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On October 4, 1957, the course of space exploration was forever changed, when the Soviet Union successfully launched Sputnik I. The world's first artificial satellite was about the size of a beach ball (58 cm.or 22.8 inches in diameter), weighed only 83.6 kilograms and took about 98 minutes to orbit the Earth on its elliptical path. While the Sputnik launch was a single event, it marked the start of the space age and the space race between the United States and the U.S.S.R.
Shortly thereafter, with the U.S. launch of Explorer 1 and subsequent missions, it was suddenly possible to send human-made instruments into space that could travel distant worlds. One key element was figuring how and exactly when to launch a satellite so that it would reach Mars in the minimum amount of time and with the least amount of power.
Video: How do you get to Mars?
At first, we had the technological knowledge to design “flyby” missions that would simply travel by Mars, taking pictures and collecting other data on their way past. For example: here is an animation of an asteroid briefly entering and exiting the Sun's orbit.
Asteroid "fly by". Image: Peter Collingridge
To get a detailed, long-term, global views of Mars, we needed to design techniques that allowed a spacecraft to be captured into orbit around Mars by approaching the planet at the correct position, velocity, and heading. Failure would result in either a flyby or a crash landing!  To place the spacecraft in orbit, you need a balance between the forward movement of the spacecraft and the gravity of the planet.  If forward motion is too great, you get a flyby; if gravity has a stronger effect, you get a collision.  When you have a balance, the spacecraft establishes a circular or elliptical path around the planet.
For example, here is an asteroid which has the correct velocity and heading such that it is captured by the Sun's gravity.
An asteroid which is captured by the Sun's gravitational pull. Image: Peter Collingridge
After that, it’s a matter of designing cameras and other instruments, a power system, a communications system, and other spacecraft systems, to make the desired discoveries and send the data back to Earth.

Alright, let’s go to Mars!