Chapter 9, Problem 9ICA

It is proposed to create a set of dimensionless numbers used to describe the phenomena of reaching the escape velocity necessary to orbit the Earth. A set of names is proposed, based on famous astronauts:

• The Gagarin number, after Yuri Gagarin, a Russian astronaut and the first human to achieve escape velocity and orbit the Earth in outer space;
• The Valentina number, after Valentina Tereshkova, a Russian astronaut who was the first female to orbit the Earth;
• The Shepard number, after Alan Shepard, the first American to orbit the Earth; and
• The Ride number, after Sally Ride, the first American woman in space.

To begin the analysis, assume the following variables are important:

g = Gravitational pull between planet and rocket	[=] meters per second squared [m/s2]
nr = Amount of rocket fuel	[=]moles [mol]
wp = Weight of planet	[=] pounds-force [lbf]
d = Diameter of planet	[=]miles [mi]
G = Newtonʼs gravitational constant	[=] newton meters squared per kilogram squared [N m2/kg2]
v = Velocity of rocket	[=] miles per hour [mph or mi/h]
η = Efficiency of the rocket engine	[=] unitless

Determine a set of dimensionless groups using Rayleighʼs method.