Chapter 3. Gravitation and Mechanics CONTINUED
Newton's Principles of Mechanics
Sir Isaac Newton realized that the force that makes apples fall to the ground is the same force that makes the planets "fall" around the sun. Newton had been asked to address the question of why planets move as they do. He established that a force of attraction toward the sun becomes weaker in proportion to the square of the distance from the sun.
Newton postulated that the shape of an orbit should be an ellipse. Circular orbits are merely a special case of an ellipse where the foci are coincident. Newton described his work in the Mathematical Principles of Natural Philosophy (often called simply the Principia), which he published in 1685. Newton gave his laws of motion as follows:
There are three ways to modify the momentum of a body. The mass can be changed, the velocity can be changed (acceleration), or both.
Force (F) equals change in velocity (acceleration, A) times mass (M):
F = MA
Where a jet engine on an airplane obtains its oxidizer for combustion directly from the atmosphere, a rocket carries its own oxidizer and can operate outside the atmosphere. Otherwise, their basic operating principle is the same.
The space shuttle main engines, and the Vulcain engine in the Ariane 5 launch vehicle, and many others, all use water as the reaction mass, as does a water-bottle rocket. In launch vehicle engines, the water in its gaseous state because it is hot from the combustion process that freshly created it by burning hydrogen with oxygen. This combustion energy (instead of the limited air pressure in a water-bottle rocket) expands and greatly accelerates the reaction mass out the nozzle, propelling the rocket forward.
The reaction mass is not always water. The nature of the exiting mass depends on the chemistry of the propellant(s). Solid-propellant rockets have been used for centuries, operating on the same basic principle, but with different reaction mass and combustion chemistry. Today they are used as strap-on boosters for liquid-fuel launch vehicles, for orbit injection stages, and for many standalone rockets. Modern solid rockets have a core of propellant made of a mixture of fuel and oxidizer in solid form held together by a binder. The solid is molded into a shape having a hollow core that serves as the combustion chamber. Once ignited, a solid rocket cannot be shut off.
The first flight of a liquid-propellant rocket was in 1926 when American professor Robert H. Goddard launched a rocket that used liquid oxygen and gasoline as propellants. It gained 41 feet during a 2.5-second flight. Liquid propellants have the advantage of fairly high density, so the volume and mass of the propellant tanks can be relatively low, resulting in a high mass ratio. Liquid rockets, once started, can be shut off. Some kinds can later be restarted in flight.
SCHEMATIC OF A PUMPED LIQUID BIPROPELLANT ROCKET
We learn from Einstein's special theory of relativity that mass, time, and length are variable, and the speed of light is constant. And from general relativity, we know that gravitation and acceleration are equivalent, that light bends in the presence of mass, and that an accelerating mass radiates gravitational waves at the speed of light.
Spacecraft operate at very high velocities compared to velocities we are familiar with in transportation and ballistics here on our planet. Since spacecraft velocities do not approach a significant fraction of the speed of light, Newtonian physics serves well for operating and navigating throughout the solar system. Nevertheless, accuracies are routinely enhanced by accounting for tiny relativistic effects. Once we begin to travel between the stars, velocities may be large enough fractions of light speed that Einsteinian physics will be indispensable for determining trajectories.
For now, spacecraft do sometimes carry out experiments to test special relativity effects on moving clocks, and experiments to test general relativity effects such as the space-time warp caused by the sun, frame-dragging, the equivalence of acceleration and gravitation (more precisely the equivalence between inertial mass and gravitational mass) and the search for direct evidence of gravitational waves. As of April 2006 there has been no test by which an observer could tell acceleration from gravitation, nor has gravitational radiation been directly observed. Some of these subjects are explored in Chapter 8.
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1 The Solar System
2 Reference Systems
3 Gravity & Mechanics
5 Planetary Orbits
7 Mission Inception
9 S/C Classification
11 Onboard Systems
12 Science Instruments
17 Extended Operations
18 Deep Space Network