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 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.
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!