Download The Physics of Orbits

Kepler’s laws
And
Orbital Velocity
Kepler’s Laws
Kepler’s improved Copernican model had orbits that
obey three laws:
1. The Planets orbit in ellipses with the sun at one
focus.
2. The speed of the planet varies so that a line
joining the sun and Planet will sweep out an equal
area in an equal time.
That is when closer faster and farther slower.
Kepler’s 3rd Law of Planetary
Motion
The period of revolution is related to the length of
the semimajor axis by:
T² = a³
T = Period in Earth Years
a = Semimajor Axis in astronomical units (AU)
For circular motion “a” = “r” using MKS measure we
obtain:
(Copy Formula and derivation)
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)
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)
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)
The shape of a projectiles path
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•
•
•
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If Tangential Velocity is…
Zero… the path is a straight line to the surface
More than zero but less than orbital velocity
… a parabola & It hits the surface
Exactly orbital velocity …the path is a circle
You are in orbit!
Greater than orbital velocity But less than escape
velocity…an ellipse
Your still in orbit!
Escape Velocity or greater… a hyperbola
You move away from the planet/star forever!
The Perception of weight
When you are falling you don’t feel the your weight,
but it is there…
Or you wouldn’t be falling
Your perception of your own weight comes from
feeling the supporting force (Normal, tension etc.)
Thus since if you accelerate up a force greater than
your weight is needed to push you up so you ‘feel’
heavier
And when you accelerate down you need less force
than your weight so you ‘feel’ you lighter
In free fall there is no support so you fell weightless
Apparent weightlessness in orbit
Astronauts in orbit are in free fall so…
No supporting force is needed
They have weight…
But ‘feel’ weightless