D.1 Gravitational fieldsIB Physics HL: Flashcards

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State Kepler's third law.

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State Kepler's third law.: T² ∝ r³ for bodies orbiting the same central mass.
When can an extended body be treated as a point mass?: When it is spherically symmetric, or very small compared with the separation.
Define gravitational field strength.: Force per unit mass on a small test mass: g = F/m = GM/r².
Define gravitational potential energy of a system.: The work done to assemble the system from infinite separation of its components.
Ep for two bodies?: Ep = −Gm₁m₂/r.
Define gravitational potential.: The work done per unit mass in bringing a mass from infinity to the point: V = −GM/r.
Why are gravitational potentials negative?: Zero is at infinity and the force is attractive, so work must be done to move a mass back out to infinity.
How is g related to potential?: g = −ΔV/Δr, the negative potential gradient.
Work done moving mass m through a potential difference?: W = mΔV, independent of the path.
How are equipotentials and field lines related?: Field lines are perpendicular to equipotential surfaces.
Escape speed?: v_esc = √(2GM/r), independent of the escaping body's mass.
Orbital speed?: v = √(GM/r).
Total energy in a circular orbit?: E = −GMm/(2r) = −Ek = ½Ep.
What does atmospheric drag do to a satellite's height and speed?: Height decreases, speed increases; total energy decreases.