Escape Velocity

Getting to another planet, or getting to the sun involves getting out of Earth’s gravity well. Essentially, Earth’s gravity extends outwards forever. If Earth were all alone in the universe, its gravity would be felt everywhere. If anything were sitting out in space and not moving at all with respect to Earth, it would feel Earth’s gravity and begin to fall towards the Earth.

Earth’s gravity well. Everything falls back towards the Earth!

Earth is not alone in the solar system, though.  The Sun is much larger than Earth, and it’s gravity well is much, much bigger than Earth’s.  So, if you get out of Earth’s gravity well, you are still inside of the Sun’s gravity well.  Between the Sun and the Earth, there is a gravitational null, where the gravity wells add together to make a little hill.  If you are on one side of the hill (the left side), you fall towards the Sun, and if you are on the other side of the hill (the right side), you fall towards the Earth.

The Earth’s gravity well is inside of the Sun’s gravity well.  In between the Sun and the Earth, the wells add together and sort of cancel each other out, making a little hill.  At the top of the hill is a little gravitational null.  If you are on one side of the hill, you fall towards the Sun.  Of you are on the other, you fall towards the Earth.

If you want to get out of Earth’s gravity well, how do you do it?

Imagine if you were really in a valley and the walls of the valley were not grass or something, but were very, very smooth – like ice.  If you tried to climb up the sides, you would constantly just fall back down into the valley.  Let’s say that you have a ball. If you roll the ball up the side of the valley, it would probably roll up for a ways, then it would slow down, stop eventually, and then come right back down to the bottom of the valley. The ball would be stuck in the gravity well.

But, I am sure that you can imagine, if you were to roll the ball fast enough, it would go up the side of the valley, but still have enough speed at the top of the valley to keep going. It would go over the top of the hill, and escape the valley.  If the sides of the valley were very tall, then you would have to roll the ball really, really fast.  If the sides were not very tall at all, you wouldn’t have to roll the ball very fast at all.

The same thing is true of a planet or the sun or a moon – really any body that has mass.  Let’s consider Earth specifically.  A super simple example is if you throw a ball up in the air: it goes up, slowing down all of the way.  It eventually stops completely, reverses course and falls back to Earth.  Just like the ball in the valley example.  You roll the ball too slow, and it will climb up the side of the valley, and then turn around and come back down. Interestingly, if you ignore air resistance, the ball would hit the ground with the same speed that it was thrown up in the air.

If you switch from a ball to a gun, and fire a gun straight up in the air, the bullet would go up and up, slowing down the whole time.  Eventually, it would stop completely and fall back to Earth.  Luckily, it is incredibly hard to shoot straight up in the air, since the bullet falls back to the ground with the same speed as it leaves the gun.  So, shooting a gun in the air is not too smart, since bullets don’t have enough speed to leave the Earth!  The bullets come down… somewhere. In fact, if you got the biggest gun ever made, it still wouldn’t be able to shoot bullets fast enough to escape into space.  The bullets would travel about 100 miles into space, then stop and fall back to Earth.  This gun, and the guy who made it, are described here. (It is a cool story!)

On the other hand, a rocket that could go a bit over 25,000 miles per hour straight up would never stop moving away from Earth.  The rocket would slow down and slow down and slow down, but would never stop.  Eventually, the rocket would be outside of Earth’s gravity well, with the Sun’s gravity influencing the rocket more than Earth’s gravity.

So, in summary, if you aimed a rocket straight up in the air and got it to go a bit over 25,000 MPH, the rocket would escape Earth’s gravity.  If you want to get to Mars or any other planet, or even the Sun, you have to have a rocket that can go at least this fast, or produce this much “delta-V”.

The term delta-V is used to describe a change in velocity made by a rocket.  So, in this case, the rocket is initially sitting on the ground not moving.  It needs to change velocities from sitting on the ground not moving at all to moving straight up with a speed of over 25,000 MPH.  Delta-V. It would then escape the Earth’s gravity well.

Interestingly, escape velocity works backwards too.  For example, let’s consider trying to land on the moon. (I consider the moon because it has no atmosphere, which complicates things). Let’s say that we have a ship that is on its way from the Earth to the moon,  and that it has just barely slipped from being in Earth’s gravity well to being in the moon’s gravity well, but is moving incredibly slow at that point. If absolutely nothing is done, the ship will fall towards the moon, gaining speed all of the time.  If nothing continues to be done, the ship will splat into the surface of the moon with a speed of about 5,300 MPH. Not coincidently, this is the escape speed of the moon.

