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# AST 2.2 PPT

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### Transcript

• 1. 2.2 ORBITAL MOTION AND TIDES
• 2. In order to stay on a closed orbit, an object has to be within a certain range of velocities: Too slow  Object falls back down to Earth Too fast  Object escapes Earth’s gravity 0 Orbital Motion http://hal.physast.uga.edu/~rls/1020/ch5/cannonball.swf
• 3. Orbital Velocity
• An object orbiting Earth is actually falling (being accelerated) toward Earth’s center.
• Continuously misses Earth due to its orbital velocity.
• To follow a circular orbit, the object must move at circular velocity .
G = gravitational constant; 6.67 x 10 -11 m 3 /kg•s 2 M = mass of the central body in question r = radius of the orbit (m)
• 4. Circular Velocity Example
• How fast does the moon travel in its orbit?
• Hint: Earth’s mass is 5.98 x 10 24 kg, and the radius of the moon’s orbit is 3.84 x 10 8 m.
• 5. GEOSYNCHRONOUS ORBITS
• 6. Escape Velocity
• The velocity required to escape from the surface of an astronomical body is known as the escape velocity .
G = gravitational constant; 6.67 x 10 -11 m 3 /kg•s 2 M = mass of the central body in question r = radius of the orbit (m)
• 7. Escape Velocity Example
• Find the escape velocity from Earth.
• 8. Newton’s Version of Kepler’s 3 rd Law
• The equation for circular velocity:
• The circular velocity of a planet is simply the circumference of its orbit divided by the orbital period:
• If you substitute this for V in the first equation and solve for P 2 , you will get:
• 9. NVK3L
• Powerful formula in astronomy because it allows us to calculate the masses of bodies by observing orbital motion.
• For example, you observe a moon orbiting a planet and can measure the size of its orbit, r , and its orbital period, P .
• You can now use this formula to solve for M , the total mass of the system.
• There is no other way to find the masses of objects in the universe  stars, galaxies, other planets.
G = gravitational constant; 6.67 x 10 -11 m 3 /kg•s 2 M = mass of the total system (kg) r = radius of the orbit (m)
• 10. NVK3L Example
• Planet Cooper has a radius of 6840 km. and a mass of 5.21 x 10 25 kg. What is the orbital period of a satellite orbiting just above this planet’s surface?
• 11. Tides and Tidal Forces
• Earth attracts the moon, and the moon attracts Earth.
• Tides are caused by small differences in gravitational forces.
• Oceans respond by flowing into a bulge of water on the side of Earth facing the moon.
• Also a bulge on the side of Earth facing away from the moon since the moon pulls more strongly on Earth’s center than the far side of the moon.
• 12. Tides and Tidal Forces
• You might wonder … If the moon and Earth accelerate toward each other, why don’t they smash together?
• They are orbiting around a common center of mass!
• 13. Spring Tides
• Gravity is universal, so the Sun also produces tides on Earth.
• Twice a month, at new moon and full moon, the moon and Sun produce tidal bulges that add together and produce extreme tidal changes.
• High tide  exceptionally high; Low tide  exceptionally low.
• These are called spring tides .
• “ Spring” refers to the rapid welling up of water.
• 14. Neap Tides
• At 1 st and 3 rd quarter moons, the Sun and moon pull at right angles to each other, and the Sun’s tides cancel out some of the moon’s tides.
• These less-extreme tides are called neap tides .
• “ Neap” means lacking power to advance.