MadSci Network: Engineering

Re: In rocket launches, when does the delta V from Earth's rotation kick in?

Date: Tue Aug 15 21:19:41 2000
Posted By: Dennis K. Van Gemert, Engineer/Scientist, Expendable Launch Systems
Area of science: Engineering
ID: 961665882.Eg

Delta, usually represented by the Greek letter of the same name in 
mathematical equations, refers to change; thus, delta-V represents a 
change in the quantity of velocity.  Delta-V is a popular quantity used in 
orbital mechanics, for it takes a specific change in velocity to get from 
one place in space to another.  Delta-V is not an idea it is a 
manifestation of Classical Newtonian physics.  It is tied directly to the 
inertial properties of a mass.  

Letís think of you on a train, facing the front of the train.  If you were 
to throw a baseball at 25 mph while the train is at rest, not moving, it 
would move at 25 mph; however, if you were to throw that same baseball in 
the same direction while the train is moving, the speed (or velocity) of 
the ball would be that of the train plus that of your throw.  For example, 
if you throw a ball at 25 mph, and the train is moving at 50 mph; the ball 
is moving at 75 mph.  The Earth has the same effect on a rocket.  If you 
think of the launch pad as a point on the surface of the Earth, then that 
point has a velocity equal to the distance it travels in 24 hours (the 
period of the Earth) divided by 24 hours (remember, velocity is distance 
divided by time).  Since a point on the equator must move a greater 
distance than a point north or south of the equator (i.e., the distance 
traveled by a point offset from the equator is shorter), it follows that a 
point on the equator must move faster.  We know that the Earth rotates 
eastward; thus, if we launch in an easterly direction we get an additional 
velocity equal to the rotation of the earth at the launch site.  This 
velocity is free since the Earth imparts it without the need to put energy 
into the system.  This velocity is not put on the vehicle at any specific 
time during flight since it is an initial condition in the launch 
equation.  The rocket, launch vehicle, starts with this given amount of 
inertia.  Thus, the rocket launching in the direction of the Earthís 
rotation is the same type of motion that the baseball on the train follows.

Any further questions, feel free to ask! Dennis

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