What can be done to save the poor astronauts who are on board the possibly doomed rocket ship? Well, the ship can fall faster and faster and faster towards the surface of the moon, gaining almost all of the 5,300 MPH, and at the last possible second, the rocket can fire, slowing the rocket down to almost zero, for a nice touch down.  This implies that the rocket needs to be capable of producing a delta-V of 5,300 MPH (slowing from 5,300 MPH to zero).  There would be an incredibly strong acceleration at the end, though. This might flatten down the poor astronauts! A much better alternative, especially of there are astronauts on board, is that the rocket can continuously fire the rockets, keeping the speed to some manageable level, so that it doesn’t have to produce so much acceleration at the very end. Interestingly, from the rocket’s point of view, these scenarios are almost identical to each other – each needs the rocket to produce a total of 5,300 MPH of delta-V. In one case, it does it all at once, and in the other case, it does it slowly, letting the rocket ship speed up a bit (due to gravity), then slowing it down using the rocket, then repeating until the rocket is safely on the ground.

So, landing on a planet/moon with no atmosphere requires a delta-V of the escape velocity, just like taking off from the planet.  I find that really cool!

Two asides here:

The first is that the moon landings were not like this at all.  The Apollo capsules went to the moon and got into orbit around the moon.  Then the landing module (which was much smaller than the Apollo capsule), took two of the astronauts down to the surface.  This small module had to burn away the orbital velocity of the Apollo capsule (plus a bit extra).  Because the landing module was so much smaller than the Apollo capsule, it saved a huge amount of fuel.  If the astronauts had landed the Apollo capsule, the Saturn-V rocket would have had to have been much bigger.  That was not possible at the time.

The second is that when we land on planets such as the Earth, Venus, and Mars, we don’t need to have the delta-V to slow all the way down, since each has an atmosphere.  We use the atmosphere to slow us way, way, way down, which saves a huge amount of fuel.  When ships return from the International Space Station, they do a very small burn to put them on a trajectory that takes them into the atmosphere a tiny bit.  This slows them down to the point where they get dragged into the atmosphere and de-orbit because of this.  If the Earth had no atmosphere, it would take about 17,000 MPH of delta-V to get from the ISS to the ground.  Since we have a robust atmosphere, it only takes a few hundred MPH of delta-V.  Mars, on the other hand, has a really weak atmosphere, and when we try to land rovers and such on Mars, the atmosphere doesn’t stop them very well (i.e., terminal velocity on Mars is too fast, and stuff will break if it hit the ground traveling at terminal velocity).  So, there needs to be some way to reduce the speed of the object a bit.  NASA comes up with crazy ways to do this type of stuff, and you should read about the Mars rovers to see these crazy ideas!

Finally, every object has an escape velocity.  For the Earth, this is about 25,000 MPH.  For the moon, it is about 5,300 MPH.  For Jupiter, it is 135,500 MPH (wow!).  Jupiter has a HUGE gravity well! But, it is nothing compared to the Sun’s gravity well. If you escaped from the Earth, then wanted to escape the Sun, you would have to go about 95,000 MPH away from the Sun – even being 93 million miles away from the Sun!  If you were near Mercury, and wanted to escape the Sun (not Mercury), you would have to go 152,000 MPH!  Solar Probe Plus, a mission to the Sun, is going to 10 solar radii.  If it wanted to fully escape the Sun at that point, it would have to be going 440,000 MPH!

Just FYI, my escape velocity is 0.1 mm/s.  So, anything that is moving away from me with a speed of about 0.1 mm/s will escape. That is pretty small!  But, I am happy that my escape velocity is so small, since otherwise I would accumulate a lot of stuff!

Anyways, escape velocity is an important concept to understand when one is trying to get off of a planet and get to some other body.  I hope this helps explain it a bit!


Max-Q and Why Does it Matter?

In a rocket launch, they almost always talk about Max-Q, which is the point in the launch sequence where the rocket experiences the maximum dynamic pressure. First, let’s talk about what that actually means.

The rocket, as it is going up into space is experiencing three forces: gravity (down), thrust (up), and atmospheric drag (down).  Gravity is probably obvious, since you are probably sitting in a chair or on the couch and are feeling its effects (well, you are probably feeling the normal force from the chair that is pushing up on your backside, but let’s just say that you are feeling gravity). Thrust is what the rocket does as it expels fuel to make it go up. I have a post on that.

