Chapter 18 - Gravitational fields

• Gravitational field strength is the gravitational force exerted per unit mass on a small object placed at a point within the field
• One astronomical unit is the mean distance between the earth and the sun
• Gravitational potential is the work done per unit mass to bring an object from infinity to a point in a gravitational field
• Gravitational potential energy is the capacity for doing work due to an objects position in a gravitational field
• A gravitational field is a field created around any object with mass extending all the way to infinity but diminishing as the distance from the centre of the object increases
• A uniform gravitational field is a gravitational field in which the lines are parallel, and the value of g remains constant
• Newtons law of gravitation states that the force between two-point masses is directly proportional to the product of the masses and inversely proportional to the square of the separation between them
• Eccentricity is the measure of the elongation of an ellipse
• Aphelion is the furthest point from the sun in orbit
• Perihelion is the closes part to the sun in orbit
• All objects with mass create a gravitational field around them which gets weaker as the distance from the centre of mass of the objects increases, becoming negligible at long distances
• Kepler's First Law: The orbit of a planet is an ellipse with the sun as one of the two foci
• Kepler's Second Law: A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time

  
• When a planet is at the point closest to the sun in its obit it moves at its greatest speed
• When a planet is at the point furthest from the sun in its orbit it moves at its slowest speed
• Comets have highly elliptical orbits
• Kepler's Third Law: the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun
• Most planets have near circular orbits, circular motion calculations can be used to relate orbital period to its distance from the sun. The centripetal force on a planet is equal to the gravitational force on a planet
• The only force acting on a satellite orbiting the earth is the gravitational attraction between the earth and it so it is always falling towards earth. However it is travelling so fast that it travels such a great distance that as it falls the earth curves away beneath it keeping it at a constant height above the earth
• Satellites must be exactly the right height and speed for a stable height. These are given by:$v^2=$$\frac{GM}{r}$ where m is the mass of the planet it orbits
• A satellite in polar orbit circles the poles offering a complete view of earth over a given period of time. As the satellite orbits the earth rotates beneath the path of the satellite, ensuring it covers all parts of the globe after a number of orbits. Uses: Mapping and reconnaissance
• A satellite in low earth orbit is in orbit close to the earth and has an orbit period of less than 2 hours. Uses: GPS
• A satellite in geostationary orbit is placed at a specific height above the earth so that it has an orbital period of 24 hours so that it remains in the same point of the earth while the earth rotates. The satellite must be in orbit above the earths equator and rotate in the same direction as the earths rotation
• All masses attract each other therefore energy is required to move the objects apart which makes gravitational potential a maximum at zero
• gravitational potential in a radial field depends on the distance from the point mass producing the gravitational field to that point and the mass of the point mass
• In a gravitational field, moving towards the point mass creating the gravitational field decreases the gravitational potential (gets more negative) and moving closer towards infinity increases the gravitational potential (approaches zero)
• Gravitational energy is defined as the work done to move the mass from infinity to a point in a gravitational field

  $E=$$mV_G$
• In a uniform gravitational field, to change the GPE of an object, its height in a gravitational field must be changed
• In order to escape the gravitational field of a mass such as a planet an object must be supplied with energy equal to the gain in gravitational potential energy needed to lift it out of the field. Therefore the loss in kinetic energy must be equal to the gain in gravitational potential energy