The reason you burn the fuel is to increase the velocity. Momentum = mass times velocity, so the faster you throw stuff out the back, the faster you move forward. (Or, to put it another way, the less fuel you have to carry.)
The shuttle is never “just high enough not to get pulled back down”. No matter how high you get, gravity will always be pulling you back down. The Moon, for instance, is much higher than the shuttle, but Earth’s gravity is still pulling on it (or else it would wander off and get lost in space). The shuttle must get a sideways velocity in order to stay in orbit. An object in orbit is always falling toward the Earth, but it keeps missing the Earth’s surface as it curves away.
Every action has an equal and opposite reaction. A force applied in one direction has a reaction force in the opposite direction.
F = m * a. (Bolded letters represent vectors.)
Inertia – as long as F remains zero, there is no acceleration, and an object’s velocity vector (which could be zero) will remain unchanged. No acceleration means no change in speed or direction.
And momentum: F = m * v / t. Send a mass in a given velocity vector over a given time, and that produces a force.
A rocket engine burns fuel, producing a low-mass gas. The engine directs this gas in a given direction at high speed. Over time, the momentum of this exhaust gas produces a force. Under Newton’s first law, that exhaust force causes a force in the opposite direction, imparted to the engine (and the craft containing the engine). That force applies an acceleration to the craft, which moves in the desired direction.
As described by other posters, a low mass sent at high acceleration in ----> direction will send a high mass at low acceleration in <---- direction.
(Rocket scientists, physics majors, etc.: Do I remember my mechanics correctly?)
A lot of the fluid dynamics depends on the Mach number but not the velocity. For example, the angle and strength of a shock wave is dependent on two things: Mach number and flow deflection angle. So if you have an obstruction in the flow (e.g. a plane) that deflects the flow through a certain angle, it will cause a shock wave which has a specific strength (pressure increase across the shock) and angle. These factors are what you care about when you’re designing a vehicle because you want to know what the pressure on the vehicle will be and whether a shock generated by one surface will hit another surface (e.g. shock from the nose hitting a wing). If your propulsion system will push you Mach 2 at sea level, you might have a much higher Mach number at altitude and this could cause problems as the shock geometry changes.
The actual velocity is important too, but when you’re designing a supersonic vehicle there are a lot of factors which depend solely on Mach number.
And yes, Mach number becomes meaningless in space. If there is no fluid around the vehicle, there is no local speed of sound and no shock waves resulting from exceeding it.
Nor correct. If the shuttle’s orbital speed was greater than or equal to Earth’s escape velocity, it would not be orbiting. It would be on an escape trajectory.
Kind of Scuba_Ben. As others have said it comes down to conservation of momentum §
p=mv
dp/dt = mdv/dt + vdm/dt = 0
Normally we ignore the second term as sliding blocks on air tables don’t really loose much mass. But in a rocket it helps. Now the change of momentum within the rocket system is zero so
mdv/dt = - v dm/dt
-1/v dv = 1/m dm
vfinal = vinitial + uln(minitial/mfinal)
Here u is the exhaust velocity of the propellant. The faster it goes the higher the vfinal will be. With chemical rockets the fuel is the propellant. The oxidation reaction heats the gases providing a higher u than simply letting air out the back of the ballon. Now with a nuclear rockets you could simply heat propellant (say hydrogen of oxygen) and have than fired out the back.
Forget Mach numbers when talking about spacecraft. Mach deals with moving thru air. Stick to MPH. Remember two figures when casually arguing with people:
This got answered, but I’ll add to it in my own words.
Mach isn’t meaningless just because it changes with altitude (and temperature, and density, and a lot of other things). It’s often important to know what an object’s speed is as a multiple of the speed of sound at that point. That’s because all those physical and geometric behaviors that micco mentioned are specific to the properties of the air you’re currently in. Who cares what’s going on at sea level when you’re at 60,000 feet?
I hope you have no difficulty believing that the speed of sound (often denoted a) changes at various places in the atmosphere. If you’re not already okay with that, the best I can do for you in a short space is give you an equation for speed of sound: a[sup]2[/sup] = yRT. In that equation, y is the closest I could get to “gamma,” a number that is basically constant for air. R is the real gas constant for air (once again, basically constant). And T is temperature. So, as you go higher in the atmosphere, and it gets colder (generally), the speed of sound decreases.
But it’s also important to remember that Mach number is tied to the local a, and not tied absolutely to a at sea level. That way, all the flow characteristics that depend on the multiple of the speed of sound (Mach number) are relevant. Again, who cares about a at sea level unless that’s where you are?
As you go up in the atmosphere, you could maintain a constant velocity, but your Mach number would keep going up (since a keeps going down). But that doesn’t make Mach meaningless. In fact, Mach number is about as important a number as any aerodynamicist could have. There are some things, like shock angles, that don’t care what the velocity is, only the Mach number. Mach number would, however, be meaningless if it were fixed to sea level conditions. Then, it would be nothing more than another way to state the velocity. Knowing how fast you’re going relative to sea-level a may give you a sense for your speed, but it doens’t tell you anything about many important aspects of the flow field you are currently experiencing.
There really is no altitute where the shuttle would not be pulled upon by the earth, although eventually the forces would be too small to notice. It’s not that the earth stops pulling on the shuttle, it’s that the shuttle is going so fast that it goes past the earth before it can fall.
A good way to picture this is to imagine a really powerfull cannon on a tall mountian. If you fire a cannonball horizontally, the cannonball will fall to earth after a period of time. If you keep firing the ball faster and faster, the distance it travels will keep getting farther and farther. Since the earth’s surface is curved, eventually the ball will go so far that it ‘falls’ at the same rate as the earth curves. This is an orbit.
Obviously you can’t do this at sea level, friction a drag with the air will bring the ball back down long before it gets that far. That is why you must orbit above an atmosphere ( this wouldn’t apply on the moon, you could orbit the moon at a hight of one inch). The lower the orbit, the more drag the atmosphere places on an object, and the less stabile its orbit. The advantage of a low orbit is that you need less fuel to get there, which means it’s cheaper.
One interesting thing with orbits is that it’s possible to orbit at a distance and speed such that the earth doesn’t appear to move. This is a geostationary orbit. This happens because as the distance from the earth increases, the force of gravity decreases. So while the space shuttle at 200ish miles high needs to orbit the earth in an hour and a half to not fall down, a weather satellite at 20k(damn forgot the exact number)ish miles can orbit once a day, and take pictures of your local weather at all times. Of course, it’s more expensive to get up to such an orbit, so it’s generally used for unmanned, relatively light things that have a pressing need to hover over one spot. Even though an object in a higher orbit is moving slower, it takes more fuel to get there. It’s like climbing a mountain.
