AE551
INTRODUCTION TO SPACE
SCIENCES
Nasim A. Mamaghani
Spring 2016
What is escape velocity?
It is the speed that an object needs to be traveling to break free of a
planet’s gravity well and leave it without further propulsion.
For example, a spacecraft leaving the surface
of Earth needs to be going 11.2 km/sec to
leave without falling back to the surface or
falling into orbit.
Physics
• To calculate the escape velocity of the earth, let the minimum
velocity to escape from the earth's surface be Ve.
• K.E. of Object should be Equal to Magnitude of P.E.
Note:
The relation shows that the escape velocity of an object does not
depend on the mass of the projected object but only on the
mass and radius of the planet from which it is projected.
Escape Velocity in
Body
Mass (Kg)
Kilometers/ Second
The
7.36*10^1
2.38 km/sec
Moon
9 5.98*10^2
Earth
11.2 km/sec
1
1.99*10^2
The Sun
618. km/sec
7
Root-mean-square speed
Root-mean-square speed is the measure of the speed of particles in a gas. It is
defined as the square root of the average velocity-squared of the molecules in a gas.
Mm : molar mass of the gas in kilograms per mole,
R: molar gas constant,
T: temperature in kelvin.
The higher the temperature, the greater the mean velocity will be.
The Question:
If the “rms speed” of a gas is greater than about 15% of the escape speed of a planet, almost all of the
molecules of that gas will escape the atmosphere of the planet.
i.
At what temperature is vrms for O2 equal to 15 percent of the escape speed for Earth?
ii. At what temperature is vrms for H2 equal to 15 percent of the escape speed for Earth?
iii. Temperatures in the upper atmosphere reach 1000 K. Could this fact account for the low abundance of
Hydrogen in Earth’s atmosphere?
iv. Compute the temperatures for which the vrms of O2 and H2 are equal to 15 percent of the escape
speed at the surface of the moon, where g is about one-sixth of its value on Earth and R = 1738 km.
How does this account for the absence of an atmosphere on the moon?