Gravitational Fields

Introduction

Gravitational fields describe how masses interact across space. The guide connects Newton’s law, field strength, field lines, circular orbits, potential, escape speed, and satellite energetics.

Guide Focus

• Use Newton’s law of gravitation and gravitational field strength.
• Apply Kepler’s laws and circular orbit relationships.
• Use HL potential, potential energy, equipotentials, escape speed, and orbital speed.

Key Concepts

1. Newtonian gravity

For point masses, F = Gm1m2 / r^2. Spherical bodies of uniform density can be treated as point masses at their centres when considering external fields.

2. Field strength and field lines

Gravitational field strength is force per unit mass: g = F / m = GM / r^2. Field lines point in the direction a small test mass would accelerate.

3. Orbits

For circular orbits, gravity provides the centripetal force. Kepler’s laws describe orbital paths, equal areas in equal times, and the relationship between orbital period and orbital radius.

4. HL gravitational potential

Potential energy for two masses is Ep = -Gm1m2 / r, and gravitational potential is Vg = -GM / r. Field strength is the negative potential gradient, g = -delta Vg / delta r, and work done is W = m delta Vg.

5. Escape and orbital speeds

The guide uses v_escape = sqrt(2GM / r) and v_orbital = sqrt(GM / r). Atmospheric drag on a satellite can reduce orbital height while increasing orbital speed.

Common Mistakes

• Forgetting gravitational potential is defined as zero at infinity and negative near a mass.
• Using surface g = 9.81 m s-2 for all orbital distances.
• Confusing escape speed with orbital speed.

Exam Tips

• In orbit questions, set gravitational force equal to centripetal force.
• For potential questions, track signs carefully: bound systems have negative total energy.
• Equipotential surfaces are always perpendicular to field lines.

Practice Questions

Question 1 (Multiple Choice)

At a distance r from a planet of mass M, the gravitational field strength is proportional to:

A. 1/r^2 B. r^2 C. 1/r D. r

Question 2 (Structured Paper 2 Style)

A satellite orbits a planet of mass 6.0 x 10^24 kg in a circular orbit of radius 7.0 x 10^6 m.

(a) Calculate the orbital speed. [2 marks]

(b) State the direction of the gravitational force. [1 mark]