Ion Drives

Previously, I talked about ions. Remember, they are atoms that have either more or less electrons than protons. For ion drives, positive ions, also called cations, are used to propel the craft ahead.

The ions are created in a chamber where the electrons are stripped from an atom or molecule (many times xenon or ammonia, depending on the thruster type), then are accelerated via an electrostatic or an electromagnetic field.

Ion drives have a very high specific impulse, which means they are very efficient engines. Specific impulse is the ratio between the spacecraft's thrust (the force at which the spacecraft is being pushed along) and the weight of the fuel used to create that thrust).

However, the thrust from an ion engine is small since ions themselves are rather tiny. Ion engines are not great from getting place to place quickly in the solar system. Typically, ion drives will be used for space stations for maneuvering or for deep space probes. Though the thrust is tiny, over time, that thrust can add up to a large velocity for the spacecraft.

Deep Space 1

Via NASA

Schematic of Deep Space 1

via NASA

Hohmann Transfer Orbit

A Hohmann transfer orbit is a method of getting a spacecraft or satellite from one circular orbit to a lower or higher circular orbit. It involves using thrusters at particular points in the orbits to either speed up or slow down the craft.

The reasoning behind using this type of orbit is that for circular orbits, the speed of the craft does not change as it is a constant distance from the center of the orbit (the center of the planet or moon that it is orbiting). A Hohmann transfer orbit is a semi-elliptical orbit with the focus of the ellipse at the center of the system.

To go from a lower orbit to a higher orbit, the spacecraft must increase its orbital speed. This increase will put it on the elliptical orbit that will transfer the craft to the higher orbit. Once the craft reaches the desired orbit, the craft must then again fire its engine to speed the craft up to the correct speed for the orbit, putting it into a new circular (higher) orbit. This is the method in which spacecraft dock with the International Space Station.

The reverse also works, but in this case, the craft's engines slow it down to get to the lower orbit, again slowing the craft at both the higher orbit (to transfer) and the lower orbit (to insert it into the new orbit).

In the picture below, the blue orbit is the lower circular orbit, the yellow/green dashed path is the Hohmann transfer orbit, and the red orbit is the higher orbit. At point A, the engines are fired to increase the speed of the craft and at point B, they are fired again to insert it into orbit. To transfer from the higher to the lower, the engines are retro-fired at B to slow the craft down and again at A to insert it into the lower orbit.



 

Geosynchronous and Geostationary Orbits

Objects can orbit the Earth in different ways. Most orbits look the same from above, a sine curve (or if you like different phasing, a cosine curve) with the Earth’s equator as the x-axis. The difference is how fast the satellite or spacecraft or space station takes to orbit the Earth.

However, there is a special orbit which does not orbit the entire Earth, but stays above a particular longitude. These orbits are called geosynchronous orbits. These orbits have a period that is just equal to the Earth’s sidereal day (23 h, 56 min, and 4 seconds). Because of this orbit, they tend to remain around the same longitude on Earth and if you were to look down on this orbit, the satellite would trace out something called an analemma, which is just a fancy term for the figure 8. Depending on the inclination of the orbit, these satellites are not visible from all parts of the Earth. These orbits are used mostly for communications and weather satellites. This is why you do not have to move your satellite dish if you have satellite television, as a non-geosynchronous orbit would be a pain if you are watching your favorite TV shows.

There is a special geosynchronous orbit called a geostationary orbit. Not only does this have a period of one sidereal day, but a satellite in this orbit does not move at all. It is always above the same place on Earth, and by definition, the location in the sky must be above the equator. If we were to build a space elevator (more on this concept later), the receiving station for the elevator must in a geostationary orbit. All geostationary orbits are geosynchronous, but not all geosynchronous orbits are geostationary.

How far up is an object in a geosynchronous/geostationary orbit? Just using some basic concepts from Newtonian mechanics, the calculation is relatively simple.

First, to be in a stationary orbit, the force of gravity on the satellite must be counteracted by the centripetal force, i.e.:

Where:

• G is the gravitational constant, 6.67x10^-11 m³/kg·s²
• M_E is the mass of the Earth, 5.972x10²⁴ kg
• m is the mass of the satellite
• v is the orbital velocity, m/s
• R is the radius of the orbit (assuming circular orbit), in m

Equating these two and we get:

We know the period of the orbit (P) has to be one sidereal day, 23h56m4s, which in seconds is 86,164 seconds (60 seconds in a min, 60 min in an hour) and the orbital velocity is just the length of the orbit (the circumference of the orbit, 2πR) divided by the period, P.

Plug v=2πR/P into the above equation and simplifying, we get:

and plugging in all the constants, we find that the orbital radius is 42,164 km. (If you like, you can solve this yourself and see if I’m right.) Note, that this is the radius of the orbit from the center of the Earth. If we take into account the Earth’s radius, the orbital altitude is 35,786 km (R_E = 6378 km at the equator).

Return to the Moon

We have not been to the Moon since Apollo 17 in 1972.  The reason the United States went to the Moon, originally, was not for science or exploration, but rather for political reasons.  The US wanted to beat the Soviet Union to the Moon.  On July 20, 1969, when Neil Armstrong made one small step for man and a giant leap for all mankind, a human being stood on another celestial body other than Earth for the first time in history.

Why haven't we been back?  One, it is extremely expensive to travel to the Moon.  Not only do we have to have enough fuel to get there, but we need enough to get back.  We'd also have to worry about keeping the astronauts safe while on the Moon.  Two, there really is no economic or political gain from going to the Moon.  At the moment, the only gains we would receive would be purely scientific.  There is no profit to travelling to the Moon, though sometime in the future, it may be profitable to mine the Moon.  Politically, it wouldn't make one country better than any other.  The only advantage would be if there was a multi-nation coalition to go the Moon and make it worthwhile for all humanity.  Lastly, we don't have the technology to go back to the Moon.  A whole class of new spacecraft would have to be designed, tested, and constructed for man to go to the Moon once again.

Why is this important?  There has been talk of a crewed mission to Mars, which is all well and good.  But to skip going back to the Moon first would be a huge mistake.  The Moon is much easier to get to from the Earth than Mars; it would only take a few days travel to get to the Moon, with a round trip only taking about a week.  To get to Mars, it would require at least 6 months of travel from Earth to Mars and almost two years for a round trip.  If humanity built a lunar base, it would be easier to use as a launching point for exploration of the rest of the Solar System.  It would require less energy to launch a ship from the Moon than the Earth because the Moon is much smaller and its gravity would not work as hard against launching a rocket or spacecraft.  Once we set up a permanent presence on the lunar surface, exploration of the Solar System should follow, with Mars being the most logical first step.

Another nice thing about using the Moon as a launching pad is that the materials needed to build rockets and habitats and create fuel for spacecraft are already on the Moon.  The challenge would be to harvest the material and convert it into useful products. That is obviously many years in the future, but we still need to return to the Moon before thinking about going to Mars.