Why does g decrease with altitude and depth?

With altitude h (above surface): g' = GM/(R+h)² ≈ g(1−2h/R) — increases distance from centre reduces g. With depth d (below surface): only the sphere of radius (R−d) contributes to gravity → g' = g(1−d/R). At the very centre, the surrounding mass pulls equally in all directions, so g = 0.

What is a geostationary satellite?

A geostationary satellite orbits Earth at about 36,000 km above the equator with a time period of exactly 24 hours — same as Earth's rotation. It appears stationary over a fixed point on Earth. Used for weather forecasting, communication, and TV broadcasting.

State Kepler's second law and what it implies.

Kepler's Second Law (Law of Areas): The line connecting a planet to the Sun sweeps equal areas in equal time intervals. This implies that a planet moves faster when it is closer to the Sun (perihelion) and slower when farther (aphelion). It is a consequence of conservation of angular momentum.

Universal Law of Gravitation and Kepler's Laws

Gravitation • Class 11 Physics • NCERT • CBSE

Newton's Universal Law of Gravitation: F = Gm₁m₂/r². Kepler's Laws: (1) Planets orbit in ellipses with the Sun at one focus. (2) Equal areas in equal times (area velocity is constant). (3) T² ∝ r³ (square of period proportional to cube of semi-major axis).

Key Formulas

F = Gm₁m₂/r²
g = GM/R²
v_escape = √(2gR) ≈ 11.2 km/s
v_orbit = √(GM/(R+h))
T² ∝ a³ (Kepler's 3rd law)

Frequently Asked Questions

Why does g decrease with altitude and depth?: With altitude h (above surface): g' = GM/(R+h)² ≈ g(1−2h/R) — increases distance from centre reduces g. With depth d (below surface): only the sphere of radius (R−d) contributes to gravity → g' = g(1−d/R). At the very centre, the surrounding mass pulls equally in all directions, so g = 0.
What is a geostationary satellite?: A geostationary satellite orbits Earth at about 36,000 km above the equator with a time period of exactly 24 hours — same as Earth's rotation. It appears stationary over a fixed point on Earth. Used for weather forecasting, communication, and TV broadcasting.
State Kepler's second law and what it implies.: Kepler's Second Law (Law of Areas): The line connecting a planet to the Sun sweeps equal areas in equal time intervals. This implies that a planet moves faster when it is closer to the Sun (perihelion) and slower when farther (aphelion). It is a consequence of conservation of angular momentum.

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