University Physics Volume 1

# Summary

## 13.1Newton's Law of Universal Gravitation

• All masses attract one another with a gravitational force proportional to their masses and inversely proportional to the square of the distance between them.
• Spherically symmetrical masses can be treated as if all their mass were located at the center.
• Nonsymmetrical objects can be treated as if their mass were concentrated at their center of mass, provided their distance from other masses is large compared to their size.

## 13.2Gravitation Near Earth's Surface

• The weight of an object is the gravitational attraction between Earth and the object.
• The gravitational field is represented as lines that indicate the direction of the gravitational force; the line spacing indicates the strength of the field.
• Apparent weight differs from actual weight due to the acceleration of the object.

## 13.3Gravitational Potential Energy and Total Energy

• The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change.
• The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion.
• Objects must have a minimum velocity, the escape velocity, to leave a planet and not return.
• Objects with total energy less than zero are bound; those with zero or greater are unbounded.

## 13.4Satellite Orbits and Energy

• Orbital velocities are determined by the mass of the body being orbited and the distance from the center of that body, and not by the mass of a much smaller orbiting object.
• The period of the orbit is likewise independent of the orbiting object’s mass.
• Bodies of comparable masses orbit about their common center of mass and their velocities and periods should be determined from Newton’s second law and law of gravitation.

## 13.5Kepler's Laws of Planetary Motion

• All orbital motion follows the path of a conic section. Bound or closed orbits are either a circle or an ellipse; unbounded or open orbits are either a parabola or a hyperbola.
• The areal velocity of any orbit is constant, a reflection of the conservation of angular momentum.
• The square of the period of an elliptical orbit is proportional to the cube of the semi-major axis of that orbit.

## 13.6Tidal Forces

• Earth’s tides are caused by the difference in gravitational forces from the Moon and the Sun on the different sides of Earth.
• Spring or neap (high) tides occur when Earth, the Moon, and the Sun are aligned, and neap or (low) tides occur when they form a right triangle.
• Tidal forces can create internal heating, changes in orbital motion, and even destruction of orbiting bodies.

## 13.7Einstein's Theory of Gravity

• According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy.
• The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances.
• Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
• Evidence for the existence of black holes is still circumstantial, but the amount of that evidence is overwhelming.