Gravitational Fields (Unit 05) - Study Guide
Newton's law of universal gravitation, orbital velocities, and satellite energy distributions.
Syllabus Core Concepts
- • Newton's Law of Gravitation: Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (F = GMm/r²).
- • Escape Velocity: The minimum velocity required for an object to escape Earth\'s gravitational field (vₑ = √(2GM/R)), which is approximately 11.2 km/s for Earth.
Marking Secrets & Traps
📘 Resource Book Summary: Gravitational Fields
Core Definitions:
Newton's Law of Gravitation: Every point mass attracts every other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
Equations:
F = G * M * m / r² (G: Universal gravitational constant, M, m: masses, r: distance between centers)
Key Points:
- • Gravitational force is always attractive. It acts along the line joining the centers of mass.
⚠️ Exam Trap Notes:
Here, r is the distance between their centers of mass, not surface-to-surface. For planets, the planet\'s radius (R) must be added (r = R + h).
Core Definitions:
Gravitational Field Intensity (g): The gravitational force acting per unit mass placed at a given point in the gravitational field.
Equations:
- • g = F / m
- • At distance r from a point mass M: g = GM / r²
Key Points:
- • It is a vector quantity directed towards the center of mass.
⚠️ Exam Trap Notes:
Inside a solid sphere (like Earth), intensity is directly proportional to distance (g ∝ r). Outside, it is inversely proportional to the square of distance (g ∝ 1/r²).
Core Definitions:
Gravitational Potential (V): The work done by the gravitational force in bringing a unit mass from infinity to that point in the gravitational field.
Equations:
- • Potential: V = -GM / r
- • Gravitational Potential Energy: U = -GMm / r
Key Points:
- • Potential is a scalar quantity. It is zero at infinity.
⚠️ Exam Trap Notes:
Gravitational potential is always negative (-). Forgetting the negative sign in calculations is a common way to lose all marks.
Core Definitions:
Geostationary Satellites: Satellites that remain in a fixed position relative to an observer on the Earth's surface.
Equations:
- • Orbital speed: v = √(GM / r)
- • Time period: T = 2π√(r³ / GM)
- • Escape Velocity: v = √(2gR)
Key Points:
- • The orbital period of a geostationary satellite is 24 hours, orbiting in the equatorial plane.
⚠️ Exam Trap Notes:
The total mechanical energy of a satellite in orbit is negative (E = -GMm / 2r). If total energy becomes zero or positive, the satellite escapes orbit.
🌍 Satellite Orbit Simulator
Adjust the velocity slider and observe its live effect on the satellite's orbit.
Exam Question Check (Mini Quiz)
What is the sign of the "Total Mechanical Energy" of a satellite in a stable orbit around Earth?