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Monday, 6 May 2013

Hypothetical Space Mission: Venusian Observatory

Hello again space fans! Welcome back to another exciting adventure into the concepts of space mission design. I would apologize for the hiatus this blog has taken but I've had a busy time of things finishing off my undergraduate degree.

As you may recall here, I have finished my undergraduate degree, my Bachelor of Applied Sciences, Specialized Honours in Space Engineering, from York University, Toronto, and have been accepted into the Masters of Space Studies program at the International Space University in Strasbourg, France!

Obviously, I am very, very excited for this opportunity and am working toward getting everything ready. I would also like to continue my hobby of exploring various space mission concepts with you and while I hinted that my next post might be about artificial gravity, that subject will have to wait until I can focus the material enough to be suitable for a blog post.

Today, we're going to be looking at a hypothetical mission to Venus, and some of the design choices needed. This was part of an assignment for my Dynamics of Space Vehicles class so I will credit Professor John Moores, of York University.

Known as the Venusian Precision Observatory, the mission goal is simple: orbit a satellite around Venus and monitor its rotation precisely. Why would we want to do that? Well, science does things for many reasons, here are a few: 1) We've never done it before. Hard to justify because of how expensive space missions can be, but it is a leading factor in many cases. 2) Venus is similarly sized to Earth so understanding it better might help us understand Earth better. This usually goes over much more smoothly than the pure, but expensive, spirit of adventure in point 1. 3) Might be using this mission to test other concepts or as a stepping stone to other things. Example, might include a transceiver on the satellite so we could communicate with the Messenger probe orbiting Mercury more easily.

Whatever the reason, we were asked to look into it, so that is what we will do now! Specifically, we will look at orbital consideration and orbital perturbation, the latter meaning that which can change an orbit over time.

Recalling the post I just linked to above, we have many different options for orbits. One idea for this mission could be to place a satellite in some sort of Venus-synchronous orbit. Like a geostationary orbit, this would allow the satellite to go around Venus with the same speed as Venus turns so that the satellite stays over the same spot of the planet all the time.

So, let's look at that. If you may recall from my lecture on Kepler's Laws, the rate at which an object orbits another, it's orbital period, is proportional to its semi-major axis.

Whoa, hold the jargon, the what axis? Well, I have included a drawing to help illustrate, get it, drawing...illustrate, oh anyway.

As you may recall, the ellipse is the more natural shape for orbits. In this case, the satellite would orbit Venus following some size of ellipse and Venus would lie somewhere along that dotted line. Instead of being in the middle, Venus would lie at either of the two focal points, or foci, as marked in the picture on the left.

The semi-major axis, is simply the name for half of the length of this dotted line, the longest part of the ellipse. It is a useful term for space scientists and engineers and there are many mathematical equations relating
this line to other factors. As I mentioned, the semi-major axis is related to orbital period.

In the picture on the left, that funny looking 'T' is the orbital period, and 'G' is the gravitational constant, (just a number really). Since we said that for this Venus-synchronous orbit, the satellite's orbital period would match the rotation period of Venus, we know, from observation, that this period is about 243 Earth days.

Hold on. 243 Earth days!? Yeah, it takes Venus almost an entire Earth year just to spin around once. It's about the same size as Earth too, so it is spinning very, very slowly.

Unfortunately, when we do the math, we find that the semi-major axis we would need for this type of Venus-synchronous orbit is about 1.5 million km.

This is bad for two reasons:
1) The first, is that if the satellite is that far away from the planet, 0.75 million km in the worst case, it is more difficult to monitor and observe. We can do it, but it requires more sophisticated technology, with a higher precision and better resolution, and the more difficult a mission is, the more expensive and the more prone it is to failure.
2) The second reason is that at this distance, the satellite falls outside of the Hill Sphere or sphere of influence of Venus. These terms have to do with the gravitational influence of one body over another. We love our metaphors here when we teach physics, so imagine that the Solar System, every planet, moon, and the Sun, exist on a sheet of paper. Each object has mass, and the more mass it has, the more it pulls down on the sheet in its spot. Now, if you roll a marble on that paper, it will obviously want to fall toward any of the depressions made by these massive objects. That, simply put, is how gravitational attraction works. If you're having a hard time seeing that, check this out. (Or search for Gravity in Einstein's Universe on Youtube). Long story short, if the satellite is outside this influence, it is not bound to Venus and will not stay orbiting around it; likely, it will drift toward the Sun.

