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| From earth to another planet |
To get to the planets in our solar system, you will need fuel. And I'm not talking about a small amount of it. The fuel is vital to send our rocket into interplanetary space, but it is also needed for maneuvers corrections and changing of orbits. There are actually many ways to reach a target – in our case, the planets – and they are all different from each other, but one thing is sure: all of them, make use of an amazing combination of math and physics knowledge.
Indeed, the planets are moving in space, and if you think that we only need to "aim and shoot", I am sorry to inform you that you are wrong. Thankfully, we have a nice description of how planets of the solar system move in space – their motion happens in the potential of the Sun, and the orbits are almost circular. Let's say, in general, they are elliptical orbits. This is indeed what Kepler found some centuries ago. So, once we understand that the aim and shoot method can't work, we need a different approach.
We could decide, for example, to reach a planet by means of the Homann transfer. This kind of transfer is basically the simplest one, and can always be performed if you want to reach your target in a reasonably small amount of time. This is accomplished by placing the craft in an elliptical orbit that is tangent to both the initial and target orbits in the same plane. The maneuver needs fuel: it uses two engine impulses, the first places it on the transfer orbit by raising the craft to the target orbit's altitude, and the second makes the craft match the target orbit. The Homann maneuver often uses the lowest possible amount of impulse to accomplish the transfer but requires a relatively long travel time than higher-impulse transfers.
The Homann transfer, however, imposes definite launch dates. The actual travel time will be given by half the time it takes to travel the entire Hohmann orbit, which is a value easily calculated through Kepler's third law. As we said, the Homann transfer makes use of a small amount of fuel in order to perform the orbital transfer, but if we wanted, we could go faster. How? Well, the answer is pretty simple: we could carry more fuel to boost our spacecraft. But this has some withdrawals.
First of all, we would have to carry around a lot of extra fuel, which would also mean increasing the speed at launch: basically, a dog biting its own tail! The third type of transfer that has gained a lot of fame and success during the last decades, is the one that makes use of the so-called invariant manifold theory. Basically, you need to picture the space surrounding the planets as filled with many highways, and every highway is characterized by some value of energy.
Basically, an object with specific energy will always travel on its own highway – that is, the highway that matches its own energy value. This is, of course, a simple and naive idea, but it gives you a taste of what's mathematics and physics beyond this. Such highways are always there and they are fixed - immutable. That's why they are called invariant manifolds. The manifolds are mathematical objects and they are created by the presence of the planet's potential.
Now, the interesting thing is that such highways connect, for example, the Moon and the Earth, or Jupiter and the Sun, as well as the Earth and the Sun. And once you manage to put your spacecraft on a specific highway, characterized by specific energy (given by the velocity of your spacecraft), you can basically go to the Moon and Back, or to the Sun and back, with basically no fuel. You would only need it at the departure, to get into the highway, and at some specific points of your trajectory, for example, when you decided to come back.
Basically, what is put on the highway, stays on the highway. But computations of such highways and the conditions to get on the invariant manifolds have to be really accurate, because these manifolds can be unstable, meaning that tiny deviations in energy, or velocity, can take you on a different highway very soon. However, this approach is -most of the times-slower than the Homann approach, because the manifold orbits might have weird trajectories to follow, meaning that the highway could basically be a mess.
Here's, for example, what the invariant manifold tube looks like in the case of the Earth-Moon system. Anyway, we also need to consider that the trip duration depends on the kind of encounter we want to have with the planet. There is indeed a lot of difference between arrival with orbital insertion and arrival with a fast flyover. For example, for a fast flyover, the departure speed can be preserved until the end, without slowing down, meaning that we can spare some fuel.
Also, you need to take into account that trips to the inner planets are really complicated, because in that case you are going toward, for example, Mercury and Venus, but you are also going closer to the Sun, and being attracted by its strong gravity is not an advantage at all, It's fine only if you're content to do fast flyovers... but if you want to orbit a planet like Mercury or Venus you have only two options: braking with retrorockets to counteract the Sun's gravity or losing speed by doing flybys with neighboring planets. Well, these were the basic principles of interplanetary navigation. Now let's see how, during the years, space missions were designed and how long they took to reach the planets in our solar system.
