The first step on the trip to Mars is the launch. Launch is the act of getting a spacecraft off the surface of the Earth and into an orbit around it. It takes a lot of energy to reach an orbit above Earth. Consider that just to jump a couple feet off the ground takes all the energy we can muster. To get a thousand kilogram spacecraft off the ground takes an incredible amount of energy. Not only do we have to overcome Earth’s gravity, but also the drag of the atmosphere.

Let’s consider the forces acting on a rocket. Look at Figure 1 showing a rocket just before liftoff. The two forces acting upon the rocket in this scenario are the rocket’s weight (W) and a normal force (N). A normal force is a force that acts on an object by a contact surface (in this case, the ground). A normal force also acts perpendicularly to the surface – because the ground is horizontal, the normal force acts vertically. If we add the forces together, we will find the net force (F_net) acting on the rocket: F_net = N – W. The weight is preceded by a minus sign because the weight of the rocket acts downward (the normal force acts upward and is thus positive, but does not require a plus sign by common mathematical sign convention). It is easy to understand from this situation that because the rocket is not moving, the weight is balanced by the normal force: N = W. Thus, the net force is zero.

Now let’s consider the scenario after liftoff. Look at Figure 2. There is no longer a normal force because the rocket is not in contact in the ground. The positive (up) force is now the thrust force (F_T; more on this later). Because the rocket is travelling in Earth’s atmosphere, there is a drag force (F_D; we can feel drag when we put our hands out a moving car’s window). Let’s find the net force acting on this rocket: F_net = F_T – F_D – W. The motion of the rocket depends on the magnitudes of these forces at an instant in time.

If the thrust force is less than the sum of the drag force and the weight (i.e., the downward forces are greater than the upward force), then the rocket will fall back to the Earth.

If the thrust force is equal to the sum of the drag force and the weight, then the rocket will continue travelling upward at the same velocity (it will not speed up or slow down). This scenario describes Newton’s 1st Law of Motion – this law (known as the “law of inertia”) simply means that if an object is in motion and is not acted upon by unbalanced forces, the object will remain in motion at the same velocity (it will not accelerate or decelerate). (The 1st Law also describes the scenario in Figure 1 – if an object is at rest and is not acted on by unbalanced forces, it will remain at rest.) In order to be travelling fast enough to orbit, the rocket must reach a minimum velocity of 8 kilometers per second (discussed later). If it does not reach this velocity, it will eventually fall back to Earth.

If the thrust force is greater than the sum of the drag force and the weight, then the rocket will accelerate upward (the velocity will continue to increase). This scenario illustrates Newton’s 2nd Law of Motion. The 2nd Law can be described mathematically by the equation F_net = ma, where m is the mass of the rocket and a is its acceleration. Thus, it is easy to see that the acceleration of a rocket is dependent upon the net force and the mass of the rocket.

If we rearrange the equation for Newton’s 2nd Law of Motion so that a is by itself (divide both sides by m), then we have:

Now we can more easily see the effect of the rocket’s mass on its acceleration. When the mass increases, the acceleration decreases. When the mass decreases, the acceleration increases. We can describe this mathematically as shown below:

This demonstrates the importance of keeping the mass of a rocket to a minimum – doing so will allow the rocket to accelerate much faster.

To figure out how much velocity we need to get into an orbit around Earth, we use the following equation:

where, ∆ means change and V means velocity.

So ∆V_Launch is the total change in velocity needed to launch a spacecraft into an orbit around Earth. ∆V is the final velocity minus the initial velocity. Since the velocity of the spacecraft is initially zero while it is on the ground, ∆V is simply the final velocity. ∆V_burnout is the leftover velocity that we need to maintain and orbit around Earth. We will talk about this velocity a little later. ∆V_gravity is the change in velocity needed to overcome the gravity of Earth. ∆V_drag is the change in velocity required to overcome drag.

To achieve the required ∆V, engineers at NASA use huge rockets. The actual size and mass of the rocket, which engineers call the launch vehicle, dwarfs the actual spacecraft, which is referred to as the payload. For a typical mission into Low Earth Orbit (LEO) the mass of the launch vehicle and the fuel is roughly 40 times the mass of the actual payload.

So, how does a rocket create the ∆V we need? (Answer: Rockets take advantage of what is described in Newton’s third law of motion.) Newton’s third law states that for every action there is an equal and opposite reaction. If you were to stand on a skateboard and push against a wall you would move in the opposite direction. This is an example of Newton’s third law. Cars use tires to push backwards against the road, which causes them to move in the opposite direction. True, rockets do not actually push against the air, but the movement of a rocket is still described by Newton’s third law of motion. A rocket works by creating super hot gasses and “throwing” them backwards very quickly. This “throwing” of the air is the action. The reaction is that the rocket moves in the opposite direction, forwards.

