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# Year 12 Physics

## Module 5 | Advanced mechanics

### Content 3: Motion in gravitational fields

#### Lesson 1 | Newton's Law of Universal Gravitation

• apply qualitatively and quantitatively Newton’s Law of Universal Gravitation to:
– determine the force of gravity between two objects ($\vec{F} = -\frac{GMm}{\vec{r}^{2}}$)
– investigate the factors that affect the gravitational field strength ($\vec{g} = \frac{GMm}{\vec{r}^{2}}$)
– predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet (ACSPH094, ACSPH095, ACSPH097)

#### Lesson 2 | Investigating the orbital motion of planets and satellites

• investigate the orbital motion of planets and artificial satellites when applying the relationships between the following quantities:
– gravitational force
– centripetal force
– centripetal acceleration
– mass
– orbital velocity
– orbital period

#### Lesson 3 | The orbital properties of planets and satellites

• predict quantitatively the orbital properties of planets and satellites in a variety of situations, including near the Earth and geostationary orbits, and relate these to their uses (ACSPH101)

#### Lesson 4 | Kepler's laws of Planetary Motion

• investigate the relationship of Kepler’s laws of Planetary Motion to the forces acting on, and the total energy of, planets in circular and non-circular orbits using: (ACSPH101)
$v_{0} = \frac{2\pi r}{T}$
$\frac{r^{3}}{T^{2}} = \frac{GM}{4\pi ^{2}}$

#### Lesson 5 | Gravitational force and gravitational potential in radial gravitational fields

• derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but not limited to:
– the concept of escape velocity ($v_{esc} = \sqrt{\frac{2GM}{r}}$)
– total potential energy of a planet or satellite in its orbit ($U = -\frac{GMm}{r}$)

#### Lesson 6 | Energy in orbits

• derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but not limited to:
– total energy of a planet or satellite in its orbit ($E = -\frac{GMm}{2r}$)
– energy changes that occur when satellites move between orbits (ACSPH096)
– Kepler’s Laws of Planetary Motion (ACSPH101)