GRAVITATIONAL FORCES

Basic principle (tested for IB before!): A field of force is a region of space in which a mass or charge experiences a force. Newton’s Law of Universal Gravitation: Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (where r is the distance between the centres of the two point masses) whereAlways attractive, only become significant when objects involved are massive (because see power of the G constant).Assumption: Point masses, masses concentrated at centre of spheres.Gravitational Field Strength (at a point): The force per unit mass exerted on the mass m placed at that point. . A vector Nkg-1, varies over Earth’s surface depending on altitude, local geology and shape of Earth (which is non-spherical)Graph of g against r, radius of uniform spherical mass:Graph of g against distance between centres of two point masses: Gravitational Potential Energy (of a mass at any point in space): The work done by an external force in moving a mass at any point in space from infinity to that point.Negative because: An object has zero Ep when no longer within gravitational field i.e. at infinity. Ep increases as it gets further and further away by getting less negative, until a maximum value of zero.Scalar quantity measured in J, independent of the path taken from infinityAt earth’s surface, an approximation, because vertical distance h moved is small.Graph of Ep against r: Gradient = Gravitational force(gradient decreases, inverse square law) Gravitational Potential (due to mass M): Work done per unit mass by an external force to bring a test mass m at any point in space, from infinity to that point. (Jkg-1)Graph of Vg against r:g = negative gradient = Gravitational field strength (acceleration) [KNOW RELATIONSHIP]Gravitational Equipotential surfaces: Points in space that have the same potential. For point mass, concentric spheres centered at the point mass, at the same distance from the charge, at right angles to the gravitational field lines. Distance between equipotential lines increases as they go further away from the object. (When objects move along equipotential surfaces, work done is zero as gravitational potential difference between the two points is zero). Escape speed: Speed of an object at the surface of a planet, which it needs to be able to move to infinity and escape the gravitational attraction of a planet (has to reach infinite distance in order to be effectively free).Assumption: Planet is isolated and there is no friction or atmosphere.Always consider Initial Energy = Final Energy where Total Energy = P.E. + K.E. Orbital motion: Gravitational force provides centripetal force for circular orbital motion,Kepler’s 3rd Law: Square of a planet’s orbital period is proportional to the cube of its mean distance from the sun.To derive:where v is the orbital speed of the planetAverage/Mean orbital radius as orbits in reality are elliptical and not circular.For an orbiting satellite:(For satellite to say within planet’s gravitational field, must have a total energy If the total energy of the satellite were reduced (becomes more negative), the PE of the satellite would be reduced and its KE increased, hence the radius of the orbit decreases and the speed of the satellite increases. The force of friction between the satellite and the atmospheric air increases as the speed of the satellite increases. Suggest why small satellites ‘burn up’ as they re-enter the Earth’s atmosphere: Friction reduces the total energy of the satellite and causes its speed to increase and its height above the planet to decrease even more. At lower heights the frictional force is even greater as the atmosphere is denser. Thus heating effect on the satellite increases as it falls and if the satellite is small enough, sufficient heating can cause its destruction. ‘Weightlessness’ of astronaut in orbiting space: Gravitational pull on both astronaut and space station/ship to provide centripetal force in order to stay in orbit, hence both in free fall. No contact force between astronaut and space station/ship hence apparent ‘weightlessness’. Explain why an object in the satellite appears to be weightless: Both the object and the satellite have the same acceleration towards the centre of the planet, thus in free fall, hence there is no reaction force between the object and the satellite and so it appears weightless.

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