Flashcards · 9630 · A Level Topic 7

Gravitational fields and satellites (A Level) flashcards

19 cards on A Level Topic 7, subtopics 3.7.1 to 3.7.4. Pick a subtopic or study them all.

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Newton's law of gravitation: Two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation: F = Gm₁m₂/r².
Value and unit of the gravitational constant G: G = 6.67 × 10⁻¹¹ N m² kg⁻² (use the value given in the question).
The distance between two masses is tripled. What happens to the gravitational force?: F ∝ 1/r², so it falls to (1/3)² = 1/9 of its original value.
In F = Gm₁m₂/r² for a satellite, what is r?: The distance between the centres of mass: planet radius + height above the surface (r = R + h).

Gravitational field strength g: The force per unit mass acting on a small mass placed at that point in the field: g = F/m. Unit N kg⁻¹ (equivalent to m s⁻²).
Field strength in a radial field: g = GM/r², where M is the mass creating the field and r the distance from its centre.
Derive g = GM/r²: Force on a small mass m: F = GMm/r². Field strength g = F/m = GM/r²; the test mass cancels.
Field lines around a planet and near its surface: Around the planet: radial, pointing inwards, spreading out as the field weakens. In a small region near the surface: parallel and equally spaced (approximately uniform).
G vs g: G is a universal constant, the same everywhere. g is a field strength that depends on the source mass and the position.

Gravitational potential V: The work done per unit mass by an external agent in moving a small mass from infinity to the point. Zero at infinity, so negative everywhere else. Unit J kg⁻¹.
Potential in a radial field, and work done moving a mass: V = −GM/r. ΔW = mΔV, where ΔV = V(final) − V(initial).
Equipotential surface (gravitational): A surface on which V is constant. The field is at right angles to it, and no work is done moving a mass along it.
Field strength from a graph of V against r: g = −ΔV/Δr: the magnitude of g is the gradient of the tangent to the V–r graph at that point.
Gravitational potential difference: The work done per unit mass in moving a mass between two points.

Orbital speed and period of a satellite in a circular orbit: GMm/r² = mv²/r gives v = √(GM/r), independent of the satellite's mass. T² = 4π²r³/(GM), so T² ∝ r³.
Kinetic, potential and total energy of an orbiting satellite: Ek = GMm/(2r) Ep = −GMm/r E = −GMm/(2r), so E = −Ek.
Geosynchronous orbit: An orbit whose period equals the planet's rotation period (23 h 56 min for the Earth).
Geostationary orbit: A geosynchronous orbit above the equator in the same direction as the planet's rotation, so the satellite stays above one point and a fixed ground antenna can point at it.
Why does a satellite speed up when drag makes it fall to a lower orbit?: Drag removes total energy, so the orbit radius falls. Potential energy falls by twice the gain in kinetic energy, so the speed increases (v = √(GM/r)).