Gravitational fields

WPH15Topic 5.63 questions

Gravitational field strength and potential, Newton's law of gravitation, and orbital motion.

Specification points

Understand that a gravitational field (force field) is defined as a region where a mass experiences a force
Understand that gravitational field strength is defined as $g = \frac{F}{m}$ and be able to use this equation

Be able to use the equation $F = \frac{Gm_1m_2}{r^2}$ (Newton's law of universal gravitation)

Be able to derive and use the equation $g = \frac{Gm}{r^2}$ for the gravitational field due to a point mass

Be able to use the equation $V_{grav} = -\frac{Gm}{r}$ for a radial gravitational field

Be able to compare electric fields with gravitational fields

Be able to apply Newton's laws of motion and universal gravitation to orbital motion

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Original practice questions written in the style of the exam.

Question 13 marks
Compare the gravitational field of a point mass with the electric field of a point charge. Give one similarity and two differences.
Mark scheme
- Similarity: both are radial fields obeying an inverse-square law ( $g \propto 1/r^2$ , $E \propto 1/r^2$ ) (1)
- Difference: gravitational forces are always attractive, whereas electric forces can be attractive or repulsive (1)
- Difference: gravity acts on mass and electric fields act on charge, or the gravitational force is far weaker for comparable particles (1)
Question 24 marks
A geostationary satellite orbits the Earth with a period of $24\,\text{hours}$ . The mass of the Earth is $5.97 \times 10^{24}\,\text{kg}$ .

Show that the radius of a geostationary orbit is about $4 \times 10^{7}\,\text{m}$ .

4 \times 1 0^{7} m

Mark scheme

Gravitational force provides centripetal force: $\dfrac{GMm}{r^2} = m\omega^2 r$ (1)
$\omega = 2\pi/T$ with $T = 86\,400\,\text{s}$ , giving $r^3 = \dfrac{GMT^2}{4\pi^2}$ (1)
$r^3 = \dfrac{6.67 \times 10^{-11} \times 5.97 \times 10^{24} \times 86\,400^2}{4\pi^2} = 7.5 \times 10^{22}\,\text{m}^3$ (1)
$r = 4.2 \times 10^{7}\,\text{m}$ (1)

3

=

4π2GMT2

6.67×10−11×5.97×1024×864002

=

7.5×

1022m3