Theme D · Fields · SL 5h + HL extension 7h

D.1 Gravitational Fields

How does an understanding of gravitational fields allow humans to explore the solar system?

Newton's universal law of gravitation, F = GMm/r², applies to every pair of masses in the universe. The concept of a gravitational field replaces the idea of action at a distance: every mass creates a field in the surrounding space, and any other mass placed in that field experiences a force. Field strength g at a point is defined as force per unit mass, and this single quantity links the acceleration due to gravity near Earth's surface to the orbital motion of satellites.

Kepler's three laws summarise what Tycho Brahe's data showed before Newton could explain why: planets move in ellipses with the Sun at one focus, sweep equal areas in equal times, and have periods proportional to the three-halves power of their orbital radius. Newton derived all three from his law of gravitation, one of the great unifications in the history of science.

The Moon orbits Earth with a period of 27.3 days at a mean orbital radius of 3.84 × 10⁸ m. Use this to calculate the mass of the Earth. Compare your answer to the accepted value of 5.97 × 10²⁴ kg.

Key equations

Newton's law: F = GMm/r²

Field strength: g = F/m = GM/r²

Kepler's third law: T² ∝ r³; specifically T² = (4π²/GM) r³

HL Gravitational PE: E_p = −GMm/r (zero at infinity)

HL Gravitational potential: V_g = −GM/r

HL Escape speed: v_esc = √(2GM/r)

HL Orbital speed: v_orb = √(GM/r)

What students must understand

Kepler's three laws of orbital motion
Newton's universal law of gravitation F = GMm/r²; treatment as point masses
Gravitational field strength g = F/m = GM/r²; gravitational field lines
HL Gravitational PE E_p = −GMm/r (defined as zero at infinity; always negative)
HL Gravitational potential V_g = −GM/r; g as potential gradient: g = −ΔV_g/Δr
HL Equipotential surfaces and their relationship to field lines
HL Escape speed v_esc = √(2GM/r); orbital speed v_orb = √(GM/r)
HL Effect of viscous drag on orbital height and speed

Linking questions

What measurements of a binary star determine the nature of its stars? → E.5 Fusion and Stars
How does circular motion relate to real orbits? → A.2 Forces and Momentum
How can electron orbits be modelled on planetary motion, and where does the model fail? → E.1 Structure of the Atom (NOS)