what is the speed of a rocket?

If a rocket is launched from the surface of the Earth, it needs to reach a speed of at least 7.9 kilometres per second in order to reach space. This speed of 7.9 kilometres per second is known as the orbital velocity, referred to in German as the 'first cosmic velocity' – it corresponds to more than 20 times the speed of sound. At the start of the space age, Russian scientists applied the term 'cosmic velocities' to certain velocities that are important for space exploration. The 'first cosmic velocity', known as the orbital velocity, will bring a rocket or other projectile into orbit around the Earth. A slower projectile will fall back to Earth.

The 'second cosmic velocity' is the so-called escape velocity from the Earth: 11.2 kilometres per second. This is the speed a rocket should attain in order to be able to escape from the Earth’s gravitational field and fly to other planets. It follows from the laws of orbital mechanics that the escape velocity (11.2 km/s) is equal to the orbital speed (7.9 km/s) multiplied by 1.414 (i.e. by the square root of 2).

The 'third cosmic velocity' is the speed that a spacecraft needs to attain in order to be able to leave our solar system. This solar system escape velocity is about 42 kilometres per second (or 0.014 percent of the speed of light in a vacuum). Again, this is the product of the orbital velocity and the square root of 2. However, the orbital velocity now refers to the speed at which the Earth revolves around the Sun: about 30 kilometres per second multiplied by the square root of 2 equals about 42 kilometres per second. The ‘fourth cosmic velocity’ is the escape velocity from our galaxy - the Milky Way. It corresponds to about 320 kilometres per second.

It is important to bear in mind that these cosmic velocities are idealised values. For instance they do not take into account the loss of speed due to air resistance when a rocket is launched. Moreover, the values mentioned above are specific to the Earth and our solar system, and they do not apply to other parts of the universe.

7.9 kilometers per second
If a rocket is launched from the surface of the Earth, it needs to reach a speed of at least 7.9 kilometers per second (4.9 miles per second) in order to reach space. This speed of 7.9 kilometers per second is known as the orbital velocity, it corresponds to more than 20 times the speed of sound.

Avudaiammal M, you described it very well.

The only clarification I want to add is that the actual speed of a satellite in orbit changes with where in the orbit it is. When the satellite is farthest from the earth, in its elliptical orbit, it travels more slowly. When it is nearest to the earth, it travels fastest.

This is similar to how a weight swinging back and forth on the end of a string is traveling more slowly at the top of its swing than at the bottom of the swing. It travels more slowly at the top of the swing because it is slowing down to zero and then reversing direction. When it reverses direction, it starts to speed up due to the pull of gravity. At the bottom of the swing, the weight has the fastest speed. If the speed is fast enough (orbital velocity), it will go up and over and all the way around the point where the string is attached.

If the satellite is going faster than the earth's escape velocity, the gravitational pull of the earth is not strong enough to pull it back. That is why it can escape the gravitational pull of the earth and will end up in orbit around the sun. That is, unless its speed is faster than the escape velocity of the sun.

7.9 kilometers per second

Any rocket can achieve a very high speed if it accelerates for a long time. A conventional rocket has a hard time doing this because a huge amount of fuel must be carried into space in order for this to happen. This may make the rocket too heavy to lift off. Conventional rockets are generally designed to meet the speeds necessary for them to go where they need to go, and not go much faster.

Generally, a conventional rocket has to be going about 17,000 mph for it to achieve orbit; otherwise known as LEO -- Low Earth Orbit. This is the minimum speed for a space going rocket. The farther from the Earth, the faster it needs to go. We list some other velocities for comparison:

Flight Plan

speed required
Earth to LEO (low Earth orbit) 17,000 mph
Earth to Earth escape 24,200 mph
Earth to lunar orbit 25,700 mph
Earth to GEO (geosynchronous Earth orbit) 26,400 mph
Earth to solar escape 36,500 mph
With increasing speed it becomes harder and harder to gain another mile per hour. This is because the amount of fuel one has to carry becomes really big, and it becomes difficult and expensive to lift that much fuel into space. Solar escape velocity is nearing the practical limit of how fast one can move with conventional rockets.