Objects which are subject to a centripetal force undergo uniform circular motion. A centripetal force constantly accelerates the object in the direction perpendicular to the velocity of the object. This causes the object to move in a circle. If a mass attached to a string is twirled in a circle, the centripetal force is the tension in the string. For a car turning in a circle, the centripetal force is the frictional force between the road and the tyres. For a satellite, the centripetal force is the gravitational pull of the planet. Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth tangential to the circle towards the centre of the circle

Solve problems and analyse information to calculate centripetal force acting on a satellite undergoing uniform circular motion about the Earth using F= mv 2 /r A geostationary satellite has a mass of 200 kg and orbits at an altitude of km. Calculate the centripetal force on the satellite. Data: Radius of Earth = 6.38 x 10 6 m For one revolution of the Earth,  t=24hrs=86400s  x10 -5 rads/sec v=(  x10 -5 )x(6.38 x x 10 7 )= m/s F=200( ) 2 /(6.38 x x 10 7 )= 44 N

Other Advantages of low-Earth orbit satellites: 1. Remote sensing of the Earth’s weather, oceans, pollution, ozone etc. need low orbits to increase resolution and sensitivity. 2.Spy satellites often need to get as close as possible. 3.Geopositioning needs high accuracy and hence low satellite orbit to reduce errors. 4.It costs more to place objects at high altitudes. Compare qualitatively low Earth and geo-stationary orbits

Kepler’s 3rd Law (Law of periods) Define the term ‘orbital velocity’ and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of orbit using Kepler’s Law of Periods Orbital velocity is the instantaneous linear velocity of an object in circular motion. It is tangential to the circular motion and can be calculated as the circumference divided by the period. and then subst. to give So, around a central body, mass M, the orbital velocity decreases as radius increases

Solve problems and analyse information using: r 3 /T 2 = GM/4  2 A planet in another solar system has three moons, all of which travel in circular orbits. Some information about these moons is given in the table. MoonRadius of orbit (orbs)Period of revolution (reps) Alpha Beta Gamma2.5 The radius of orbit and period of revolution are measured in orbs and reps respectively, which are not metric units. (a) Use the data to show that Kepler’s third law is obeyed for the moons Alpha and Beta. (b) Calculate the speed of moon Gamma in orbs/rep. We can then find the orbital speed = v=  r=2  r/T =2  x 2.5/7.9 = 2.0 orbs/rep

There may be unpredicted drag due to solar winds producing unexpected heating and expansion of the atmosphere Account for the orbital decay of satellites in low Earth orbit