Orbital Motion & Satellites
Launch satellites into orbit, adjust velocities, and observe Kepler's laws in action with stunning visuals.
Key Notes
Newton's Law of Gravitation: Every mass attracts every other mass with force F = Gm₁m₂/r².
The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².
Orbital velocity of a satellite: v₀ = √(GM/r) = √(gR²/r), where r is the orbital radius.
Escape velocity from Earth's surface: vₑ = √(2gR) ≈ 11.2 km/s. It is √2 times the orbital velocity at surface.
Kepler's Third Law: T² ∝ r³ — the square of the period is proportional to the cube of the orbital radius.
Geostationary orbit: T = 24 hours, r ≈ 42,164 km from Earth's center, above the equator.
Total energy of an orbiting satellite: E = −GMm/(2r) — it is negative (bound state).
At the surface: g = GM/R². As you go up: g decreases as GM/(R+h)². Inside Earth: g decreases linearly.
Formulas
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.
Important Points
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.
Orbital Motion & Satellites notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.