CONCEPTUAL PHYSICSSatellite Motion

Earth SatellitesAn earth satellite is a projectile that falls

around Earth rather than into it.It has to have a tangential velocity fast enough

to make its curved path match the curvature of the Earth.

Earth’s curvature drops a vertical distance of 4.9m every 8000m.

If you throw a projectile at a horizontal velocity of 8km/s(29000 km/h), then it would follow the curvature of the Earth.

Orbital speed for close orbit to Earth is 8km/s. But, at this atmospheric friction would burn it. Thus, satellite must stay at about 150km above Earth’s surface.

Circular Orbits In circular orbit, the speed of a satellite is not

changed by gravity. For a satellite close to Earth, the time for a

complete orbit about Earth, called the period, is about 90 minutes. For higher altitudes it is longer.

Elliptical OrbitsIf a projectile is given a horizontal speed greater

than 8km/s, it will overshoot a circular path and trace an oval shaped path called an ellipse.

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A satellite’s speed varies in an elliptical orbit. As it moves away from Earth it looses speed until it reaches a point where it no longer recedes and falls back to Earth and it regains its initial speed. (fig 12.9 p167)

Energy conservation and satellite motionIn circular orbit, the Kinetic Energy and

Potential Energy is always constant, thus the speed is constant.

In an elliptical orbit, speed and distance vary. Potential energy is greatest the farthest away (the

apogee) and least when the satellite is the closest (the perigee)

At every point, the sum of potential energy and kinetic energy is the same.

Satellites - Elliptical Orbits

Escape speed “ What goes up must come down”What vertical speed is sufficient enough to

insure that what goes up will escape and not come down?

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1) What is the escape speed for the moon if its mass=7.35x1022 kg and its radius (d)= 1.74x106 m?

2. How fast would the moon need to travel to escape the gravitational pull of the Earth, if Earth has a mass of 5.98x1024 kg and the distance from the Earth and the moon is 3.84x108 m?

CONCEPTUAL PHYSICSSatellite Motion