I also have a post on drag and terminal velocity if you would like a refresher on what all of that means. But, as a tiny backstory, atmospheric drag is like friction that an object feels as it moves through a fluid. So, when you are riding a bike, you feel drag, which makes it so you have to pedal harder into a headwind than a tailwind. This force is proportional to the density of the medium (it is MUCH harder to ride a bike underwater than it is in the atmosphere!), and the velocity squared (when you go twice as fast, you have to pedal four times as hard).

Returning to the subject at hand:

When the countdown ends and the rocket starts to fire, but before it starts to move, there are two forces acting on the rocket: gravity and thrust.  Thrust has to be a bit bigger than gravity for the rocket to start moving, otherwise the rocket will just sit there.  When the rocket starts moving upwards, it gain speed, and starts to experience a drag force.

Now, if the rocket flew horizontally, or if the atmosphere extended upwards forever, the drag force would increase and increase and increase as the rocket got faster and faster and faster.  As it happens in reality, the rocket launches mostly in a vertical state, and the atmospheric density decreases quite rapidly with altitude.  By about 23 km altitude, the atmosphere has decreased down to about 10% of its density.  For reference, airplanes fly at about 1/2 of this altitude, so the density is about 33% of its sea-level value.

The situation with the rocket, then, is that it starts to accelerate and the drag force starts to grow dramatically, since the force is related to velocity squared:  whenever the speed doubles, the force quadruples.  But, at the same time, the density is decreasing, so the force is weakening because of this.  At some altitude, the decreasing density wins out over the increasing velocity, and the drag force starts to decrease.

It is this point – where the increasing velocity is balanced by the decreasing density of the atmosphere and the drag force starts to decrease that is called Max-Q.

Screen Shot 2018-06-24 at 4.27.21 PM
A plot of the drag on the rocket as a function of altitude (in meters). The drag force is negative at this stage, since it is towards the ground.  Max-Q happens around 11 km in altitude in this simulation.

Now the question is – why do people care?

Well, rockets are really unstable. The thrust is coming out the back end and they are extremely long and narrow.  The thrust vector has to be right through the center of mass of the rocket in order for it to not rotate.  If the thrust vector is off, it could easily start to roll over.  If thrust and gravity were the only forces, it would be a bit complicated to control, but when you add in aerodynamic forces, it becomes even more complicated.  Older rockets (and model rockets!) used to have fins in order to help with this.  The fins made it so that if the rocket tipped at all, the aerodynamic forces on the fins would help correct for the tipping and apply a restorative force back into a non-tipping orientation. See the picture below.  There are aerodynamic forces all along the rocket, but the fins have the largest forces, so those forces win, and the rocket will rotate around the center of gravity and restore back to vertical.  With no fins, this restorative force doesn’t exist, since the forces along the rocket are all roughly equal, which makes it so that the rocket may or may not rotate one way or the other around the center of gravity.  Because of this, the rocket motors have to solve the issue all on their own.


So, the drag force makes is a bit harder to control the rocket. Most rockets use computers to figure out how the rocket is tilting and adjust the thrust vector of the engine to rotate the rocket back to vertical.

If the computer stopped working and the rocket couldn’t adjust back to vertical, what would the problem be? The problem is that the rockets are not exactly super rigid and made out of super-strong materials, since they are designed to be as lightweight as possible.  It is designed to fly like an upright pencil through the atmosphere.  If you were to turn the pencil over and try to shove the pencil in a sideways configuration through the atmosphere, the rocket would probably shred to bits.  This is very bad.  So, the rocket needs to be aimed upwards as much as possible.  Any deviation from this upright position, and the aerodynamic forces could rip the rocket apart.

If the rocket tilts too far, the forces on both sides of the center of gravity with cause the rocket to break apart. That is not good.

Max-Q is the time during the rocket’s flight in which the aerodynamic (drag) forces are the strongest.  So, you really don’t want the rocket to tip or do anything wonky during this time.  After Max-Q, the force decreases quickly, and the engineers can relax a bit.