So, this orbit will not work as it is too far away and not bound to Venus. Later in the assignment, we were given a different set of orbital parameters. You can contact me for the details, but essentially, this orbit had a semi-major axis of 20 000 km, a lot smaller and probably better suited to our mission.

The picture posted above represents the next step in our considerations and that is looking at the periapsis and apoapsis distances. These are fancy words meaning the closest and farthest points of approach, respectively, from the satellite to Venus. The equations use the semi-major axis and something known as the eccentricity, that letter 'e'.

The eccentricity is a number ranging between 0 and 1 and basically means the flattening of an orbit. If an orbit has an eccentricity of 0 it is not flattened at all and acts like a circle. However, if the value is closer to 1, the orbit is flattened from a circle to an ellipse, and finally into what looks like a line. Such a path is not an orbit at all, but rather a parabola, a curved shape which doesn't connect to itself. At this point, an object with an eccentricity of 1 is moving in a parabolic shape around the planet and leaves the planet behind.

Earth's orbit around the Sun has an eccentricity of 0.016 so as you can see, it's nearly circular.

Among the many values we were given about the second choice of orbit, eccentricity was one of them and so we use it to find that the closest the satellite will come to the planet is about 14 000 km and the farthest point is about 26 000 km. Subtracting the radius of Venus, (which again, is similar to that of the Earth), we find that the satellite, will hover over Venus with heights between 8 000-20 000 km. This would be similar to middle and high Earth orbits, so we know this would work for observation as we have satellites around Earth in orbits like these for observation.

Alright, so a lot of explanation and some math later, we realize this orbit would work out just nicely. But, is it stable?

Things in space are a little more complicated than they are here on the Earth. For example, you want to observe something, you simply place a camera in front of it and walk away. However, in space, tiny changes, called perturbations, can cause the situation to change over time. That same camera, orbiting around Venus, will feel other factors pulling on it and this will change the orbit. If the orbit is changed, our mission could fail.

In our hypothetical mission, we have been told that if our orbit changes by as much as 1 km from where it started, our satellite's systems will not be able to complete the mission. While we could use thrusters and other systems to keep the satellite in place, the more we have to do and add to a mission, the more expensive, difficult, and prone to failure that mission becomes.

So, that camera, sitting on the table. It might feel wind, but unless it's a really strong wind, it is not likely to move the camera. In space, however, solar radiation pressure, effectively solar wind, can push our satellite out of its orbit over time, and this problem gets worse as you get closer to the Sun, like when we move from Earth to Venus.

There is a formula we use to find out the pressure caused in this situation. Let us assume that the satellite has a mass of 1 000 kg, and that the solar panels have an area of 50 m^2, and that these panels are perfectly reflective. (They wouldn't be, and shouldn't be as they would not work, but this is a worst-case approach. If we plan for the worst, we will always be prepared)

So, the formula is as follows: Pressure/mass = (4.58*10^-6)*(Cr)*(R_Earth/R_Venus)^2*Area
Where R_Earth means the distance between the Earth and the Sun, about 149.6*10^6 km, and R_Venus means the distance between Venus and the Sun, about 108.6*10^6km.

Cr is the coefficient of reflection ranging between 1 and 2, and since we said the panels were perfectly reflective in the worst case, we'll say this value is 2.

All in all, the pressure is about 1.75*10^-6 Newtons/kg. Now, what does any of this mean?

Well, to put it in perspective: the gravity you're feeling right now, unless you're Chris Hadfield or another brave astronaut, is about 10 Newtons/kg, so this pressure is really really small compared to that.