Mercury
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| Earth to Mercury |
Let's start with Mercury. Distance from the Sun: 36 million miles (58 million km). Minimum distance from Earth: 56.5 million miles (91 million kilometers). Despite being so close to Earth, Mercury is probably the most difficult planet to reach. To reach this planet we have to follow the Hohmann orbit.
This orbit would be huge: 192.6 million miles or 310 million kilometers long! However, given the right amount of fuel, we can cover this distance in something like 100 days. This would be the case for a nice flyover of the planet. Our spacecraft will travel and 37 miles per second, which means more than 124.000 miles per hour. We won't see much of Mercury. That's why, in 1974, when Mariner 10 made the flyover, becoming the first probe to approach Mercury, engineers slowed it down to allow more time for photographic shots...
The trip lasted 133 days. Mariner 10 isn't the only probe we've sent to Mercury. Bepi Colombo, for example, was launched in 2018 and will reach the planet in 2025. The mission aims to orbit Mercury to study this amazing planet. But to do that, the probe has to slow down. This can be done by losing the probe's momentum by encountering another planet. In fact, Bepi Colombo will fly by Earth, Venus and Mercury. Performing gravitational slingshot maneuvers on such occasions would reduce fuel consumption, making it less overall than the need for a direct route from Earth to Mercury, which might be faster, but certainly more expensive.
Venus
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| Earth to Venus |
As for Venus, its distance from the Sun is 79.5 million miles (128 million km), and the minimum distance from Earth is 25 million miles (41 million km). A long way of 249 million miles – 402 million kilometers – is the distance an average probe can travel in less than 150 days. Venera 1, launched in 1961, was a Soviet probe that reached Venus in 97 days.
However, it performed a flyby at a very high speed and was then lost in orbit around the Sun. meet? It happens when you get close to the sun! But we didn't give up. The following year NASA's Mariner 2 probe flew by the planet - but more cautiously, taking 115 days. The mission was a success. Most recently, in 2006, ESA's Venus Express reached Venus using the main engine to capture it in Venus's gravity. After launch and separation from four launcher stages, Venus Express spent 153 days in an interplanetary transfer orbit.
During the Venus trip, the spacecraft was contacted daily for health checks and navigation using high gain antennas. The spacecraft was placed on a Venus arrival trajectory with mid-course navigation and a final course adjustment was made on 29 March 2006 to fine-tune the arrival hyperbola for Venus orbit insertion.
Venus Express studied the complex dynamics and chemistry of the planet, and the interactions between the atmosphere and surface, which provided clues about surface properties. It studied the interaction between the atmosphere and the interplanetary environment (solar wind) to better understand planetary evolution. Venus Express observed the Venusian atmosphere and clouds with unprecedented detail and precision.
Mars
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| Earth to Mars |
Let's go to Mars. The distance from the Sun is 141 million miles (228 million kilometers), and the shortest distance from Earth is 34.7 million miles, 56 million kilometers. A journey lasting about 8 months would be required to reach Mars without any rush, which is necessary to cover Hohmann's orbit. However, the first missions were faster than that, as they were only programmed to fly over the planet and take some quick pictures. They were Mariner 6 and 7. Slower and heavier missions, such as the 1976 Viking mission, take twice as long to enter orbit around the planet, about 300 days. Today instead, if we want to land on Mars and do in situ science, we can reach the planet in 203 days, as the Perseverance mission - now in the Martian sands - did.
Jupiter
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| Earth to Mercury |
Now is the time of Jupiter. Distance from Sun: 483 million miles, shortest distance from Earth: 385 million miles. Pioneer 10's flight to Jupiter took 640 days. Pioneer left in March 1972 and arrived in December 1973. It flies over the planet, maintaining the same orbit as the Homan transfer orbit, never slowing down. Later, in the late 1970s, the Voyager 1 and 2 probes also passed close to the planet, taking as much as 550 days to make the trip. The first really beautiful pictures we have of Jupiter came from the Galileo probe. It was the first evidence of an attempt to enter orbit and it took 2,242 days to do so! In fact, after leaving in 1989, it had to make two gravitational flyovers of Earth and one to Venus to gain enough initial velocity and then decelerate enough to succeed in entering a stable orbit around Jupiter more than 6 years later in 1995! Galileo visited Jupiter's moons. Here's a nice picture of Europe, clearly covered in snow.