It is around Max-Q, where the rocket starts to tilt a bit and rotate towards the horizontal direction.  This is because rockets only go upwards to get to their correct altitude.  They really need to go horizontally at about 7.6 km/s (that is fast).  If the rocket were to go straight up to like 500 km, then tilt over, it wouldn’t work very well, since it takes a long time to accelerate up to 7.6 km/s. Turning down low allows the rocket to take a while to get up to 500 km and take a while to get up to 7.6 km/s speed.  The rocket times it just right so that both are met at about the same time.  The location of Max-Q is where this tilting starts.





Engines, Rockets

Why the Falcon Heavy Makes Good Business Sense

This week, Space-X had a test launch of the Falcon Heavy, the largest rocket ever launched besides the Saturn-5. It was a great success, putting a Tesla Roadster into trans-Martian orbit. Space-X has taken a fantastic first step. If you have not seen the launch, you should definitely watch it – it is fantastic.

Falcon Heavy at liftoff (Elon Musk via SpaceNews).

While the Falcon Heavy is very cool and a great achievement, it is also a good business investment.  There are two reasons for this.

The first reason is that the Falcon Heavy is a good business decision is that the Falcon Heavy is simply three Falcon-9s strapped together. Other rocket companies have different lines for different weight classes.  For example, Orbital/ATK has the Pegasus rocket, which last launched the eight CYGNSS satellites.  The next mission that will use the Pegasus is ICON, which will launch later this year.  That is about 1.5 years between launches.  The Pegasus launches off of an airplane, which is super cool.  The next size up from the Pegasus that Orbital makes is the Minotaur-C, which is capable of of carrying about four times as much mass to orbit as the Pegasus.  The Minotaur-C uses some of the same components as the Pegasus, but they are pretty different.  This means that Orbital needs to keep up two lines of production, which is quite difficult and costly.

The Falcon-9 uses 9 Merlin 1D engines in the first stage and 1 Merlin 1D (Vacuum) engine in the second stage. So, it uses essentially 10 of the same engines.  The Falcon Heavy uses 3 Falcon-9 first stages for a total of 27 Merlin engines in the first stage, with a second stage that is identical to the Falcon-9 second stage, for a total of 28 Merlin engines.  The engines and first stages can be used as Falcon-9s or Falcon Heavies.  This makes the production costs much lower, since they don’t have to maintain different manufacturing lines for different rockets.

What would be super awesome is if they could have a rocket that used one Merlin engine (a Falcon-1 rocket, which used to exist) that could compete with the super small rockets, like the Pegasus or the Electron (as discussed in a previous post).  But, Space-X made a choice that their smallest rocket would be the Falcon-9, which was a good decision, since the Falcon-1 could not really be expanded, like the Falcon-9 to the Falcon Heavy.

(Side Note: The Falcon Heavy is a relatively small rocket compared to the BFR that Space-X is planning for going to Mars.  There are plans for more, extremely large, rockets. The BFR is going to be a fundamentally different design than the Falcon Heavy, which is somewhat sad, since I just wrote a bunch of words above about how awesome it is that Space-X are combining the same rockets to get bigger rockets. I have no real idea how much development has gone into the BFR yet.  I will find out and get back to you!)

The future of rockets compared to the Saturn V. The Falcon Heavy is the biggest rocket available today, but it is very small compared to what is needed to go to the moon or Mars with humans. (

The other thing that Space-X has done is to make the Falcon-9s reusable. The fact that they can fly back down and land makes them very valuable.  While the reusability of the rocket engines, and the number of times that they can be reused, is still questionable, it is quite certain that they will get there and the engines will be able to be used many times.

The other reusable space vehicle has been the Space Shuttle.  The problem with the shuttle was that it was extremely costly to reuse it – about $500,000,000 to launch the shuttle. (I will write a post on this soon!) The Space-X rockets are fundamentally different things.  They do not have a super complicated heat shield, or relatively complicated solid rocket boosters.

Interestingly, the primary reason that the Falcon-9 lands the way that it does, standing up using thrust, is that this is the way that it would have to land on Mars. Because Mars has such a weak atmosphere, it is very hard to land with parachutes or with wings, like the shuttle. Space-X therefore designed the Falcon-9 so that it could land vertically.  Not that there will be any Falcon-9s on Mars, but the vertical landings are great tests of the technology so that when rockets do land on Mars, they will have undergone significant real-world tests. That is in addition to making the rockets reusable, which drives the price down significantly.

In summary, Space-X is making really good business decisions in its Falcon-9 and Falcon Heavy lines: using the same engines and the same structures is really smart, and making the rockets reusable is genius.