Edexcel IAL Physics revision · A2 — Mechanics & fields
Gravitational fields
Newton's inverse-square law, applied from lab bench to geostationary orbit. The algebra is short; the marks concentrate around one negative sign — gravitational potential — and one satellite: the geostationary one.
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What the syllabus demands
- —Use Newton's law of gravitation: F = GMm/r²
- —Define gravitational field strength g = F/m; use g = GM/r²
- —Define gravitational potential; use φ = −GM/r
- —Analyse circular orbits: equate gravitational and centripetal force
- —Describe geostationary orbits and derive orbital speed and period relationships
Definitions that earn marks
Clear definitions to practise — check your course mark scheme
- Newton's law of gravitation
- The gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation: F = GMm ÷ r².
- Gravitational field strength
- The gravitational force per unit mass at a point: g = F ÷ m. Units: N/kg.
- Gravitational potential (φ)
- The work done per unit mass in bringing a small test mass from infinity to the point: φ = −GM ÷ r. Negative because gravity is attractive and the potential at infinity is defined as zero.
- Geostationary orbit
- An equatorial orbit with a period of 24 hours in the direction of the Earth's rotation, so the satellite remains above the same point on the equator.
The equations
More equations to practise: the Edexcel IAL formula sheet.
Where the marks die
Common mistakes to check
- 01
Dropping the minus sign on potential. φ = −GM/r: potential is always negative, rises towards zero at infinity, and 'higher potential' means less negative. Escape questions live and die on this sign.
- 02
Using surface g for orbital altitude. g falls as 1/r² — and r is measured from the centre of the Earth, not from the surface. Adding the altitude to the radius is a required step.
- 03
Geostationary answers missing a condition. Three are needed: period 24 hours, orbit above the equator, moving in the same direction as the Earth's rotation.
- 04
Confusing field strength (vector, N/kg, −dφ/dr) with potential (scalar, J/kg). Field strength is the gradient of potential — where potential flattens, the field weakens.
One worked example, done properly
Question
Calculate the orbital speed of a satellite 400 km above Earth's surface. (M = 6.0 × 10²⁴ kg, R = 6.4 × 10⁶ m, G = 6.67 × 10⁻¹¹)
Method
- 1.r = R + h = 6.4 × 10⁶ + 4.0 × 10⁵ = 6.8 × 10⁶ m.
- 2.Gravity provides centripetal force: GMm/r² = mv²/r, so v = √(GM/r).
- 3.v = √(6.67 × 10⁻¹¹ × 6.0 × 10²⁴ ÷ 6.8 × 10⁶).
v ≈ 7.7 × 10³ m/s (7.7 km/s)