Planetary and Satellite Motion 12.2. Man-made Satellites To successfully launch a satellite, physicists must be very precise in terms of speed, direction,

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Presentation transcript:

Planetary and Satellite Motion 12.2

Man-made Satellites To successfully launch a satellite, physicists must be very precise in terms of speed, direction, and force.

What is an orbit? An orbit is a controlled freefall that provides an illusion of weightlessness due to relative motion Newton was the first to figure this out

Newton’s Mountain His idea: Put a cannon on the top of a very high mountain. Shoot a cannon ball horizontally. There are two options: A) The cannon ball falls to the ground B) The cannon ball goes far enough to actually start travelling around the Earth.

Newton’s Mountain Objects at rest fall 4.9 m in the first second under the influence of gravity (on Earth). If they travel at 8km/s horizontally, they will fall 4.9 m, matching the curvature of the Earth which also “falls” 4.9m every 8km.

Where does this math come from? Think back to grade 11 physics (kinematics) d = 0 + ½ (-9.81m/s 2 )(1 s) 2 d = -4.9m

Only one problem… Air resistance! This can be overcome by being on a truly high mountain (where the air is so thin that air resistance is negligible).

So how do we launch satellites into orbit? We need to perform calculations to decide how fast we need the object to travel We need to take into account weather (which affects our air resistance) We need to take into account how close to Earth the satellite will be orbiting. It isn’t launched horizontally Dy7p4

Geostationary Orbit Satellites in geostationary orbit stay the same distance from Earth and so travel in a circular orbit They appear to hover over one spot on Earth’s surface so that we can receive signals from them constantly This occurs because they are orbiting once around the Earth every 24 hours (just like one day on Earth) T = 24 hours Examples: GPS, cellular phone, TV satellites

Example 1 What altitude is required for geostationary orbit? What do we already know? T = 24 hours Mass of Earth = 5.98 x kg Radius of Earth = 6.38 x 10 6 m What are we looking for? Altitude = radius from earth’s centre to satellite subtract the earth’s radius

What is the force holding the satellite in orbit? Fc = Fg km above Earth’s surface

Example 2 What velocity must a satellite be travelling at to stay in orbit? 3070 m/s

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