UNIVERSAL GRAVITATIONand

SATELLITE MOTION

Chapters 12 and 14

Isaac Newton wanted to know why the moon travels in a circular path

around the Earth.

As a student of physics, Newton knew that

any object moving in a circular path is experiencing a centripetal force

– a force directed toward the axis.

He knew it had to be a centripetal force

that makes the moon travel in a circular

orbit around the Earth, as well.

But nobody knew what it actually was out there

that provides that centripetal force.

Newton realized he had already studied a force that pulls on

objects and is pointed to the center

of the Earth…

GRAVITY!

• Remember, Isaac Newton did not discover gravity.

• He discovered that gravity is universal.

• He recognized that the force that pulls an apple from a tree to the ground, is the same as the force that keeps the moon in orbit.

The Falling Moon

• So if the Earth’s gravity pulls on the moon, why doesn’t the moon fall onto the Earth?

The Falling Moon

• The same reason the rubber stopper didn’t get pulled in and hit your hand in the lab… it was moving too fast to get pulled in.

The Falling Moon

Think back to projectiles that are fired or launched horizontally.

Imagine what would happen if the projectile were fired faster... and faster…

The projectile would follow the curvature of

the Earth if it were fired fast enough.

How fast would you have to throw something to put it in orbit?

Gravity pulls the object down 5 meters in the first second… so it would have to move 8 kilometers horizontally

in order to “miss” the Earth as it falls.

That’s farther than the

distance from J.R. Tucker

High School to Short Pump Town Center!

• Anything moving 8 km/s horizontally is moving fast enough to avoid hitting the Earth as it “falls”.

• In other words, it will be in orbit. This is how satellites stay up.

• 8 kilometers per second = 17895.5 mph… or 5 miles per second!

• http://science.nasa.gov/temp/HubbleLoc.html

J-Track

• http://science.nasa.gov/Realtime/JTrack/3d/JTrack3D.html

• The higher the orbit of a satellite, the less its speed and the longer its period.

• The period of orbit is the time to complete one revolution.

Orbits

Orbits

- Satellites that orbit close to the Earth (altitude ~400 km) have a period of ~90 minutes. (ISS, Hubble, communications)

- Satellites that orbit at a higher altitude (~36,000 km) have a period of 24 hours – “geosynchronous” (GPS, spy satellites)

- The moon orbits at an altitude of nearly 400,000 km and its period is 27.3 days.

• If a projectile is given a horizontal speed that is just slightly more than it needs to attain orbit, it will overshoot the circular path and trace an elliptical orbit.

Elliptical Orbits

• Remember, a satellite that is farther away orbits more slowly than one that is closer.

• For an elliptical orbit, a satellite is farther away at some times than at others. Therefore, it does not keep a constant speed.

• The satellite moves slowest when it is farthest away (apogee), and fastest when it is closest (perigee).

Elliptical Orbits

Elliptical Orbits

Elliptical Orbits

Geography of Launches

• Where would be the easiest place to launch from, in order to achieve a horizontal speed of 8 km/s?

• Where would be the hardest place to launch from, in order to go that fast?

Remember that objects with the same rotational speed can have different linear speeds if they are different distances from the axis of rotation…

Geography of Launches