Space Concepts Review of Astrodynamics

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Space Concepts Review of Astrodynamics
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(No Transcript)
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Agenda

• Discussion of Homework Assignment
• Solutions to homework 5
• Review of Astrodynamics

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Homework Problems    

• ( 20 pts)The innermost moon of Mars, Phobos, is
  potato shaped , and like Mars , made of earthlike
  rock, and is 13 x 11x 9 km and is very dark. It
  orbits in a circular orbit around Mars every
  7and ½ hours keeping the same face to Mars
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• Find the mean surface temperature of Phobos
  surface facing the Sun after it has been in the
  sunlight for a while.

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Solar Power Flux at Mars
Solar flux at 1AU, SEarth 1.4kW/m2 At Mars
orbit 1.5AU SMars S (REarth/RMars) 2 S /(
1.5)2 .4444 S 622W/m2
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Assume Radiation Equibrium
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• ( 20pts) A spacecraft is designed for a deep
  space mission and thus requires minimum weight.
  It also carries a small chemical rocket engine.
  It will require aerobraking at the Planet is will
  go to and this will be done using the backs of
  the solar panels , which will carry roughly the
  weight of the spacecraft as it slows.
• What would you build the major parts of the
  spacecraft out of and why?
• Graphite composite for weight with titanium backs
  for solar panels, and engine for heat resistance
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• B. Assume the same spacecraft will be put into a
  permanent earth orbit. What changes in materials
  should occur?
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• Aluminum , for cost

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• ( 30 pts) A space plane is to be built that will
  take off into orbit on a Atlas V and return like
  the space shuttle, only it will be much smaller,

• what materials would you use the thermal
  protection system of this craft and why?
• -Titanium or reusable glass tile
• What power systems would you use to power the
  spaceplane in orbit?
• -Fuel cells or solar panels and batteries
• What power systems would you use to power the
  landing gear deployment and flight systems on
  reentry?
• -APUs or silver zinc batteries

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D.( Extra credit) ( 10 pts) What will be the
impact of including an internal cargo bay that
can carry either additional orbital fuel or
return payloads. It will raise surface area and
also heating rate when carrying loads on reentry,
it will also mean it can reach higher orbits with
more fuel. If it is crewed this will lower safety
margin.  
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The two-body problem
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Gravitational parameter
If m1 gtgt m2,
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Kinetic energy
m1
m2
CM
r
r2 rm1/(m1 m2)
r1 rm2/(m1 m2)
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Potential energy
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Circular orbit
e 0, r rc
or
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Circular Satellite Orbit Energy
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Circular orbital period for tight orbit
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Eccentricity Vector
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Eccentricity vector Cont.
Points from focus to perigee!
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The Orbit Equation
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Elliptical Relationships
foci
a semi-major axis
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Elliptical Relationships Cont.
c
b
a
f1
f2
ea
For any point c on the ellipse , the
circumference of the of the triangle f1f2c
2a(1e)
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Elliptical Relationships Cont.
a
ea
foci
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Keplers Laws

• The planets orbits the sun in elliptical orbits,
  with the sun at one focus of the ellipse.
• The radius vector sweeps out equal areas in equal
  times.
• The period of orbit squared is proportional to
  the semimajor axis cubed.

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Conic section geometry
Parabola e 1
Hyperbola e gt 1
Circle e 0
Ellipse 0 lt e lt 1
From http//www.sisweb.com/math/algebra/conics.htm
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Elliptical orbitKeplers 1st law
a semimajor axis b semiminor axis e
eccentricity p semilatus rectum n true
anomaly rp radius of perigee ra radius of apogee
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Dynamical constant and orbit geometry -angular
momentum
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Keplers second law
dA
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Keplers third law
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Dynamical constant and orbit geometry energy
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Eccentricity
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Keplers Equation For Satellite Motion
Problem When satellite moves in noncircular (
elliptical) orbit, its motion is not uniform, how
does one find its position on the orbit in time?

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Area of a triangles
Case 1
a
Case 2
y
Area of abcabc-acc ½(xx)y- ½xy ½xy
Area of abc ½xy
Area of triangle abc with base x and height y is
always ½ xy even if one angle is oblique
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Area swept
E eccentric anomaly
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Areal rate
constant
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Keplers equation
M mean anomaly E esinE n mean motion
Ö(m/a3) E eccentric anomaly t current time T0
time of perigee passage
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From n to E
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From n to E
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From n to E
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Half-angle formula
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From E to n
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Keplers eq.parabola orbit
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Keplers eq.hyperbola orbit
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Classical orbital elements

• a Semimajor axis of the orbit
• e Eccentricity of the orbit
• i Inclination of the orbital plane
• W Longitude of the ascending node
• w Argument of perigee
• T0 Time of perigee passage

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Orbital plane orientation
n