PHYSICS S5 UNIT 8: Motion in Orbits.

What Will You Learn?

• The course Unit 8: Motion in Orbits will teach you the fundamental principles of celestial mechanics, focusing on how the Gravitational Force governs the stable motion of planets, moons, and artificial satellites in space. It is a direct application of Newtonian mechanics and energy concepts.
• I. The Physics of Stable Orbits
• You will learn the core force and motion principles that define orbital paths, primarily focusing on circular orbits initially:
• • Newton's Law of Universal Gravitation: You will apply this law to understand that the gravitational force (Fg) is the sole centripetal force (Fc) required to keep an object in orbit:
• Fg = Fc → G Mm/r2 = mv2/r
• • Orbital Speed and Period: By equating the forces above, you will derive formulas to calculate the orbital speed (v) and the orbital period (T) of a body in a circular orbit, showing that these depend only on the mass of the central body (M) and the orbital radius (r).
• II. Orbital Energy and Escape Velocity
• This section uses the scalar approach of energy conservation to analyze orbital transitions and stability:
• • Gravitational Potential Energy: You will use the general definition of gravitational potential energy, defined as zero at infinity: UG = -G Mm/r.
• • Total Orbital Energy: You will learn that the Total Energy (E) of a stable orbit is the sum of its kinetic and potential energy and is always negative.
• • Escape Velocity: You will apply the Conservation of Energy principle to calculate the escape velocity—the minimum initial speed required for an object to have zero total energy (E=0) and therefore escape the gravitational pull of a central body permanently.
• III. Kepler's Laws of Planetary Motion
• You will study the three empirical laws that accurately describe all planetary and satellite motion:
• 1. Law of Orbits (Ellipses): You will understand that stable orbits are ellipses (with a circle as a special case), with the central body located at one focus.
• 2. Law of Areas: You will learn that a line segment joining a planet and the Sun sweeps out equal areas in equal times, a principle rooted in the conservation of angular momentum. This means satellites move faster when closer to the central body.
• 3. Law of Periods: You will study Kepler's Third Law, which relates the orbital period (T) to the semi-major axis (a) of the orbit: T2 α a3. You will use this to calculate orbital radii and periods for different satellites, including the conditions necessary for a geostationary orbit.