The Satellite of Makemake

Makemake is a dwarf planet in the outer edges of the solar system in the Kuiper Belt. It was discovered in March 2005, and announced by Mike Brown in July of 2005. It is about 2/3 the size of Pluto, so it is relatively small. However, it was recently discovered that Makemake has a companion body discovered in April of 2016 (from images taken in April of 2015 from the Hubble Space Telescope). It is not the only dwarf planet with a satellite.

Pluto has five, including Charon. Eris, the largest dwarf planet by mass (Pluto is larger by volume), has one (Dysnomia). Haumea has two. Satellites around dwarf planets may be pretty common.

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).

Titan

Cassini Image of Titan showing the atmosphere of the moon

Image Credit:

NASA/Cassini

 

Titan is the largest Saturnian moon and the second largest in the Solar System behind Jupiter's moon Ganymede. Like Ganymede, it is also larger than Mercury. Christian Huygens, who discerned the rings of Saturn, also discovered Titan in 1655, making it the fifth satellite discovered with the telescope.

 

It is the only moon known to have a dense atmosphere, where atmospheric pressure is measurable on the surface. Though Europa, Ganymede, and Callisto may have liquid oceans below their outer crusts, Titan is the only body in the Solar System to have surface liquid besides the Earth. However, you wouldn't want to swim in those oceans as they are bodies of methane.

 

Because it has liquid methane oceans and lakes, much like Earth has a water cycle, Titan experiences a methane cycle. Surface methane evaporates and forms clouds in the Titan sky. The rain Titan experiences is methane.

 

Although Titan is smaller than Earth, its atmosphere is dense enough to create higher surface pressure than on Earth, at about 1.45 atmospheres (146.7 kPa). One atmosphere on Earth is the normal pressure at sea level which is 101.5 kPa (kilopascals). As shown in the above image, the atmosphere is extended with a composition of 98.4% Nitrogren (N₂), 1.4% methane (CH₄), and trace other molecules including water in the stratosphere (higher levels) and 95% N₂, 4.9% CH₄, and other molecules in the troposphere. Because of the methane clouds, the sky is very hazy on Titan so would have poor visibility on the surface when we make our first crewed mission to Titan sometime in the future.

 

The gravity on Titan is only 85% of that on the Moon even though it is larger because of its smaller density. If you were to stand on Titan, your weight would only be 15% of that on Earth.

 

Much like the Moon and Earth are tidally locked, Titan is tidally locked to Saturn, so for every orbit around Saturn, which is almost 16 Earth days, it only rotates once on its axis.



Ida and Dactyl

Galileo Probe image from NASA

Typically, asteroids are too small to have their own satellites. The gravitational force exerted by an asteroid is too minor to hold on to any object larger than a boulder if that object passes close by. The object are moving faster than the escape velocity of the asteroid. However, there are exceptions. The prime example is the dual system of Ida and Dactyl.

243 Ida was the 243rd asteroid discovered in the Asteroid Belt. It was originally discovered by Austrian astronomer Johann Palisa in 1884. Based on the spectroscopy, Ida is an S-type asteroid with an albedo of 0.2383. It has a semi-major axis of 2.862 AU, taking 4.84 Earth years to orbit the Sun. It has an average diameter 31.4 km across which is kinda weird to use since it is longer than it is wide.

In 1993, the space probe Galileo visited Ida on its way to explore Jupiter. It was in this visit where Dactyl was discovered. Dactyl is only 1/20th the size of Ida, only about 1.4 km in diameter. It is difficult to determine Dactyl's orbital characteristics without much more observation, but because it is so small in relation to Ida, to determine how it orbits Ida, Dactyl and Ida will have to be visited. Constraints to its orbit did allow a density to be roughly detemined and Dactyl is lacking metallic minerals. Ida and Dactyl share similar characteristics, so it is possible that they formed at the same time.

Our Nearest Neighbor

The nearest celestial body to the Earth is obviously our Moon.  We've already discussed the phases of the Moon and how they relate to the Moon's position with respect to the Sun and the Earth.  In the next few posts, we will learn about the Moon.

For example, how come eclipses don't happen every month? Why is there a supermoon? Where did the Moon come from?  What would life be like if the Moon had never existed or what would life be like if we decided to blow up the Moon (it was actually thought of at one point)?  Why should did we go to the Moon originally, why haven't we gone back, and should we go in the future?

Before we get into these topics, let's learn a little about our Moon. 

• It is the only natural satellite of the Earth and is the fifth largest satellite in the solar system, behind Ganymede, Titan, Callisto, and Io. It is the only celestial object, besides the Earth, that humans have stood on.
• It is approximately 238,900 miles from Earth or about 384,400 kilometers, and it took Neil Armstrong, Buzz Aldrin, and Michael Collins about 4 days to reach it from Earth. 
• It has a sidereal period of 27.3 days and a synodic period of 29.5 days. We will talk about this in a future post. 
• It has no atmosphere to speak of and therefore, no life. 
• The Moon has a radius of 1,737 km (27.3% of Earth's) and a mass of 7.35x10²² kg (1.23% of Earth’s). On the Moon, you would weight approximately 1/6 of what you weigh on Earth. That’s why in videos, the astronauts on the moon always looked like they were bouncing.  It would actually be more difficult to walk normally.
• At one point in its history, the Moon was active. This was likely to the cooling it went under after it formed and its constant bombardment by asteroids early in its life.
• It has an inclination of about 5° to the ecliptic, which I realize now I have never talked about.  To learn about the ecliptic and what it is, click here.