: r³ = GMT²/4π² = 6.67×10⁻¹¹ × 6×10²⁴ × (8.64×10⁴)² ÷ 39.5 ≈ 7.55×10²².
Step 2 — cube root: r ≈ 4.23×10⁷ m.
Step 3 — minus Earth’s radius: h = 42,300 − 6,400 ≈ 36,000 km.
You just derived the most famous number in satellite TV. ✔
Answer: h ≈ 36,000 km
- Field vs force. Field (N/kg) exists without a test mass; force (N) needs one. MCQs swap them.
- ‘Zero field at the centre = zero trap.’ Zero pull, deepest trap — different questions, different answers.
- ‘Geostationary’ vs ‘geosynchronous’. Geosynchronous: any orbit with a 24-h lap (may swing in a figure-eight). Geostationary: 24-h lap AND over the equator AND circular — parked. NEET tests the vocabulary.
- Weightlessness as ‘no gravity’. 89% of gravity is present at the ISS — the float is shared falling.
This Physics in Your Daily Life
- Every TV dish on every rooftop points at one invisible point 36,000 km above the equator — INSAT-class satellites parked there by this card’s maths, photographing weather and beaming channels for two decades.
- Zero-g research on the ISS — crystal growth, protein folding, fluid behaviour — is really ‘shared free fall’ research; pharma companies pay millions for it.
- The 2,000+ satellites in that one narrow ring make it the most valuable real estate in space — slot assignments are internationally regulated, and dead satellites are pushed to a graveyard orbit.
- Gravity-gradient stabilisation: a satellite’s near side feels slightly stronger pull than its far side (field changes with distance!) — enough to keep it pointing at Earth, no fuel needed.
Practice set (answers hidden — try first)
(NEET-level) Field at 3R (surface value E₀):
(Concept) Inside a hollow spherical shell:
(Concept) Astronauts float because:
(NEET-level) A geostationary satellite must have:
(Concept) At a planet’s centre, weight and gravity trap are:
- 🧠 Inside a shell = zero gravity, exactly — ‘near-small cancels far-big’, every direction.
- 🧠 GEO number: 36,000 km — ’24-hour lap over the equator’ forces it; no choice.
- 🧠 Weight is contact: floating = falling together, not missing gravity (89% of gravity is present at the ISS).
- 🏠 Daily: every rooftop TV dish points at the 36,000 km parking ring — INSAT satellites have beamed weather and channels from there for decades.
- 🏠 Daily: medicines grown on the ISS — ‘shared free fall’ is a pharma laboratory worth crores.
- field E = GM/r² — pull per kilogram; exists in empty space
- inside a hollow shell: gravity exactly zero (near-small cancels far-big)
- planet centre: field zero, trap deepest (−1.5GMm/R)
- weightlessness = shared free fall; weight = contact force
- geostationary = 24-h lap + equator + circle → exactly 36,000 km
Quick revision
- Field = gravity felt per kilogram (E = GM/r²) — exists even in empty space
- Inside a hollow planet shell: gravity is exactly ZERO everywhere
- At a planet’s centre: no pull, but the deepest gravity trap
- Weightlessness = falling together, NOT zero gravity
- TV satellites sit at exactly 36,000 km — here’s why
- Gravity field: the ‘pull per kilogram’
- 1Escape Velocity: The Speed That Ends Gravity’s Grip
- 2Orbital Velocity: Why the ISS Never Falls
- 3Kepler’s Laws: The 1609 Prediction Machine NASA Still Uses
- 4Angular Momentum: Gravity Can Pull, It Cannot Twist
- 5Gravitational Potential Energy: Why the Minus Sign Matters
- 6Satellite Energy: Why Total Energy Is Negative KE Over Two
- 7Variation of g: Why You Weigh Less at the Equator
- 8Black Holes, LIGO and Lagrange Points: Gravitation’s Research Frontier
- 9Gravitation Bonus: Field Intensity, Shell Theorem, Weightlessness and GEO Satellites
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External references for fact-checking and further reading.
