Jordi Isern Institut de Ciències de l’Espai (CSIC-IEEC) MSc in Economics of Science & Innovation Innovation & Challenges: Nanotechnology & Space (2) Orbits & Space Travel

r m1m1 m2m2 Newton laws: 1 Inertial mass 2 F = ma 3 Action and reaction law Gravitation law Cavendish pendulum: G=6.67x Nm 2 /kg 2. Is the weakest force of the Nature, but its range is infinite and it cannot be screened.

Kepler’s laws 1st law: Planets follow elliptical orbits with the Sun in one of the foci.

Kepler’s laws 2nd law: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Kepler’s laws 3rd law: M is the total mass In the case of an Earth satellite

E < 0

Eccentricity e = 1 Energy E = 0 Eccentricity e > 1 Energy E > 0

Aries point or vernal equinox is defined by the intersection of the equator with the ecliptic Node: intersection of the orbit with the equator (ascendent if South-North ) Orbital Elements : Inclination, i, Defines the orientation of the orbit with respect to the Earth's equator. Argument of Perigee, ω,Defines where the low point, perigee, of the orbit is with respect to the Earth's surface. Right Ascension of the Ascending Node, Ω Defines the location of the ascending and descending orbit locations with respect to the Earth's equatorial plane. True/Mean Anomaly, υ, Defines where the satellite is within the orbit with respect to perigee.

Low Earth orbits (LEO) Medium Earth orbits (MEO) Geostationary orbits (GEO) Types of orbits

Geostationary orbits # A GSO orbit circles the Earth above the Equator at a height of abou 36,000 km # Its period is equal to the rotation period of the Earth, so from the ground the satellite looks stationary # If the inclination is larger an analema appears

Solar analemma

42% b3 Advantages Stationariety: Large coverage Unique ground segment, No tracking

b3 Inconvenients: Distance: large emission power only passive systems low resolution Slot system Important drifts

b3 Molniya orbit T = 12h i = 63.4 very eccentric

Low Earth Orbites (LEO) Equatorial & tropical orbits TRMM: h=325 km, i= 35 o Polar orbits Sunsynchronus Arbitrary inclination orbit MIR: h=350 km, i=51,6 o TOPEX/POSEIDON: h=1330 km, i=65 o b1

Polar orbits Inclination ~ 90 o The height is a compromise: * Resolution and orbital period  h  * Width of the observed zone  h  Typical values: h=850 km T=100 minutes Swath

Polar orbits They cover all the Earth Adjusting the swath and the period [T(h)] it is possible to ensure the observation of any point within a given time (revisite time). Polar meteorological satellites have a 24h of rt because the swath is 3300 km

Medium Earth Orbits (MEO) They are used when visibility from the ground and the power are important but resolution is not a requirement: h : thousands of km T: hours b2

GPS 4 satellites permanentmently visible T: 12 h, h km, i: 55

Orbital trade-offs: Highly eccentric orbit (HEO) Ellipsoidal orbit, any revolution time Long uninterrupted observations observing efficiency 60-70% Long time spent outside the radiation belts Generally higher background, but slower varying, higher radiation dose Extra propulsion for perigee raising Near real time operations, no data storage Higher launch costs Orbital trade-offs: Highly eccentric orbit (HEO) Ellipsoidal orbit, any revolution time Long uninterrupted observations observing efficiency 60-70% Long time spent outside the radiation belts Generally higher background, but slower varying, higher radiation dose Extra propulsion for perigee raising Near real time operations, no data storage Higher launch costs Low earth orbit (LEO) ~90 min revolution Eclipse by the Earth observing efficiency 24-35% Below radiation belts, except South Atlantic Anomaly (SAA) Lower background, but variable Propulsion needed against atmospheric drag, or orbit decay No-real time response, data storage required Complex thermal control due to Earth shadow

Example of a software package to support mission evaluation: Satellite Tool Kit (STK) Key Features: Analytical capability. STK includes complex algorithms that take care of number-crunching exercises in a matter of seconds. With STK, the user can quickly and accurately calculate a satellite's position and attitude in time; evaluate complex in-view relationships among space, air, land and sea objects; and compute satellite- and/or ground-based sensor coverage areas. Orbit/trajectory generation. STK provides multiple analytical and numerical propagators (Two-body, J2, J4, MSGP4, imported ephemeris data) to compute satellite position data in a wide variety of coordinate types and systems. For the novice, STK provides the Orbit Wizard to guide the user through quick creation of commonly-used orbit types such as geo-stationary, circular, critically-inclined, sun synchronous, molniya, and retrograde. Satellite database. In addition to generating satellite positions via the standard propagators, STK also provides the Satellite Database which utilizes up to date NORAD two-line element sets (TLE)obtained maintained and updated at AGI's website. This database, which includes over 8,000 objects (active and inactive satellites as well as orbit debris), can then be queried against parameters such as orbital elements, owner, mission, status, etc. The selected results are then automatically propagated using the MSGP4 propagator and imported into STK. Example of a software package to support mission evaluation: Satellite Tool Kit (STK) Key Features: Analytical capability. STK includes complex algorithms that take care of number-crunching exercises in a matter of seconds. With STK, the user can quickly and accurately calculate a satellite's position and attitude in time; evaluate complex in-view relationships among space, air, land and sea objects; and compute satellite- and/or ground-based sensor coverage areas. Orbit/trajectory generation. STK provides multiple analytical and numerical propagators (Two-body, J2, J4, MSGP4, imported ephemeris data) to compute satellite position data in a wide variety of coordinate types and systems. For the novice, STK provides the Orbit Wizard to guide the user through quick creation of commonly-used orbit types such as geo-stationary, circular, critically-inclined, sun synchronous, molniya, and retrograde. Satellite database. In addition to generating satellite positions via the standard propagators, STK also provides the Satellite Database which utilizes up to date NORAD two-line element sets (TLE)obtained maintained and updated at AGI's website. This database, which includes over 8,000 objects (active and inactive satellites as well as orbit debris), can then be queried against parameters such as orbital elements, owner, mission, status, etc. The selected results are then automatically propagated using the MSGP4 propagator and imported into STK.

Hohmann transfer orbit Orbital velocity Venus 5.2 km/s faster than Earth Mars velocity 5.7 km/s slowerer than Earth Earth scape velocity 11.2 km/s ! Transfering a probe from Earth to a planet is extremely costly by brute force Hohmann transfer orbit minimizes the cost! Cheap but slow! This technique uses gravity of moons and planets to modify the speed and direction of the probe. It obtains the energy from the orbital and rotational energy of the moon/planet Gravitational slingshot

Voyager flight

Lagrangian points The forces of the trhree bodies equilibrate

L4 and L5 are estable. If they are perturbed thay tend to recover the initial position. They are called triangle or Trojan points L1, L2 & L3 are unstable equilibrium points L1 is excellent for observing the Sun (Genesis, SOHO) L2 is excellent for astronomy since detectoirs are not blinded by the Sun, Earth, Moon shine (Wilkinson observatory)

Interplanetary Transport Network