Newton's Law of Gravitation
F = Gm₁m₂/r² — inverse-square force between two masses.
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Class 11 · Notes
Gravitation— Notes, Formulas & Revision
Complete revision notes and formulas for Gravitation (Class 11). Curated for JEE, NEET, AP Physics, SAT, and CUET. Tap any topic to open the live simulation and full PYQ set.
g at Height & Depth
g(r) ∝ r inside, 1/r² outside — single curve across both regions.
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Gravitational Potential
V(r) = −GM/r — well shape with smooth transition at the surface.
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Escape Velocity
v_esc = √(2GM/R) — launch a rocket with various v₀ and see if it escapes.
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Orbital Velocity
v_orb = √(GM/r) — satellite at altitude h with period and g(h).
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Kepler's Laws
Elliptical orbit with Sun at focus — equal-area sweep demonstrated live.
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Orbital Motion & Satellites
Launch satellites into orbit, adjust velocities, and observe Kepler's laws in action with stunning visuals.
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Newton's Law of Gravitation: Every mass attracts every other mass with force F = Gm₁m₂/r².
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The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².
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Orbital velocity of a satellite: v₀ = √(GM/r) = √(gR²/r), where r is the orbital radius.
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Escape velocity from Earth's surface: vₑ = √(2gR) ≈ 11.2 km/s. It is √2 times the orbital velocity at surface.
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Kepler's Third Law: T² ∝ r³ — the square of the period is proportional to the cube of the orbital radius.
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Geostationary orbit: T = 24 hours, r ≈ 42,164 km from Earth's center, above the equator.
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Total energy of an orbiting satellite: E = −GMm/(2r) — it is negative (bound state).
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At the surface: g = GM/R². As you go up: g decreases as GM/(R+h)². Inside Earth: g decreases linearly.
Gravitational Force
Attractive force between two masses.
Orbital Velocity
Speed needed for circular orbit at radius r.
Escape Velocity
Minimum speed to escape gravitational pull.
Kepler's Third Law
Period-radius relation for orbits.
Gravitational PE
Potential energy (zero at infinity).
Total Orbital Energy
Total energy of satellite in orbit.
Escape velocity is independent of the mass of the escaping object and the direction of projection.
If a satellite's speed is increased beyond orbital velocity but below escape velocity, it enters an elliptical orbit.
At exactly escape velocity, the orbit becomes parabolic. Above it, hyperbolic.
Inside a uniform spherical shell, gravitational field is zero — Shell Theorem.
Weightlessness in orbit is not absence of gravity — it's free fall. Gravity provides centripetal force.
For JEE: relate v_orbital, v_escape, and energy — they're deeply interconnected.
Gravitational Superposition
Three masses; drag a probe and see net F as the vector sum from each.
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Net gravitational force on a body is the vector sum of forces from each other mass.
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Always attractive — each force points from the test mass toward each source.
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For continuous distributions, sum becomes an integral.
Superposition
Vector sum.
At symmetric points (e.g. center of equilateral triangle of equal masses), forces cancel.
Inside a uniform spherical shell, F = 0 (shell theorem).
Gravitational Field Lines
g points always toward masses — single mass and binary system fields.
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Field lines point in the direction of the gravitational field g — always toward masses (always attractive).
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Density of lines is proportional to |g|. Lines start at infinity and end on masses.
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Lines never cross — at each point g has a unique direction.
Point mass field
Negative sign = attractive.
Unlike electric fields, gravitational fields have no sources of repulsion (no negative mass).
For two equal masses, midpoint field is zero — saddle point.
Geostationary Satellite
Tune altitude until T = 24h — satellite locks above the same point on Earth.
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A satellite in circular equatorial orbit with period T = 24 h appears stationary above one point on Earth.
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Required altitude ≈ 35,786 km above Earth's surface (radius from center ≈ 42,164 km).
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Used for telecommunications, weather imaging, broadcast TV.
Orbit radius
From T = 2π√(r³/GM).
Orbital speed
≈ 3.07 km/s for geostationary.
Must be in equatorial plane; otherwise it traces a figure-8 (geosynchronous but not stationary).
Three geostationary satellites cover almost the entire planet (excluding polar regions).
Gravitation on sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs). Free physics revision for Class 11, JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT Subject Physics, and CUET-UG.