Gravitational Fields | A-Level Physics | Doodle Science

a gravitational field is a region around one mass which affects on the nearby masses it is very weak however which is why the effect is only significant on large objects like the earth we can represent the Earth's gravitational field by drawing field lines showing the direction of the gravitational force on masses in the field in this case the field is radial and equally spread around the earth on the surface of the earth the gravitational field is approximately uniform because the field lines are virtually pointing in the same direction and are equally spaced this is why we assume the acceleration due to gravity is a constant of 9.81 m/s^2 because the change at small vertical Heights is negligible Newton's law of gravitation states that all masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between the centers of mass this gives us the equation F equals minus GMM over R squared where G is the universal gravitational constant of six point six seven times 10 to the minus 11 M is the mass of the larger body M is the mass of the smaller body and R is a distance between the centers of mass of the two bodies the minus sign simply refers to the fact that the force is attractive for example two bodies one of mass six kilograms and the other of mass 20 kilograms are placed 50 centimeters apart from this we can work out that the gravitational force acting on each object is 3.2 zero times ten to the minus eighth Newton's the force acting on each body is equal because they are attracted to each other the gravitational field strength is the force per unit mass at a point in a gravitational field for a uniform field the equation is G equals F over m where F is the force experienced by the body and M is the mass of the body for a radial field the gravitational field strength obeys an inverse-square law the equation for it is G equals GM over R squared you can see how the gravitational field strength would decrease the further you are from the center of the body producing the field this formula can be used to work out the masses of celestial bodies for example given that the gravitational field strength on the Earth's surface is 9.81 Newton's per kilogram and the radius of the earth is 6,400 kilometers we can work out the mass of the earth to be 6.02 times 10 to the 24 kilograms when considering planetary motion the gravitational force acting on the body orbiting is equal to the centripetal force because the force acts perpendicular to the direction of motion by equating the two formulas and using the formula for the speed of an object in circular motion we get the equation T squared equals four PI squared over G M R cubed where T is the orbital period in seconds and R is the distance between the centers of mass of the orbiting body and the body being orbited this equation shows Kepler's third law which states that T squared is directly proportional to R cubed this also suggests that for a set of celestial bodies eg the planets of our solar system orbiting the same large body each of the Sun t squared over R cubed is a constant and is equal for all the celestial bodies for example given that it takes 365 days for the earth to orbit the Sun and that the distance of the Earth from the center of the Sun is 1.5 times 10 to the 11 meters we can work out the mass of the Sun to be about two times 10 to the 30 kilograms given that the orbital period of Mars is 687 Earth days we can use the Earth's orbital characteristics to work out how far Mars is from the Sun as being 2.2 9 times 10 to the 11 meters a geostationary orbit is an orbit around the Earth whose orbital period is 24 hours they are located above the equator and are always vertically above the same point on the surface of the earth this makes them useful for TV satellites because the dishes can be pointed to a fixed point in the sky which is quite convenient I'd say thanks for watching make sure to hit the like button if you like the video and if you want to see some more you can subscribe

Channel: DoodleScience

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Keywords: A level, Physics, Revision, G484, OCR, AQA, Edexcel, doodlescience, gravitational, fields, force, field, strength, kepler's, third, law, newton's, gravitation, planetary, motion

Id: ViY0-lOzbg0

Length: 5min 0sec (300 seconds)

Published: Mon Feb 01 2016