Applications of our understanding of ‘G’ Fields Calculate the gravitational potential at the surface of the Earth (Data on data sheet). Answer = Now state how much energy it would take to move 1 kg of a spacecraft from Earth to infinity. Answer = Conclusion: The energy needed to move 1 kg from the surface of a planet / moon to infinity is simply the magnitude of the gravitational potential on the surface. So what is the formula for the energy needed to move a spaceship of mass M 2 from the surface of a planet / moon to infinity But spacecraft are launched by giving them KE right at the beginning of their ‘flight’, so E actually tells is the amount of KE needed 1. ‘Escape velocity’ and changing a satellite’s orbit

Which means we can calculate the ‘escape velocity’ for a spacecraft just from the Mass and the radius of the planet it is ‘escaping from’ ! We can also calculate the energy needed to move launch satellites into orbit at a certain height, or to move them from one orbit to another just by calculating the change in gravitational potential, and multiplying it by the mass of the satellite. The idea of a ‘potential well’ illustrates this nicely

Satellite Motion 2. Orbits of planets, satellites and electrons around nuclei. Use the formulae for the force which is caused by the field and equate it to the centripetal force required to keep the orbiting object in orbit. EG 1. To show that Keplers 3rd Law () is correct: For orbiting body r 3  T 2 For an orbiting body: Cancel M 2 and r v = Orbital Distance/Orbital Time Make r 3 the subject This gives Orbital time for a satellite at any particular height (r)

Exercise 1. (a) Calculate the height for a geostationary satellite. (Data in data sheet) (b) Complete the diagram below to show approximately where the satellite orbits (c) Comment on the ability of far northern and far southern communities to receive satellite TV.

Exercise 2. (a) Calculate the orbital time for a satellite in polar orbit at an altitude of 2000 km above the surface of the earth. (b) How far will Earth rotate during one orbit of such a satellite ? c (c) Comment on a use for such a satellite.

Applications of our understanding of ‘G’ Fields Calculate the gravitational potential at the surface of the Earth (Data on data sheet). Answer = Now state how much energy it would take to move 1 kg of a spacecraft from Earth to infinity. Answer = Conclusion: The energy needed to move 1 kg from the surface of a planet / moon to infinity is simply the magnitude of the gravitational potential on the surface. So what is the formula for the energy needed to move a spaceship of mass M 2 from the surface of a planet / moon to infinity But spacecraft are launched by giving them KE right at the beginning of their ‘flight’, so E actually tells is the amount of KE needed 1. ‘Escape velocity’ and changing a satellite’s orbit

Which means we can calculate the ‘escape velocity’ for a spacecraft just from the Mass and the radius of the planet it is ‘escaping from’ ! We can also calculate the energy needed to move launch satellites into orbit at a certain height, or to move them from one orbit to another just by calculating the change in gravitational potential, and multiplying it by the mass of the satellite. The idea of a ‘potential well’ illustrates this nicely

Satellite Motion 2. Orbits of planets, satellites and electrons around nuclei. Use the formulae for the force which is caused by the field and equate it to the centripetal force required to keep the orbiting object in orbit. EG 1. To show that Keplers 3rd Law () is correct: For orbiting body r 3  T 2 For an orbiting body: Cancel M 2 and r v = Orbital Distance/Orbital Time Make r 3 the subject This gives Orbital time for a satellite at any particular height (r)

Exercise 1. (a) Calculate the height for a geostationary satellite. (Data in data sheet) (b) Complete the diagram below to show approximately where the satellite orbits (c) Comment on the ability of far northern and far southern communities to receive satellite TV.

Exercise 2. (a) Calculate the orbital time for a satellite in polar orbit at an altitude of 2000 km above the surface of the earth. (b) How far will Earth rotate during one orbit of such a satellite ? c (c) Comment on a use for such a satellite.

Questions Page a) b) 2. a)(i) (ii) b)

3. a) b)Yes. Change is very small compared to value of ‘g’ at surface. c) 4. a) b)

Questions Pg a) The slower satellite is higher. Low satellites have to go faster than the rate of rotation of the Earth so that gravitational attraction is not greater than the centripetal force needed to keep them in orbit. Higher satellites may be geostationary and appear stationary in the sky Even Higher satellites will appear to go backwards across the sky ! b) Geostationary satellites remain in the same position above the equator. 2. a) b) c)

3. a) Acceleration in a ‘g’ field is equal to g 3. b)