But, when we look at how it will change the orbits, running it through some equations you learn here and there, we find that the semi-major axis would change by about 62 metres/second, which means that in 16 seconds the orbit will be out of specification. So, in 16 seconds, the solar radiation pressure will push the satellite into an orbit which will not work for us.

Well, that's pretty bad. Before we go about fixing it, let's look at other factors which may add to this.

Normally, we have to consider the gravitational influence of other bodies. Satellites around Earth have to deal with the Sun, Earth, and Moon pulling on the satellite in odd ways, changing orbits, but Venus has no moon, and we said we were well inside its gravitational sphere of influence. So it won't be an issue here. Moving on.

Atmospheric drag is one way a satellite can fall out of orbit. The International Space Station, which only flies about 400 km above the Earth's surface, feels the drag of flying through the thinner but still present atmosphere at that height and has to correct for it. If it didn't, it would eventually fall, although it would take a while.

For our orbit, we said the closest point of approach, the periapsis, was about 8 000 km. This is well above the atmosphere of Venus so even though there might be a drag force, it will be very very small.

And finally, there is something known as obliquity. When we think of the Earth, and other planets spinning, it is tempting to think of them like the globes our teacher's desk: solidly spinning together.

However, planets are rarely entirely solid and so their spinning more closely resembles a floating ball of jello. As the planet spins, the mass tends to concentrate in the centre, creating a bulging shape. This bulge means there is a difference in the gravity as felt above the centre (or equator) of the planet, and the poles. This difference in gravity can cause an orbit to change over time.

There are some interesting formulas to consider here, and if you're interested, contact me (my email is on the top of the page), or check out the Nodal Regression Wikipedia page. To make a long post short, what we find is that it would take about 3.75 orbits before the satellite would veer off course and be out of specified parameters.

It makes sense that this perturbation would be small. As I mentioned before, this obliquity is caused by a bulge created when the matter of a planet moves toward the centre, caused by its rotation. However, Venus is spinning very slowly, so the force pulling the matter toward the centre would not be very large. It's like when you're on a carnival ride which hasn't started to speed up yet; you can feel some pull toward the side, but not too much.

So, at the end of all of that, we find that solar radiation pressure dominates. While obliquity is a problem, it takes much longer to become so and the solar wind only takes 16 seconds to cause our mission to fail.

So, what to do now? Well, these perturbations are inevitable. There are ways of mitigating them, of making them smaller, but even the best orbit, as in well designed, will be subject to changes.

Sometimes, you can't get rid of the risks. Sometimes, you just have to work with them and try to make them as small as you can. Looking at the formulas we've used, we can conclude that the solar panels are the big concern here. They are large, and they are reflective, and they will act like sails to push the satellite off course.

We could make them smaller, but the smaller they are, the less power they'll absorb, and we have a limit on the amount of power we will need to keep our satellite running. We could use an on-battery system. This is true, but could be more complicated to implement (and thus you might remember means more costly and prone to failure). So, we'll stick with panels, but they have to be above a certain size.

We could make them less reflective. True, but again, there are limits.

Finally, we could angle the arrays somewhat so they don't feel the pressure straight on. This could work, but a balance will have to be taken so that power is still absorbed by the Sun.

And there you have it! That's a more in-depth look into how to think and design for a space mission. I realize this post had a lot of information in it so I will reiterate.
  • Venus turns really slowly, Venus-synchronous orbit is not a good idea
  • The semi-major axis, the longest part of the orbiting ellipse, is related to the time it takes an object to orbit another. (Kepler's Third Law)
  • Once you know this semi-major axis length, you can find the closest and farthest points on the orbit between the object and the planet.
  • Orbits are not stable, and factors like gravitational effects, solar wind, and atmospheric drag can cause a satellite to veer off course.
  • Risk cannot always be eliminated and sometimes we have to work with what we have.
And most importantly, "The more complicated a space mission is, the more expensive and prone to failure it is."

I hope you've enjoyed this foray into space engineering. I will be working away at my next post and getting ready for grad school. Should you have any questions, or wish to see the assignment along with the solutions for further detail, please don't hesitate to contact me.

As always, thanks for reading.

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