# Chapter 6 - Objectives and Summary

### for the OUP text New Century Senior Physics by Walding, Rapkins and Rossiter

LEARNING OBJECTIVES
Knowledge & Understanding

• Distinguish between the heliocentric and geocentric theories of the solar system.
• Know briefly the contributions of Aristotle, Ptolemy, Copernicus, Brahe, Kepler, Galileo, Newton, Einstein, Wheeler and Hawking.
• State Kepler's law of planetary motion.
• State Newton's law of gravitation (F = G.m1m2/d2).
• Distinguish between g and ‘big G’.
• Apply Newton's law of gravitation and principles of circular motion to satellites and other planetary bodies.
• Describe the motion and uses of satellites orbiting the Earth.
• Explain the terms: apogee, perigee, aphelion, perihelion, ellipse, eccentricity, focus, escape velocity.
• Calculate the period of motion of a satellite and determine its centripetal acceleration, centripetal force and critical velocity.
• Explain what a gravitational field is. Indicate the shape of the gravitational field of the Earth.
• Describe what a black hole is and define the terms: quasar, pulsar, Schwartzchild radius, event horizon.
• Explain briefly two models for the future of the universe.
• Distinguish between astronomy, astrology and cosmology.

Scientific Techniques

• Graph gravitational field strength against displacement for a simple gravitational system.
• Read and interpret an article on weightlessness in space.
• Analyse the results of Cavendish’s experiment on the value of G.
• Verify Kepler’s Law by plotting and interpreting data about the four Galilean moons of Jupiter.
• Use secondary data to find the meaning of terms, historical backgrounds and the progress of various satellite missions. Write reports on findings.

Complex Reasoning Processes

• Solve challenging problems related to satellite and planetary motion.
• Combine centripetal motion formulas with gravitational field strength formulas to solve complex problems.
• Examine critically the authority on which astronomical models have been based.
• Locate logical fallacies in astronomy vs. astrology arguments.

### CHAPTER 6 SUMMARY

• The heliocentric view of the heavens is based on the work of Copernicus, Kepler, Galileo, Brahe and Newton. Ptolemy and Aristotle favoured a geocentric view. Modern theories also rely on Einstein.
• Kepler proposed three laws:
(1) Planetary orbits are eccentric with the Sun at one focus;
(2) The speed of a planet along this path is not uniform, but varies with its distance from the Sun in such a way that a line drawn from the planet to the Sun would sweep out equal areas in equal times;
(3) For orbiting satellites or planets of any system, the ratio: radius of orbit cubed (r³) to period squared (T²) is constant for all satellites of that system: r³/T² = constant
• Newton's Law of gravity: The force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them: Fg = G m1 m2/d², where G is called the universal gravitational constant.
• For elliptical motion the point closest to the Sun is called the perihelion and the opposite point farthest from the Sun is called the aphelion. When referring to an elliptical orbit in general, these points are called the perigee and apogee respectively. The eccentricity is a measure of the out-of-roundness of the ellipse.
• Objects travelling along in circular orbits at constant speed have an acceleration directed towards the centre of the circular path. Such an acceleration is called centripetal acceleration: ac = v²/r
• Because of centripetal acceleration, an object of mass m experiences a centripetal force Fc also directed towards the centre of the circular path: Fc = m ac = m v²/r
• For an object travelling at uniform speed v in a circle of radius r, the distance travelled during one full circuit s = 2 p r. The time taken to complete one full circuit (the period, T), is: T = s/v = 2 p r /T
• ac = 4π2r/T² and Fc = 4p2r m/T²
• A satellite is a small body held in orbit around a larger body by gravitational attraction. They can be natural or artificial.
• The minimum speed for a satellite to keep a circular path is called it's critical velocity: vcrit = (gr)½
• The minimum speed needed to escape gravitational attraction is called escape velocity: vesc = (2Gm/r)½
• The weight of a body is a measure of the net force acting on it due to a nearby astronomical object such as a planet. The force causing the weight is mostly gravity, but it is affected by whether the planet is rotating (Fw = Fg - Fc) or non-rotating (Fw = mg).
• A gravitational field is a region of space where an object experiences a force due to its mass. The gravitational field strength is given by: g = G me/d2
• Black holes are regions of space with huge mass and intense gravitational fields.