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How to Get to Mars

This is going to be the first in a series on issues surrounding colonizing Mars.  I will talk about why it is so incredibly difficult to actually get there and get back as well as some ideas on how we should realistically be looking at minimizing the costs to do this.

Ever since the 1960s, we have been trying to get to Mars and take pictures and explore.  Mars has always captured our imagination, since it seems to tantalizing that it could contain life. It is right there within our grasp.  But, still, it is so far away.

Almost 2/3 of all missions that have been slated to go to Mars have failed.  Some of these include rockets that have blown up.  Others include a Russian lander that returned about half of one image before it stopped working.  Viking was the first lander that actually took pictures and really worked.

We can go to Mars about every other year.  This is because a Mars year is pretty close to two Earth years, so Mars and Earth have the correct positions once every Mars year.

In this post, I will walk through how we actually get to Mars right now, independent of cost or any real consideration – just the basic facts.  In the next post, I will walk through some of the costs in terms of rocket fuel needed to actually do this. Here we go!

The first thing that the spacecraft has to do is to get off the Earth.  The easiest way to do this is to pick a good direction and just accelerate up to just over the escape velocity of the Earth.  This is about 11.2 km/s (about 25,000 MPH) on the surface of the Earth.  That means if you launch something with >11.2 km/s, it will escape Earth’s gravitational field and won’t return. (Hmmm, I need to write a post on escaping Earth and other gravity wells.)

Slide1
To escape the Earth gravitational well, pick a direction and go at a speed larger than 11.2 km/s. You will get away with it!

Now that the spacecraft has escaped Earth, let’s switch frames of reference.  It may seem like 11.2 km/s (25,000 MPH!) is super fast and our spacecraft is definitely on its way to Mars.  Nope.  It has escaped Earth, but that just means that it is going around the sun with the Earth.  Take a look at the illustration below.  This shows that if a spacecraft ONLY escapes Earth, it will just orbit the sun with the Earth, staying in roughly the same position with respect to the Earth. Interestingly, the Earth is moving at 29,800 m/s, which is about 66,650 MPH.  So, our spacecraft went from moving 0 MPH with respect to the Earth to moving 66,650 MPH with respect to the sun.

Slide2
If the spacecraft escapes the Earth, but doesn’t do anything else, it will just orbit the sun next to the Earth.  Something more is needed!

In order to go towards Mars, you have to do what is called a Hohmann transfer.  This is where you go from having a roughly circular orbit to having an elliptical orbit, with one side of the ellipse being at Earth’s orbit, and the other side being at Mar’s orbit. In order to do this, you have to go to a higher orbit, which requires the spacecraft to accelerate and increase its velocity.  To get to Mars, the spacecraft has to speed up to 32,700 m/s, or 72,150 MPH.  This is a difference of 2,900 m/s or 6,500 MPH, so the spacecraft has to speed up by this amount in order to change trajectories towards Mars.

Slide3
In order to get on an Earth-Mars transfer orbit, the spacecraft has to increase its velocity once it escapes the Earth.

Time passes.  The worlds and our spacecraft move.  We don’t need to use any fuel at all, since the spacecraft is just coasting towards where Mars is supposed to be in a few months.Slide4

After about 8 months, the spacecraft arrives at Mars!  Yeah!

Slide5
The spacecraft arrives!

Now, if we do nothing, the spacecraft will continue to be on an elliptical orbit, and will fall back towards the Earth.  This is very bad, so we have to do something about it!

Slide6

Interestingly, in order to stay in Mars’s orbit, the spacecraft has to accelerate again.  This is because Mars’s orbit is above the elliptical orbit, so it demands an increase in velocity. Mars is moving at about 24,100 m/s or about 54,000 MPH. Our spacecraft, when it arrives at Mars, is moving at about 21,500 m/s or 48,100 MPH.  This means that the spacecraft has to speed up by about 2,600 m/s or 5,900 MPH.

Slide7

In order to not fall back toward Earth when the spacecraft arrives at Mars, it needs to speed up again!

Now, the spacecraft is in a very similar circumstance as when it was near the Earth.  If we do nothing, it will just orbit the Sun next to Mars.  We want to either have the spacecraft orbit Mars, or we want to have it land on Mars.  In order to do that, the spacecraft has to slow way down. If it orbits Mars, it has to slow down a fair bit, but less than if it were going to land.

The change in velocity needed to get into orbit is a bit complicated to figure out.  First we have to figure out the escape velocity of Mars.  The reason for this is that if the spacecraft is way far away from Mars and doesn’t do anything at all, it will smash into the surface at the escape velocity, which is 5,000 m/s or about 11,200 MPH.  To stop this from happening, the rocket has to slow down by this much (assuming that there is no atmosphere!)

Orbital velocity at 400 km above Mars’s surface is about 3,360 m/s or 7,500 MPH. From a long way away from Mars, the spacecraft can fall toward Mars, and slow down to about 3,360 m/s from the hypothetical escape velocity of 5,000 m/s.  That means that the spacecraft has to slow down by about 1,640 m/s or about 3,700 MPH. The spacecraft will then be in orbit around Mars.

To get to the surface (assuming that there is no atmosphere), the spacecraft has to slow down another 3,360 m/s or 7,500 MPH.

One of the cool things about spacecraft around Mars is that they often use aerobraking to change their orbit or slow down enough to land.  Aerobraking is where the spacecraft enters the upper atmosphere a tiny bit to experience drag and will slow down.  It is a time consuming, but very inexpensive way to slow down enough to get into Low Mars Orbit, or to land.  The spacecraft could save about 5,000 m/s by using aerobraking.  But it is complicated to do that.

Slide8
Now, when it is close to Mars, it has to slow way down in order to not be slammed into the planet.

In summary, the total delta-V that is needed to get to Mars, including escaping from Earth, getting into an elliptical orbit towards Mars, then getting out of the elliptical orbit near Mars, and landing on the surface (not using aerobraking!), is close to 22,000 m/s or about 49,000 MPH. This is a huge amount of delta-V, and almost all spacecraft end up using aerobreaking to save around 5,000 m/s.

In the following post, I will talk about how much fuel is needed in each of these steps and we can figure out how large of a spacecraft we can land on Mars.

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