9702 · 13.3
Gravitational field of a point mass flashcards
Revision flashcards for Cambridge 9702 Gravitational field of a point mass (syllabus 13.3). Flip, recall, then mark a real past-paper question.
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What is a gravitational field?
A region surrounding a mass where other objects with mass experience an attractive force.
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How do we model a uniform spherical mass for external gravitational calculations?
As a point mass concentrated at its centre.
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State Newton's Law of Gravitation (mathematical form).
$F = G \frac{m_1 m_2}{r^2}$
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What does the universal gravitational constant, $G$, represent?
The fundamental constant that determines the strength of the gravitational force between masses, approximately $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$.
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How are gravitational field lines typically drawn for a point mass?
They are radial lines, always pointing inwards towards the mass, with their density indicating field strength.
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Define gravitational field strength ($g$).
The gravitational force per unit mass experienced by a small test mass, also equal to the acceleration of free fall.
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What is the formula for gravitational field strength at distance $r$ from a point mass $M$?
$g = \frac{GM}{r^2}$
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Define gravitational potential ($\phi$).
The work done per unit mass to move a test mass from infinity to a specific point within the field.
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Why is gravitational potential always negative?
By convention, potential at infinity is zero. Work is done *by* the field as a mass moves from infinity towards the source, meaning energy is released, resulting in a negative potential.
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What is the formula for gravitational potential energy ($E_p$) of two masses $M$ and $m$ at separation $r$?
$E_p = -\frac{GMm}{r}$
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How much energy is needed to completely remove an object from a gravitational field?
An amount equal to the negative of its initial gravitational potential energy (to bring it to zero potential at infinity).
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What is the relationship between gravitational field strength `g` and gravitational potential `φ`?
`g` is the negative of the potential gradient: `g = -Δφ / Δr`. It means the field strength points in the direction of the steepest decrease in potential.
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How does gravitational field strength `g` vary with distance `r` from a point mass?
`g` is inversely proportional to the square of the distance: `g ∝ 1/r^2`.
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How does gravitational potential `φ` vary with distance `r` from a point mass?
`φ` is inversely proportional to the distance: `φ ∝ -1/r`.