NASA provides a good Brief History of Rockets which summarizes in concise form many of the historical advances in rocketry and space exploration, including Wan-Hu's unfortunate attempt at a rocket-powered chair.
The simple rocket in the form kids light on the Fourth of July, invented by the Chinese, has been generally around by the end of the 13th century, used as a supplement to more traditional armament, as in Francis Scott Keys "rocket's red glare" from the bombardment of Fort McHenry during the War of 1812.
When the western Renaissance brought in the telescope, the concept that there was space to be explored began to come into focus. Before Galileo could look through a pair of lenses at Jupiter and see its four largest moons orbiting the planet, scientists and philosophers often thought of the distant stars and planets as residing on vast transparent spheres rotating about the Earth. Copernicus' sun-centered theory of the universe shattered the awkward and never-quite-right theory of epicycles, by which astronomers had tried to reconcile, in an Earth centered universe, their observations with their mathematics.
In the early 1600s, Johannes Kepler inherits years of precise astronomical data from the school of Tycho Brahe and, after many false starts, derives his laws of planetary motion:
- The orbit of a planet is an ellipse with the Sun at one of the two foci.
- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
By providing a mathematical solution which finally agreed with the tricky orbit of Mars, Kepler proved Copernicus right. Today Keplerian conic sections are a staple of orbital dynamics and astronavigation.
In 1687. Sir Issac Newton provided the science still used for many basic tasks of space exploration:
The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically).
As to serious consideration of space travel and exploration, one should look to the putative father of space exploration, Konstantin Tsiolkovsky. His 1903 publication, Exploration of Outer Space by Means of Rocket Devices and subsequent writings proved (for the first time) that a rocket could perform space flight, calculated the speed required for a successful Earth orbit and escape velocity, introduced the concept of the multistage rocket and liquid fuel/oxidizers.
Tsiolkovsky's most important contribution was the formulation of the rocket equation:
$$\Delta v=v_e ln\frac{m_0}{m_f}$$
where:
$\Delta v$ is the required change in velocity;
$v_e$ is the effective exhaust velocity of the combusted propellants;
$ln$ is the natural logarithm;
$m_0$ is the starting mass of the rocket including propellant; and
$m_f$ is the empty mass of the rocket.
$\frac{m_0}{m_f}$ is the mass ratio of the rocket
This is what is being referenced when you hear the phrase, on this site and many others, "the tyranny of the rocket equation." You can find a good discussion here, and I'll use the answers from that question to briefly explicate. Since your exhaust velocity is a constant, in order to achieve linear increases in $\Delta v$, you need exponentially greater mass ratios. The devil is the natural logarithm function. Here's a graph:
The mass ratio is always going to be greater than one, so I've ditched lower values. You can see that to get one unit of $\Delta v$ an approximate mass ratio of less than three; to double it you need more than seven; to triple it you jump to over 20. Rather than try to engineer absurdly high mass ratios, rocket research tries the more rational approach of finding engines, such as ion thrusters, that substantially increase the exhaust velocity.
