# Rocket with higher velocity than its own thruster.

1. Jun 1, 2013

### schonovic

If I'm traveling at 22000 miles per second and fire a thruster with an exhaust velocity of 1700 miles per second does the thrust creat drag because I'm going faster? If not what is the effect?

2. Jun 1, 2013

### Janus

Staff Emeritus
The thrust will increase your speed. Exhaust speed does not limit rocket speed. It does however determine how much propellent you need to reach a given speed.

The basic equation, known as the rocket equation, is

Delta V = V_e ln (MR)

V_e is the exhaust speed, and MR is the ratio of the mass of the ship + fuel divided by the just the mass of the ship.

Thus for your example, to reach 22,000 mps with a exhaust velocity of 1700 mps, you would have to have 417139 kg of fuel for every 1 kg of ship mass.

3. Jun 2, 2013

### VantagePoint72

Bear in mind that these velocities are relative to two different things. The rocket's is (presumably) relative to the earth and the exhaust's is relative to the rocket. The exhaust still travels down from the rocket at 1700 miles per second, though it is has net upwards velocity relative to the earth. It doesn't get stuck under the rocket or something if that's what you're thinking. The only thing that matters for thrust is the relative velocity between the rocket and the exhaust.

4. Jun 3, 2013

### cjl

It still creates thrust. If you want to think of it from the frame of the observer, the rocket and the fuel are both initially going by you at 22000 miles per second. Then, if the rocket fires as it passes you, the rocket is taking its fuel and slowing it down (relative to you) from 22000 miles per second to 20300 miles per second. Even though the fuel is still traveling the same direction as the rocket, it slowed down from the speed of the rocket (since it was initially in the rocket's fuel tank) to the speed of the rocket minus the exhaust velocity. This requires that the rocket exerted a backwards-facing force on the fuel, and thus (by newton's third law) the fuel exerted a forward force on the rocket, which speeds it up.

This can be contrasted with a jet aircraft - in the case of a jet aircraft, the reaction mass is primarily the air which the jet is flying through. Because the air is not traveling with the jet, the jet must have an exhaust velocity higher than its flight velocity in order to continue producing thrust.

5. Jun 3, 2013

### rcgldr

Wouldn't this also be an issue for a rocket in the atmosphere (although this post's example speeds are way to high for a rocket in the atmoshpere)? In reasonbly dense atmosphere, if rocket thrust is slower than rocket speed, you'd end up with a net drag at the aft end of a rocket.

6. Jun 3, 2013

### VantagePoint72

No, just think of it in terms of changing momentum. For the rocket to increase its forward momentum, it needs to increase the backwards momentum of something (or decrease the forwards of momentum of something, but that's not how propulsion works). We can choose any frame to work in and the rocket's is the most convenient. In the rocket's frame, the propellant starts out at rest and is shot backwards. This accelerates the rocket relative to this frame, which of course is also acceleration relative to the earth. The speed of the rocket, density of the atmosphere, and anything else are all irrelevant (well, ignoring aerodynamic drag which is something else altogether).

On the other hand, a jet has air entering its intake at the jet's airspeed (in the jet's reference frame). In order to push the jet forward, it must leave the jet faster than it came in. Thus, the propellant velocity must exceed the jet's air speed.