Download Orbital Velocity

Orbital Velocity
and
Escape Velocity
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)
In one second near Earth an object will fall 5
meters
The Earth curves 5 meters “down”` for 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)
The Shape of an Orbit
At 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
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.
It is:
(copy formula)
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 and object in orbit
must remain the same.
In a circular orbit neither GPE nor KE change
In an 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)
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)