We use two basic numbers to characterize rockets. The first of is the thrust — the force that pushes the rocket into orbit. We calculate the amount of thrust a rocket produces by using the following equation:

where the thrust force (F) is equal to the mass flow rate (m) multiplied by the exhaust velocity (V_e). The mass flow rate is how fast mass is coming out of the rocket. The mass is the exhaust gas that comes from the burning fuel. Mass flow rate is measured in kilograms per second (kg/s). The exhaust velocity is a measure of how fast the hot gas leaves the rocket nozzle.

The other number we use to characterize rockets is the specific impulse (I_sp) — a measure of the energy content of a propellant and how efficiently it is converted into thrust. Basically, the specific impulse tells us how much “bang for the buck” we get out a certain type of rocket. To calculate the specific impulse, we divide the thrust by the weight flow rate:

The weight flow rate is the mass flow rate (m) multiplied by the gravitational acceleration of Earth (g = 9.81 m/s²). The specific impulse has units of seconds. The I_sp measures how much thrust we are getting for how much fuel weight we are using. A higher I_sp means that we are getting more thrust for less fuel, and it is a more efficient system.

Three different kinds of rockets are currently used in space applications: chemical, electrical and cold gas. Chemical rockets are the most common typein use today, and include liquid fuel rockets, solid fuel rockets and a hybrid of the two. Chemical rockets rely on chemical combustion that creates a super-heated, high-pressure gas. This high-pressure gas can only escape through the nozzle. According to Newton’s third law of motion, this gas leaving the rocket at a very high velocity is the action, while the rocket moving in the opposite direction is the opposite reaction.

Liquid fuels are stored in large tanks and are pumped into a combustion chamber where they ignite before leaving the rocket through the nozzle. Figure 1 shows a diagram of a liquid fuel rocket. Liquid fuel systems are complicated since they require several tanks, complex valves and intricate piping, but they create a lot of thrust, have a high Isp, and can be throttled and restarted if needed. The space shuttles main engines use a liquid fuel that is a mixture of liquid oxygen and liquid hydrogen. Figure 2 shows the liquid fuel tank and the liquid fuel main engine on the space shuttle.

Solid fuel rockets can be described as a tube, filled with a solid fuel, capped at one end and with a nozzle at the other end. The solid fuel is highly flammable and works in the same way the liquid fuel system works. As the fuel burns, a hot and high-pressure gas comes out of the nozzle creating thrust. Solid fuel systems are very simple, cheap and reliable, but they cannot be turned off once they start and they are not as efficient as liquid fuels. An example of a solid fuel system is the Solid Rocket Boosters (SRB) on the space shuttle (see Figure 2). They are the two white rockets strapped to the side of the vehicle and are used to help get the space shuttle off the ground. Once the fuel inside the boosters is exhausted, they are released from the shuttle and dropped into the ocean. Bottle rockets and model rockets are both considered solid fuel rockets.

Electrical rockets use electricity to accelerate particles that are directed out the back end of the spacecraft, thus creating thrust. The rockets generally use charged atoms called ions that have a positive or negative charge associated with them. An electrical source, such as solar cells, or a nuclear reactor is used to charge plates in the engine with different charges so that the ions are pushed and pulled out of the spacecraft. The downside to electrical rockets is that they cannot create much thrust. If you hold one sheet of paper in your hand, the force with which the paper pushes on your hand due to its weight is roughly equal to the thrust of an electrical rocket. The plus side to electric rockets is that they are very efficient and have a high Isp. Since the thrust of an electrical rocket is so small, it is impossible to launch a rocket into space; but, once a spacecraft is in an orbit around Earth, an electrical rocket can be used to escape the Earth’s gravity and head to different places around our solar system. The small thrust means it takes a long time for the craft to build up sufficient escape velocity, but the high efficiency of the system means less fuel is needed to achieve the desired velocity. The first use of electrical rockets in space was on board Deep Space 1, which launched onboard a conventional liquid fuel rocket on October 24, 1998. Once it was in orbit, it started its own engine and eventually reached the Comet Borrelly in September of 2001.

Cold gas rockets use pressurized gas that is not ignited. This is usually a nonflammable gas such as nitrogen or helium. A balloon that is filled and then released is an example of a cold gas system. The pressurized gas can only escape out the nozzle, and as it does, it creates thrust. Cold gas systems have very low thrusts and are very inefficient (low I_sp), but they are very simple and cheap. They are often used on spacecraft to make very small velocity changes where large rockets are overkill. The rocket packs that astronauts use when they are outside the space shuttle or international space station use cold gas rockets.

Table 1 shows the different types of rockets and the typical thrusts and specific impulses for each system.

