HSC Physics

Module 5: Advanced Mechanics5.1 Projectile Motion

5.2 Circular Motion

5.3 Motion in Gravitational Fields2 Topics

Module 6: Electromagnetism6.1 Charged Particles, Conductors and Electric and Magnetic Fields

6.2 The Motor Effect1 Topic

6.3 Electromagnetic Induction

6.4 Applications of the Motor Effect1 Topic

Module 7: The Nature of Light7.1 Electromagnetic Spectrum3 Topics

7.2 Light: Wave Model

7.3 Light: Quantum Model2 Topics

7.4 Light and Special Relativity

Module 8: From the Universe to the Atom8.1 Origins of the Elements5 Topics

8.2 Structure of the Atom3 Topics

8.3 Quantum Mechanical Nature of the Atom2 Topics

8.4 Properties of the Nucleus2 Topics

8.5 Deep Inside the Atom4 Topics
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Overview of Formulae
Potential Energy  Kinetic Energy  Total Energy 

[katex]U=\frac{GMm}{r}[/katex]  [katex]K=\frac{GMm}{2r}[/katex]  [katex]E=\frac{GMm}{2r}[/katex] 
Potential Energy
Gravitational potential energy is always less than zero, unless a body is an infinite distance away from other bodies or gravitational fields.
Kinetic Energy
The formula for orbital kinetic energy may be derived by substituting the equation for orbital velocity into the standard equation for kinetic energy.
Total Energy
The total energy of an orbiting object, like any other object, is the sum of its potential and kinetic energies. Creating a formula specific to orbital energy involves simply adding the specific formulae for orbital potential and kinetic energies.
E=U+K=\frac{GMm}{r} + \frac{GMm}{2r}=\frac{GMm}{2r}
Energy Changes due to Changing Orbits
When an object is moved to another position within a gravitational field, energy is converted between gravitational potential and kinetic energy. An object moving to a lower orbit will see a decrease in gravitational potential energy and thus an increase in kinetic energy, for example.
The magnitude of change of potential/kinetic energy will be equal to the work done to alter the orbit.
It is easiest to calculate a change in energy based off the change in potential energy as this change is determined by the difference in orbital radius. Calculate the energy change by subtracting the initial potential energy from the final potential energy, as seen below.
\Delta E_\text p= GMm\Big [\frac{1}{R_\text i  R_\text f}\Big ]