Gravitational Field, Potential & Applications
Shell theorem, field lines, potential graphs, real-world applications. NEET & JEE Main heavily test this section.
The Shell Theorem
Newton's most powerful tool — it simplifies all shell/sphere calculations.
Shell Theorem — Part 1
A uniform spherical shell of mass M behaves as if all its mass is concentrated at its centre for a point outside the shell.
Exam Insight
This is WHY Newton's law works for extended bodies — Earth (a sphere) pulls you as if all 5.97×10²⁴ kg are at its centre 6400 km below your feet.
Shell Theorem — Part 2
A point inside a uniform spherical shell experiences zero gravitational force due to that shell.
Common Mistake Alert
This applies to HOLLOW shells only. For a solid sphere, the inner shells still contribute. A point inside a solid sphere feels g = GMr/R³ (not zero).
Gravitational Field: Solid Sphere vs Shell
g vs r graph: Green = solid sphere, Blue = hollow shell
Thinking Step: Reading the Graph
For a solid sphere: g increases linearly from 0 to R, then decreases as 1/r² outside. The peak is at the surface. For a hollow shell: g = 0 inside, then suddenly jumps and decreases as 1/r² outside. This graph appears directly in JEE Main.
Gravitational Field (g) vs Gravitational Potential (V)
| Property | Gravitational Field (g) | Gravitational Potential (V) |
|---|---|---|
| Nature | Vector quantity | Scalar quantity |
| At a point | Force per unit mass | Work done per unit mass to bring from ∞ |
| Formula | g = GM/r² (outside) | V = −GM/r |
| Inside solid sphere | g = GMr/R³ (linear) | V = −GM(3R²−r²)/2R³ (parabolic) |
| Inside hollow shell | g = 0 | V = −GM/R (constant) |
| Relation | g = −dV/dr (field = −ve gradient of potential) | |
| Sign | Directed toward mass (attractive) | Always negative (reference at ∞) |
Real-World Applications
Satellite types, uses, and the physics behind each.
Geostationary Satellite
Fixed above equator, T = 24h. Used for TV, communication, meteorology.
GPS Satellites
Low-medium orbit, multiple satellites, triangulation for position.
Hubble Space Telescope
Low Earth orbit, no atmospheric distortion, superior imaging.
ISS (International Space Station)
Astronauts in free fall = weightlessness. Gravity still acts (g ≈ 8.7 m/s² at 400 km).
Moon (Natural Satellite)
Earth's only natural satellite. Tidal forces caused by differential gravity.
Polar Satellites
Orbit pole to pole, Earth rotates beneath → covers entire surface. Used for mapping.
Exam Insight: Weightlessness
Weightlessness occurs when the only force acting is gravity (free fall). It does NOT mean gravity = 0. An astronaut in ISS is in continuous free fall — centripetal acceleration = g at that altitude. CBSE asks this definition, NEET asks MCQs about it.
Potential Energy Applications
Energy to place satellite of mass m at height h from Earth's surface:
Thinking Step
You need to give the satellite BOTH height (PE) AND velocity (KE). Both are required. JEE asks total energy needed = ΔKE + ΔPE.
Moving satellite from orbit r₁ to r₂:
If r₂ > r₁: ΔE > 0 → need to ADD energy to move satellite outward. Counter-intuitive but true.
When escape velocity ≥ speed of light (c), even light can't escape → Black Hole!
This is beyond CBSE but appears as a conceptual question in JEE Advanced.
Energy Comparison at Different Orbits
| Orbit | KE | PE | Total E |
|---|---|---|---|
| Inner orbit (r₁) | Higher | More negative | More negative |
| Outer orbit (r₂) | Lower | Less negative | Less negative |
| Escape (r→∞) | → 0 | → 0 | = 0 |
Strategy Tip
When orbit radius increases: KE ↓, PE ↑ (less negative), Total E ↑ (less negative). Speed decreases but energy increases. JEE Advanced tests this paradox every few years.