Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical...

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Satellite Motion

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Transcript of Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical...

Page 1: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Satellite Motion

Page 2: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Curvature of Earth

8000 meters

8000 meters

5 meters

5 meters

The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface

Page 3: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

How fast does an object need to go to become an Earth satellite?

• How far does an object fall in 1 second?– 5m

• How far along the horizon must you go for the Earth to curve 5m down?– 8000m

8km/s for orbital speed close to Earth!

Page 4: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

• Does the force of gravity affect the speed of a bowling ball down an alley?– Nope!

• Similarly, the force of gravity of the Earth does not affect the speed of a satellite in circular orbit. – Why?– 90 degrees between force and direction of motion…No

Work!

Circular Orbit

The period for a satellite in low-Earth

orbit is about 90 minutes.

Page 5: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

At which position does the satellite have its greatest speed? Why?

A

B

C

D

Same speed Everywhere along path!

A close Earth satellite has a

period of about 90 minutes.

Page 6: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

• What if an object above the atmosphere has a horizontal speed of more than 8km/s?– Its path is that of an ellipse

instead a circle.

• Most satellites actually have elliptical paths!

• Speed varies in elliptical orbit

Kepler’s 1st Law of Planetary Motion

Johannes Kepler

Page 7: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Ellipse

• Foci- Where the main body of an orbiting pair lies

Page 8: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

At which position does the satellite have its greatest speed? Why?

A

B

C

D

Greatest Speed

Lowest Speed

Page 9: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Kepler’s 2nd Law of Planetary Motion

Faster closer to other source of gravity

Slower when far away

Equal areas swept out over same amounts of time time!

Apogee- when satellite is at farthest position

Perigee- when object is at closest position

Page 10: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Energy Conservation and Satellite Motion

The sum of potential and kinetic energies of

a satellite remains constant

Page 11: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

KE+PE

KE+PE

KE+PE

KE+PE

KE+PE

KE+PE

KE+PE

KE+PE

Page 12: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

“What goes up must come down”or does it???

Page 13: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Escape Velocity• The speed necessary to put a payload

infinitely far from Earth.

• 11.2 km/s horizontally or about 25,000 mph

vesc 2GM

r11.2km/s on Earth

Page 14: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.
Page 15: Satellite Motion. Curvature of Earth 8000 meters 5 meters The Earth’s surface drops 5 vertical meters for every 8000 meters tangent to its surface.

Bonus• List all the planets in our solar system from

lowest escape velocity to highest and explain how you did it.


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?8000/400=20 8000/400=20 12000/400= 30 8000/400= 20 20 …361 Lec 10 Thur13sep12?8000/400=20 8000/400=20 ‐12000/400= ‐30 ‐8000/400= ‐20 20 30 10 0 ‐ =‐ No Way!! 1

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