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Out into space 3

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  • 1. IN THIS LESSON YOU WILL LEARN WHAT IS GOING ON HERE…
  • 2. AND HERE…
  • 3. “THERE IS NO GRAVITY” • Cannot be the answer. • Gravity is everywhere in the universe. • You need very large objects to notice it, for example planets. • But it is inescapable….. So what is going on?
  • 4. ORBITAL MOTION Out into Space Lesson 5
  • 5. LI.. • Understand that objects stay in orbit because of the pull of gravity and the speed they are moving. • Describe orbits • Solve problems about orbits using Newton’s Gravitational and Kepler’s Laws
  • 6. Here is my thought experiment. Imagine a big cannon on a tall mountain…. The cannon ball would travel very far in a curved path
  • 7. An even bigger cannon and mountain and the ball would travel even further….
  • 8. Always falling under the effect of gravity
  • 9. …but the Earth is curved. So the cannon ball actually goes even further
  • 10. What about a massive cannon on a massive mountain?
  • 11. What if the cannon and mountain were even bigger? The cannon was above the Earths atmosphere? What might happen?
  • 12. The cannon ball orbits the Earth! Continually falling under the effect of the gravity field. Never hitting the ground because of it’s speed and the curvature of the Earth. Never slowing down because there is no air resistance.
  • 13. Things in orbit are there because gravity is pulling them How clever towards the am I? Earth but they are travelling too fast to hit it. Isaac Newton
  • 14. http://galileo.phys.virginia.edu/classes/109N/m ore_stuff/Applets/newt/newtmtn.html
  • 15. ROCKETS RATHER THAN MOUNTAINS • We put space craft and satellites in orbit around the Earth using rockets rather than impossibly high mountains. • Once the rockets has carried the spacecraft above the atmosphere booster rockets speed it up to it’s orbit speed.
  • 16. WHAT IS THIS IDEA TO LAUNCH SATELLITES? • In the 1950’s the USA had the X-Plane project it flew planes to the edge of Earth’s atmosphere. • Virgin Galactic launch small spacecraft from the back of aeroplanes.
  • 17. SO WHY DO THINGS FLOAT AROUND INSIDE SPACECRAFT IN ORBIT? • Orbit is freefall • The spacecraft and everything in it are falling under gravity (around the Earth) • Everything falls with same acceleration. • Staying the same distance apart (floating)
  • 18. DEMONSTRATE YOUR LEARNING • Explain using ideas about gravity and orbits what is happening in this video clip. • It was taken by the camera on an astronaut working on the International Space Station.
  • 19. KEPLER’S LAWS 1. The orbit of every planet is an ellipse with the Sun at one of the two foci. 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Ellipses are hard. We will treat orbits as circular motion.
  • 20. FIRST AND SECOND LAWS NOT THAT RELEVANT FOR CIRCULAR ORBITS • Circular orbits are types of ellipses (both foci at the same point) • The speed doesn’t change in a circular orbit.
  • 21. LET’S DERIVE THE THIRD LAW • What is the only force acting on a planet orbiting the Sun? • What is the expression for centripetal force? mv2/r • And if the planet is moving at constant speed in a circle it must have centripetal force acting on it. • For the gravitational force? Gm1m2/r2 • Equating these expressions, we have GMm/r2= mv2/r
  • 22. KEPLER’S THIRD LAW Circle Circumference C = 2πr Period, T • speed v can be calculated as distance travelled in one orbit (2πr) divided by the time taken, T: v =2πr/T • Plugging this into the previous equation, and cancelling the m terms on both sides gives us: GM/r2 = 4π2r/T2 • Rearranging again gives: T2 = (4π2/GM) r3 3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
  • 23. GEOSYNCHRONOUS ORBITS • We know from Kepler’s third law that the further away a satellite is from the body it is orbiting, the longer its orbital period. • If an orbiting satellite had a period of 24 hours, and you saw it overhead at, say 10.00 am, when would you next see it overhead? (Because both the Earth would have completed one rotation in the same time it took the satellite to complete one orbit, it would next be overhead at 10.00 am the next day. Such a satellite is said to be geosynchronous.)
  • 24. GEOSTATIONARY ORBITS • A difficult question – if you wanted the satellite to remain directly overhead at all times (not just once per day) where on the Earth would you have to be? • The only points on the Earth’s surface that orbit around the centre of the Earth are those on the equator. Thus, you would have to be on the equator. • If a satellite has a period of 24 hours and orbits above the equator such that it always appears to be above one point on the equator, it is known as a geostationary satellite, and its orbit is a geostationary orbit.
  • 25. GEOSTATIONARY ORBITS • Geostationary satellites are predominantly used for communications. Satellite TV companies use geostationary satellites to cover a constant area on the Earth’s surface – hence you point your satellite dish receiver in the direction of the geostationary satellite. • 3 geostationary satellites placed into orbit 120 degrees apart above the equator would be able to cover the entire Earth (except for very near the poles). • Because geostationary satellites have to be launched so high (other satellites orbit as low as a few hundred km), the energy and costs required for launching a satellite into geostationary orbit are high.