Once a launch vehicle has taken the spacecraft out of the Earth’s atmosphere, it now must enter into an orbit. An orbit is a circular or elliptical path around a celestial body (sun, star, planet, asteroid, etc.) on which an object such as a spacecraft follows. One common misconception is that no gravity exists on the space shuttle and international space station. In fact, gravity is acting on a person in orbit around the Earth, but s/he does not feel it like we feel it on Earth, because no ground exists to push back on a person in space. So, why doesn’t a spacecraft just fall back to Earth once the rockets shut off? This is because the velocity of the spacecraft wants to move it past the Earth, while gravity pulls it back. These two actions cancel out to form an orbit. An orbit can be explained by Newton’s first law of motion, which tells us that an object in motion stays in motion unless a force acts against it. This means that an object will move in a straight line unless a force pushes it in a different direction. For any object to change the direction in which it is moving, a force must act upon it. For example, when you are on a bike and want to turn (change directions), your tire must apply a force to the ground. This force is called friction; without friction, it would be like biking on perfectly smooth ice. If you tried to turn, there would be no frictional force; you would keep moving in a straight line as Newton’s first law describes. Just like your bike, a spacecraft will not turn unless a force acts on it. The force that acts on objects — ultimately causing them to orbit a planet or a star — is gravity. An orbit is just a balance between the velocity of an object and gravity.

Figure 3 shows how gravity affects the path of a spacecraft. The diagram on the left shows the path of a spacecraft if there was no gravity. In this case, the spacecraft would continue along in a straight line. The diagram on the right shows the path of a spacecraft under the influence of gravity. Gravity is pulling the spacecraft towards the center of the Earth, while the velocity of the spacecraft makes the spacecraft want to keep going past the Earth. The balance of these two opposing actions is known as an orbit. For a low Earth orbit (LEO), which has an altitude between 600 and 2000 kilometers above the Earth’s surface, the spacecraft must have a velocity of about 8 kilometers per second. That means that it can go all the way around the Earth in 90 minutes. So, what happens if the spacecraft is not moving (that is, it has no velocity)? If there is no velocity, then the only force acting on the spacecraft is gravity. This means that a spacecraft would fall to Earth just as a stone falls to the ground when you drop it. So, what happens if the spacecraft is moving much faster than the 8 km/s needed to maintain a LEO? In that case, the gravity will not be able to hold the spacecraft as close to the Earth, and the spacecraft will either move into an orbit that is further away from the Earth, or if it is moving fast enough it will overcome the Earth’s gravity entirely. This is called the escape velocity, and it is the minimum velocity needed to escape the Earth’s gravity.

Sir Isaac Newton performed a famous mind experiment to demonstrate how an orbit works that involves shooting cannons off the top of a mountain. See a demonstration of the cannon ball orbit on the NASA website at http://spaceplace.nasa.gov/how-orbits-work/.

Now that our spacecraft has left Earth’s gravity, our mission is to arrive at Mars. We have left the influence of Earth’s gravity, but we are not free of gravity altogether. Since we are now orbiting around the Sun, we are now under the influence of the Sun’s gravity.

Thus far, we have talked about circular orbits — the simplest kind of orbit. However, most orbits are actually ellipses, a stretched circle. Ellipses are often called ovals. Figure 4 shows a diagram of an elliptical orbit.

Two foci (each one called a focus) define an ellipse: the periapsis, which is the point on the elliptical orbit that is closest to the planet or sun; and the apoapis, the point furthest from the planet or sun. You may have also heard these points called perigee and apogee. These are the periapsis and apoapsis for an elliptical orbit around Earth, respectively. In an elliptical orbit, the Earth (or other massive body) is located at one of the two foci. Elliptical orbits enable movement between planets. Using the Sun as one of the foci, and the Earth as the periapsis, the spacecraft will actually be closer to the Sun when it is at the periapsis. When the spacecraft is at the apoapsis, it will be further away from the sun. This is useful for traveling to planets further from the Sun such as Mars. Figure 5 shows how half an elliptical orbit can be used to get from Earth to Mars.

In addition to great engineering and excellent calculations by scientists, it takes good timing to reach Mars. Since the Earth and Mars are both moving, it is like standing on a moving platform and trying to shoot a basketball into a hoop that is moving as well. To make things worse, since it takes about 6 months for a spacecraft to go from the Earth to Mars, scientists and engineers have to anticipate where Mars is going to be when the spacecraft gets there. If we try to shoot a spacecraft right at Mars, by the time it actually gets there, the great Red Planet will be long gone. Once we get to Mars, we must slow down so that we are in an orbit around our destination. From our orbit, we can take photographs of Mars, take scientific readings, or even land on the planet.