Posts Tagged ‘rocketry’

Escape Velocity

The escape velocity is the velocity required by an object (spacecraft, gas molecule, photon of light or whatever) to escape the gravitational pull of an astronomical body.

The more massive an astronomical body is, the greater the escape velocity will be. This is because a gravitational field is a property of mass. Another factor that needs to be taken into account is how concentrated the mass is – for two bodies with the same mass but different diameters, the one with the smaller diameter would have the greater escape velocity. This is a simplification of escape velocity, for a more advanced treatment, including the maths, see the Wikipedia article.

When the Americans landed men on the moon, the Lunar Module engines needed to develop considerably less thrust to return the astronauts to the Earth than the original Saturn V rocket since the Moon has a much smaller gravitational field. Had this not been the case, the whole process would have been considerably more difficult, if not impossible.

Another factor that worked in the Lunar astronaut’s favour is the lack of an atmosphere on the Moon. In direct sunlight, the surface of the Moon can reach temperatures in excess of 100 degrees Celsius. Any gas molecules near the surface will gain kinetic energy i.e. move faster. The actual speed of a gas molecule also depends on other factors such as its atomic or molecular mass but take for example, oxygen. At a temperature of 100 Celsius, the average velocity will be in excess of 5 km per second so the Lunar gravity will be unable to hang on to it. Without an atmosphere to create drag, the thrust from the engine will be unopposed so much less fuel would be needed to propel the Lunar module up into orbit. From there, with just a little extra effort, escape velocity could be achieved for the Lunar Module/Command Module combination.

For the Earth, escape velocity is 11.2 km per second whilst for the Moon, it is just 2.4 km per second. The largest planet of the Solar System, Jupiter, has an escape velocity of almost 60 km per second whilst the Sun’s escape velocity is over 600km per second.

The gravitational attraction of a black hole is so great that an object would need to be travelling faster than the speed of light in order to escape. That is why black holes are essentially invisible, even photons of light cannot travel fast enough to escape the immense pull of the gravity of a black hole.

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