Orbital Mechanics and Interplanetary Trajectories--Interplanetary Trajectories

Traveling to other planets is just like rendezvousing with another spacecraft in a different orbit, because that is exactly what you are doing. The interplanetary spacecraft is moving from Earth’s orbit to, say, Mars’ orbit, to rendezvous with the red planet. In traveling to Mars, the spacecraft is moving to a higher orbit. Remember from Orbital Mechanics part 1, to raise the apogee of an orbit, we fire the engines at perigee. On a Mars mission, Earth orbit is the perigee—but since we are leaving the home planet and moving into solar space, it is now called perihelion. Mars’ orbit is aphelion. A Hohmann Transfer Orbit trajectory does the job nicely, with the engines fired in the direction of Earth’s movement in it’s’ orbit.

Of course, there are some differences. The spacecraft must be accelerated to about 25,000 mph to escape Earth’s gravity. It must start its journey at a time that will allow it to cross Mars’ orbit when the red planet is at that same point in its orbit. And it should be moving in the same direction Mars is moving. That requires some serious orbital calculations.

Once the spacecraft arrives at Mars, it must fire its rockets to slow itself sufficiently to go into orbit around the fourth planet. Even most landers first achieve a ‘parking’ orbit before making their descent to the surface.

But, suppose we want to travel to the second planet in the solar system—Venus? The Hohmann Transfer maneuver still applies, as does the need to achieve escape velocity. Remember from Part 1, to lower the apogee the engines must be fired opposite to the direction of travel. Since the Earth’s orbit is at aphelion and Venus’ at perihelion, the engines are fired opposite to the direction of Earth’s motion so the spacecraft falls toward the sun.

With today’s rockets, even using LH2, the energy requirements for reaching planets beyond Mars and Venus are at best at the edge of their potential. To get to the outer planets, rocket scientists have had to take advantage of nature’s own energy store—gravity.

Mars is a ‘mere’ 35 million miles away at closest approach. A low energy Hohmann trajectory can take a spacecraft there easily. Jupiter, the next planet in the solar system, is 365 million miles distant at its closest approach. Even the giant SATURN V could not send a spacecraft of any significant size that far.

But gravity can.

Let’s say we launch a spacecraft towards Mars, but not to orbit or land on it—to use its gravitational pull to speed the spacecraft up to a velocity that will allow it to continue on to Jupiter. This is known as a gravity assist.

As the spacecraft approaches Mars, that planet’s gravitational field pulls it ever faster towards it. As we approach the planet we begin to also pick up its angular momentum. This gives the spacecraft sufficient velocity to exit the planet’s gravity well without being slowed. It whizzes past the helping world with more velocity and on a different trajectory, which, if we’ve done our calculations correctly, will take it to Jupiter

And think where we could go if we used massive Jupiter to sling shot our way out into the solar system. That’s exactly what NASA did with Pioneer and Voyager. Both used Jupiter’s gravity assist to send them on to Saturn, and in Voyager’s case to Neptune and Uranus.

The Cassini spacecraft used Jupiter’s gravity assist. But not just that giant. Cassini first flew to Venus, whipped around it, came back to Earth’s orbit, went back to Venus, picked up more speed, flew back to Earth to gain more velocity, and headed to Jupiter. Jupiter’s huge gravity field sped the craft up more and sent it on the Saturn, where it remains in orbit today, still sending pictures of that giant and its’ moons. At one point in Cassini’s flight, it was travelling more than 28,600 mph.

Voyager 2, one of our first interplanetary probes, today has left the solar system with the speed it obtained from the gravity assist it received from Uranus. It is drifting in interstellar space. On its side is a plaque containing symbols we hope some spacefaring species or future humans can decipher. Inside the plaque is a video disc containing music and greetings in many languages.

Perhaps in some distant future, astronauts from a planet orbiting a distant star will find our celestial message in a bottle, calculate where it came from, and come to visit...