Saturn
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| Earth to Saturn |
Another gas giant, Saturn is found about 793.5 million kilometers from Earth. Pioneer 11 was the second space mission, after Pioneer 10, to reach the first flybys of Jupiter and Saturn. Only 4 spacecraft have reached Saturn. They are Pioneer 10 and 11, Voyager 1 and 2, and Cassini-Huygens. Our most comprehensive look at the planet comes from NASA and the European Space Agency's Cassini mission, which spent 13 years exploring Saturn and its moons. NASA's Pioneer 10 mission on March 2, 1972 launched, and on April 5, 1973 followed by Pioneer 11. Although the missions were launched about a year apart and had different trajectories, they accomplished several historic feats together: Pioneer 10 provided unprecedented insights. The first flybys of the asteroid belt and Jupiter were performed, while Pioneer 11 was the first spacecraft to perform a flyby of Saturn. Both probes continue their journey into space but NASA is no longer communicating with either spacecraft. Pioneer 10 and 11 are both on trajectories that will eventually take them out of the solar system entirely, each carrying a map back to Earth if intelligent life ever intercepts them. Speaking of Voyager missions, Voyager 2 was actually launched first, in August 1977, but Voyager 1 was sent on a faster trajectory when it launched about two weeks later. They are currently the only two operational spacecraft in interstellar space outside the environment controlled by the Sun. Voyager 2's path passed Jupiter in 1979, Saturn in 1981, Uranus in 1985, and Neptune in 1989. It is the only spacecraft to have visited Uranus or Neptune and provided much of the information we now use to characterize them. Due to its higher speed and more direct trajectory, Voyager 1 overtook Voyager 2 just months after their launch. Finally, Cassini reached Saturn. It was launched in 1997 and arrived in 2004, then it began orbiting the planet until 2017. At the end of its mission, Cassini performed a maneuver called the "Grand Finale". It orbits closer and closer to Saturn's cloud tops, between the planet and the rings. Then, on September 15, 2017, it plunged into the planet's atmosphere — the only way to ensure it would never crash into Saturn's moons and contaminate them with any Earth microbes it might cling to. It continues to transmit data for the expected 30 seconds, but eventually, it burns out. This is an amazing image of Saturn taken by the Cassini mission. We are running out of planets! Let's talk about Uranus.
Uranus
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| Earth to Uranus |
Distance from Sun: 1783 million miles. Shortest distance from Earth: 1690 million miles So far, only one mission has reached the solar system's seventh planet, Voyager 2, which took just 8.5 years to cross the gas giant. It should be noted that the expected time to make the Earth-Uranus path following the Homan orbit is 16 years. Voyager 2 managed to make it about half that, thanks only to the gravitational assistance of Jupiter and Saturn.
Neptune
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| Earth to Neptune |
Finally, there is Neptune. With a distance of about 2702 million miles from Earth, it is the most distant planet we have ever seen. Only one probe has visited Neptune, the legendary Voyager 2, which flew by Neptune after its encounter with Uranus in 1989, taking 12.5 years to complete the journey from Earth. If there was no gravitational assistance, the journey would have taken over 30 years instead!
Pluto
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| Earth to Pluto |
You think we're done, right? Well, we also want to talk about Pluto. Because, even if it is no longer considered a planet, we take care of it! Its distance from Earth is about 2672 million miles and we sent a mission to study it in more detail. The mission is called New Horizons. Launched in January 2006, it was the fastest man-made object to leave Earth at 36,372 miles per hour. The spacecraft flew by the Solar System's largest planet, Jupiter, on February 28, 2007 for a gravity assist maneuver. The collision accelerated the spacecraft to about 9,000 miles per hour (14,000 kilometers per hour), shortening its trip to Pluto by three. Thus, New Horizons was able to see the dwarf planet in just 9.5 years! Taken by New Horizons, this is possibly the most breathtaking image of Pluto you'll ever see.