1. Orbital Velocity
and
Escape Velocity

2. Orbital Velocity
Orbital Velocity is the tangential speed a satellite needs to stay in orbit. It depends on the Mass of the Planet or Star (M) And the radius of the orbit (R) It is: (copy formula)

3. Another way to look at orbiting
In one second near Earth an object will fall 5 meters The Earth curves 5 meters “down” about every 8000 meters you go horizontally. Thus if a satellite is going 8 km/sec it will fall 5 meters but not get closer to Earth! So Near Earth orbital velocity is about 8000m/sec. (or 8 km/sec)

4. At exactly orbital velocity the shape of the orbit is a circle.
The Shape of an Orbit
At exactly orbital velocity the shape of the orbit is a circle.
Any faster it becomes an ellipse,
Fast enough and it leaves orbit on an hyperbola.
The velocity at which this happens is called….
Escape Velocity

5. Energy and Orbits
There are two types of Energy involved with orbits: Kinetic Energy, Energy an object has because it is moving It is: (copy formula) Gravitational Potential Energy(GPE) is energy an object has because of where it is in a gravitational field.

6. Conservation of Energy in Orbits
Energy cannot be created or destroyed it can only change its type or be transferred to another object.
The sum of the GPE and KE of an object in orbit must remain the same.
In a circular orbit neither GPE nor KE change
In Elliptical Orbit:
Far away it has more GPE.
As it get closer GPE turns into KE and it goes faster.
It is therefore going fastest when it is closest and slowest when its farthest. (Kepler’s 2nd Law)

7. Escape Velocity
The faster an object goes the more “stretched” its elliptical orbit becomes… If it is going fast enough it will escape the planet/star’s gravity And continue to move away from the planet, star on an hyperbola … Forever. It is the Escape Velocity of the Planet/star etc. (copy formula)