Satellites

What keeps them in orbit?

Satellites

A satellite is any projectile given a large enough velocity so its path follows the curvature of the earth.

How fast is the earth moving?

The earth moves 8000 m in the “X” direction and 4.9 m in the “Y” direction every second.

Therefore, if a projectile moves equal or greater than that speed it will follow the curvature of the earth (it will never collide with earth)

What makes a satellite go?

All objects in circular motion must have a force.

The centripetal force (inward force) acting on a satellite is gravity.

Gravity pulls any satellite towards the center of the earth.

Gravity must equal centripetal force in order for satellites to orbit

What happens if its less? greater?

Facts about satellites

As the distance from earth increase: Radius increase Force of gravity decreases Acceleration decreases

Result = required velocity is less

Satellite problem constants

Radius of the earth = 6.38 x 106 m Mass of the earth = 5.97 x 1024 kg

Remember…the radius of a satellite is the height above the surface of the earth plus the radius of the earth.

Satellite Practice Problems #1

Find the altitude of a satellite orbiting earth if it is moving at 6,900 m/s and the pull of gravity is 5.69 m/s2

Answer: a = v2

r Solve for “r”

Satellite Practice Problems #1

R = (6,900 m/s)2

5.69 m/s2

R = 8.4 x 106 m - 6.38 x 106 m R = 2.02 x 106 m

Satellite Practice Problems #2

Find the velocity needed to keep a satellite orbiting if it is accelerating at a rate of 8.2 m/s2 and it is 500 km above the surface of the earth.

Answer: a = v2

r v2 = a x r …v = (sqrt)8.2 x 6370000.5m v = 7227.3 m/s