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Satellite Orbits

Space vs orbit

Requirements for reaching space

  • Go up 100 km.

Video clips of helium weather balloons carrying teddy bears and hamburgers "to space" are entertaining but only get about one third of the way to space.

The official edge of space is at 100 km altitude, known as the Kármán line. This is the altitude where aeronautical flight (wings) will not produce any further lift, so rockets have to be used to get any higher. (More precisely, wings will not provide enough lift to get a vehicle any higher unless it's travelling at more than orbital speed, in a straight line, ignoring centrifugal force.)

It's possible to get to space but be nowhere close to achieving orbit. To achieve orbit a rocket has to go even higher and be moving "sideways" much much faster.

To stay in orbit a high horizontal velocity is required because objects in space are continually falling toward Earth. Gravity continually accelerates them toward the centre of the planet. If an object is travelling forward fast enough it basically misses the planet (or star, moon, asteroid, etc) by the time it has fallen far enough where it would have hit the planet. As the object travels forward the direction of "down" continually changes and gravity accelerates it in a different direction.

Almost all orbits are at more than 300 km altitude. Much less than this and atmospheric drag starts to be too much of a problem, although orbit can be achieved as low as 160 km. Very low orbits decay very quickly. For example an orbit at 250 km will take just one month to deorbit and either burn up or hit Earth.

To stay in orbit a satellite must have a forward (sideways) velocity of 28,000 km/h (7.8 km/s). Lower velocity is required for a higher orbits but it takes more energy to get to the higher altitude.

Orbit types

A geocentric orbit is centred on Earth. Not all useful geocentric orbits are eastward. There are other kinds of orbits that are very useful for particular purposes.

Requirements for achieving low Earth orbit

• Go up 350 km.
• Be travelling sideways
  at 28,000 km/h.

Low Earth orbit.

  • Orbits up to 2,000 km high.
  • Most satellites are in low Earth orbit, including Iridium satellites.

Earth's gravity is not significantly lower in low Earth orbit than at Earth's surface, but because objects (and people) are in freefall they experience weightlessness.

Polar orbit.

  • Takes a satellite to high latitudes on each orbit (over the poles or very close to them).
  • The satellite covers a different north-south strip each time around, because Earth has turned in the time the orbit takes.
  • Polar orbits are often sun-synchronous, so the satellite passes over each strip at the same time each day.
  • A commonly used altitude is approximately 1000 km, which produces an orbital period of about 100 minutes.
  • Inclining the orbit 8° off the pole results in the orbit staying synced to the Sun.
  • Used by weather satellites.

Geosynchronous orbit.

  • High enough and slow enough to take 23 hours 56 minutes 4 seconds, the same as Earth's sidereal rotate period (the time it takes to rotate once compared to the fixed stars rather than the Sun).
  • The orbit might be circular or elliptical. If the latter, the satellite drifts backward and forward relative to a particular latitude.
  • If the orbit in inclined the satellite also wanders north and south of the equator.
  • This makes the satellite trace out a wandering figure 8 path as viewed from Earth.

Requirements for achieving geostationary orbit

• Go up 35,786 km.
• Be travelling sideways
  at 11,068 km/h.

Geostationary orbit.

  • A type of geosynchrosous orbit that's circular and above the equator, meaning it stays above one fixed point above the planet. (There is a bit of drift toward three particular points above the equator. Without compensating for this drift – known as stationkeeping – these three points would gradually collect satellites.)
  • Have a radius of 42,164 km.
  • Used by telecommunications satellites because antennae (normally parabolic dish-shaped) on the ground and on the satellite can always be pointed in the same direction. There is a noticeable lag by the distance signals need to travel.
  • Also called a Clarke orbit, named after writer Arthur C Clarke who proposed it in 1945.

A geostationary orbit is normally achieved in several steps.

  • Attain low Earth orbit of about 350 km altitude.
  • Convert to a geostationary transfer orbit. This is a very elliptical orbit with perigee (the orbit's closest point to Earth) at 350 km and apogee (the point in the orbit furthest from Earth) at 35,786 km.
  • Convert into the final circular geostationary orbit.

Because of the much greater height, more energy is required to attain a higher orbits than low Earth orbits. It's easier to get things into low Earth orbit.

Semi-synchronous orbit.

  • Takes half a sidereal day, or about 11 hours 58 minutes.
  • Viewed from Earth satellites appear to go around once during a day.
  • Used by GPS satellites.

Graveyard orbit.

  • An orbit about 300 km beyond a geosynchronous orbit where old geosynchronous satellites are permanently parked to get them out of the way.
  • Requires the same fuel as three months stationkeeping. Returning to Earth (to burn up on re-entry) would require the same fuel as 34 years of stationkeeping.

Launch direction

Earth is spinning, and being the size it is, it makes it significantly easier to launch rockets into orbit by launching them in the direction of Earth's spin (east) than across its spin (north or south) or especially against its spin (west).

The metre was originally defined as being 1/10,000,000 the distance from the North Pole to the equator (through Paris). That's 10,000 km. Earth is roughly spherical, so it's about 40,000 km around the equator. That means a point on the equator is travelling east at 40,000 km per 24 hours, or 1,667 km/h.

Any object launched eastward from the equator is thus already travelling at 1,667 km/h of the 28,000 km/h necessary for orbit, making it easier to get to the required speed – you're already 6% of the way there.

NASA launches many of its orbit-bound rockets from the Kennedy Space Center in Florida, at 28.5°N. If launching eastward this gives a head start of 1667 * cos 28.5° = 1,465 km/h for orbital insertions, or 5.2% of the total speed required.

In February 2016 North Korea announced it was going to launch a space rocket south. Now, North Korea has managed to get the odd item into orbit, but with many failures along the way, and it's not known for any particularly effective orbital launching capability. If space is really the intended destination, the intention to launch to the south makes the attempt harder.

The advantage of heading south is that the take-off will pass over less land and the resulting polar orbit (or near polar orbit) will pass over most of Earth's surface.

The rocket was launched from North Korea's Sohae Satellite Launching Station on the west coast, at 39.66°N, launching to the south at a bearing of about 165° – the rocket went just east of the Japanese island of Okinawa. That means North Korea was missing out on a 1667 * cos 39.66° * (1 – sin 15°) = 951 km/h boost if launching due east from that location.

Beyond orbit

Getting beyond orbit requires going even faster. Going to the Moon requires even more speed, but when close enough to the Moon, its gravitational pull will be stronger than Earth's.

After that, the next step is escape velocity – the velocity that something needs to go to escape from Earth's gravitational pull. At Earth's surface that's about 11.2 km/s, but that isn't practical because of the atmosphere. Escape velocity is normally achieved from low Earth orbit, where escape velocity is a bit lower at 10.9 km/s and the rocket already has 7.8 km/s in order to stay in orbit.

The Moon's escape velocity is 2.37 km/s, while Earth's escape velocity at the Moon is just 1.44 km/s. The Moon would thus make quite a good staging post for launching to the rest of the solar system.

The Sun has its own escape velocity, and it's quite a bit higher than Earth's because the Sun's gravity is quite a bit stronger than Earth's. At Earth's orbit the Sun's escape velocity is 42.1 km/s. This means it's much harder to escape the solar system than it is to escape Earth's gravity, and why gravitational slingshot manoeuvres using big planets like Jupiter are required to increase velocity enough for space probes to head off into deep space. (The manoeuver also decreases the amount of time to get to the outer solar system.)