Orbits Flashcards
Kepler’s first law
the orbit of each planet is an ellipse, with the sun at one focus
Kepler’s second law
the line joining the planet to the sun sweeps out equal areas in equal times
Kepler’s third law
(Period) ^ 2 ∝ (mean radius) ^ 3
Give gravitational force equation
F = MmG / r^2
What assumptions are made when calculating orbits
- The motion of an aircraft is governed by attraction to a single central body
- The mass of a spacecraft is negligible with respect to the central body
- This central body is spherically symmetric
What is the general equation to find velocity at orbital point
V = SQRT( 2μ / r - μ/a)
What is the equation to find velocity for circular orbits only
- a = r therefore:
V = SQRT( μ / r )
Give equation to find time period of a circular orbit
P = 2πr / V
Give equation to find energy of a keplerian orbit
ɛ = - μ / 2a
Circular: a = r
Elliptical: a is +ve, ɛ is -ve
Parabola: a = ∞, ɛ = 0
Hyperbola: a is -ve, ɛ is +ve
Give equation for eccentricity, e
e = SQRT ( 1 - (H^2/μA) )
e = c / a
where c = distance from centre of orbit, to a focus point
for circular c = 0
What is the eccentricity value for each of keplers orbits
e = 0 circular
e < 1 elliptical
e = 1 parabola
e > 1 hyperbola
Give equation for ‘a’
a = (r(a) + r(p)) / 2
Give equation for spacecraft position in an elliptical orbit with respect to a, e and ϴ
r = a(1-e^2) / (1 + ecos ϴ)
Give equation for flight path angle γ
tanγ = eSinϴ / (1 + ecos ϴ)
What is the flight path angle
The angle between the local horizontal and the spacecraft velocity vector
