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).

Lunar Eclipse of April 4, 2015

Even though we just had a total solar eclipse on March 20th, just two weeks later, there will be a lunar eclipse. In fact, most of the western hemisphere will be able to witness at least part of this eclipse on April 4, 2015.


Remember that eclipse seasons happen every six months and always have a solar eclipse and lunar eclipse two weeks apart. The alignment of the Sun, Earth, and Moon will always determine which one occurs first. However, there are sometimes when the alignments are right, there may be three - a solar eclipse sandwiched between two lunar eclipses. However, this eclipse season there are only the two this year.


From before, we learned that a lunar eclipse will happen during a full moon. The Earth will be between the Moon and the Sun and the shadow of our planet will fall on the Moon, obscuring it. This eclipse will begin at 9:01 UTC. If the Moon is out during this time for you, you will be able to see the eclipse occur.

Year-long Mission in Space

Today, astronaut Scott Kelly and cosmonaut Mikhail Kornienko will launch from Baikonur in the Ukraine to begin a year-long mission in space on board the International Space Station. The unique thing about Scott Kelly is the mission will allow us to look at how extended time in space can affect the human body as Scott Kelly has a twin brother, retired astronaut Mark Kelly.


The science we will learn from this is remarkable because it will give us an understanding of how the human body will react to extended time in space, and give us knowledge of how to alleviate problems on the body for longer duration flights, for example, to Mars.


Follow Scott Kelly on twitter here.
Follow Mark Kelly on twitter here.
Follow the International Space Station here.


Watch the launch live here.

Update on Pluto

A while back, I posted an argument about why Pluto is not a planet. Recently, there has been a movement to reinstate Pluto as one of the planets in our solar system. Let's delve into this a bit further.


From the previous post, here are the IAU definitions of a planet and a dwarf planet.

• A planet is a spherical body that orbits the Sun and has cleared its orbit of other objects, i.e. it does not share an orbit with other bodies (not including moons).
• A dwarf planet is a spherical body that orbits the Sun but has not cleared its orbit of other objects. They may co-orbit with other bodies. Many of the Trans-Neptunian Objects, Kuiper Belt Bodies, Oort Cloud comets may have the same semi-major axis as other objects, therefore are not planets.

As to these current definitions, we can see that Pluto is not a planet. All the arguments I made are in the previously linked post. A nice thing about science is that new information can change our understanding of nature and the universe. Science is a fluid subject. Our perceptions can alter. So that is why it may be important to reinvestigate the idea of a planet.


If we were to redefine what makes a planet, we should be clear on what is and what is not a planet. Pluto is smaller than seven moons in our solar system, including our Moon. However, Mercury is also smaller than the two largest moons, Ganymede (orbiting Jupiter) and Titan (orbiting Saturn). We can all agree that Ganymede, Titan, the three other Galilean satellites, Triton (orbiting Neptune), and our Moon are NOT planet, they are moons. They orbit around planets which in turn orbit around the Sun. Pluto, only orbits the Sun (though it can be argued that it also orbits around the common center of mass of its system (Pluto, Charon, and its other orbital companions).


If the IAU does change the definition of a planet, it will have to get rid of the idea of co-orbiting bodies that are a significant fraction of the largest body's mass and radius. Remember, Charon is about 11.6% the mass of Pluto and has a radius about half that of Pluto. Our Moon is only 1.2% the mass of Earth and has a radius just over a quarter of the Earth. Looking at all the large satellites of the gas giant planets shows that all of them are significantly smaller in comparison to their parent planet than our Moon is to the Earth.


So if the definition is changed, what other objects in our solar system will have to be redesignated as a planet? Pluto is obviously the first. Eris will also have to redefined as it is a larger body than Pluto. After that, it depends on what the lower limit the IAU wants to use. Makemake may become a planet, Ceres may as well, though if Ceres does get redefined, than all the trans-Neptunian objects larger than Ceres will have to be classified as planets. Not only that, we will have to add a third type of planetary body along with terrestrial and Jovian. This will have to be something in between, though that type is not really a bridge between terrestrial and Jovian.


At the moment, I personally like the definition we have for planets. It's clear, concise, and makes a lot of sense. But as I said before, science can change and our understanding of what is going on can help us make more informed conclusions. Only if the IAU changes the definition of a planet, only then will Pluto, Eris, and some of the other dwarf planets/minor planets in our solar system become full-fledged planets.


We will learn more about Pluto once New Horizons reaches the Plutonian system in July of 2015. Then we will know more about Pluto and its sisters and may be able to make more informed conclusions about what they are.

Gravitational Coupling Constant

Much like there is a coupling constant for the electromagnetic force (also called the fine structure constant), there is one for the gravitational force, called, believe it or not, the gravitational coupling constant. It is used to define the gravitational attraction between two elementary particles having some mass.


The way it is defined is as the gravity between two electrons and is a unitless quantity.

Where:

• G is the gravitation constant  (6.67x10^-11 m³/s²kg)
• m_e is the mass of an electron (9.109x10^-31 kg)
• ℏ is the Planck constant over 2π (called the reduce Planck constant, 1.05457x10^-34 J*s)
• c is the speed of light (3x108 m/s)

Compare this to the fine coupling constant which is approximately 1/137 and we can see that the electromagnetic force is 10⁴³ times stronger than the gravitational force for electrons. Depending on what elementary particles are used (proton-electron or proton-proton), the ratio between them can vary, but in all cases, the electromagnetic coupling constant is magnitudes greater than that for gravity. In Martin Rees' case, he compares the fine structure constant to the gravitational coupling constant for two protons, and the ratio is 10³⁶. Any variance of this ratio can lead to the universe not being the way we see it.


To calculate the gravitational coupling constant for two protons, replace m_e with m_p in the top equation. To calculate it for the attraction between a proton and an electron, replace one m_e with m_p.    

Seasons on Earth

Recently, everyone on Earth went from one season to the next. In the northern hemisphere, we went from winter to spring and in the southern hemisphere, summer gave way to the fall (autumn). How exactly are the seasons defined?


Just this past Friday, the northern hemisphere experienced the vernal equinox, while in the southern hemisphere, the autumnal equinox occurred. We already know why they call these the equinoxes as they were explained in the previous posts. However, why does the northern hemisphere experience one season, while the southern hemisphere experiences the opposite (spring-fall and summer-winter)? It all has to do with the Earth's axial tilt.


The Earth rotates on its axis once a day. Most everyone knows that. However, the rotational axis of the Earth is tilted with respect to its orbital axis by about 23.5º.

So what does this mean?


When one half of the Earth is tilted towards the Sun, that half will receive more direct sunlight. The other half will not. It is like when you take a flashlight and aim it at a wall. If you keep the flashlight parallel to the wall, the light circle is tight and compact, if you tilt the flashlight away from the wall, the light circle becomes elongated. The same amount of light is hitting the wall, but in a larger area.

 

Another interesting thing about the seasons is that the time of year they occur change over time. However, none of us will be alive when January will be summertime in the northern hemisphere. This will occur in about 13,000 years. If you can wait until 28,500 CE (common era, formerly known as AD), April will be the middle of summer for the northern hemisphere. This is because the Earth wobbles on its axis, causing precession of the equinoxes (which in turn, also causes the solstices to precess). Currently, the summer solstice occurs when the Sun is in the constellation Gemini, but will someday be in the constellation Sagittarius.