| Application and Skills |
|---|
| Describing the relationship between gravitational force and centripetal force |
| Applying Newton’s law of gravitation to the motion of an object in circular orbit around a point mass |
| Solving problems involving gravitational force, gravitational field strength, orbital speed and orbital period |
| Determining the resultant gravitational field strength due to two bodies |
| Understandings |
|---|
| Newton’s law of gravitation |
| Gravitational field strength |
$$ F = G\frac{Mm}{r^2}\\ g = \frac{F}{m}\\ g = G\frac{M}{r^2} $$
The law of gravitation makes it possible to calculate the orbits of the planets around the Sun, and predicts the motion of comets, satellites and entire galaxies.
Newton’s second law implies that whenever a particle moves with acceleration, a net force must be acting on it. A planet that orbits around the Sun also experiences acceleration and thus a force is acting on it Newton proposed that the attractive force of gravitation between two point masses is given by the formula:
$$ F = G\frac{M_1M_2}{r^2} $$
where $M_1$ and $M_2$ are the masses of the attracting bodies, r the distance between their centres of mass and G a constant called Newton’s constant of universal gravitation of value $G = 6.667 × 10^{−11} N m^{2} kg^{−2}$. The direction of the force is along the line joining the two masses.
The average distance between the Earth and the Sun is r = 1.5 × 1011 m. The mass of the Earth is $5.98 × 10^{24}$ kg and the mass of the Sun is $1.99 × 10^{30}$ kg.
Estimate the force between the Sun and the Earth.
A mass M is said to create a gravitational field in the space around it.
This means that when another mass is placed at some point near M, it ‘feels’ the gravitational field in the form of a gravitational force.
The gravitational field strength at a certain point is the gravitational force per unit mass experienced by a small point mass m placed at that point:
$$ g = \frac{F}{m} $$
The gravitational field strength is the same as the acceleration of free fall.
