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Sunlight Exerts Pressure

Falling Eastward

What if an Asteroid Hit the Earth

Using a Jeep to Estimate the Energy in Gasoline

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How Long is a Light Year?

How Big is a Trillion?

"Seeing" the Earth, Moon, and Sun to Scale

Of Stars and Drops of Water

If I Were to Build a Model of the Cosmos...

A Number Trick

Designing a High Altitude Balloon

Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Calendar Calculations

Telling Time by the Stars - Sidereal Time

Fields, an Heuristic Approach

The Irrationality of

The Irrationality of

The Number (i)i

Estimating the Temperature of a Flat Plate in Low Earth Orbit

Proving that (p)1/n is Irrational when p is a Prime and n>1

The Transcendentality of

Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions

Maxwell's Equations: The Vector and Scalar Potentials

A Possible Scalar Term Describing Energy Density in the Gravitational Field

A Proposed Relativistic, Thermodynamic Four-Vector

Motivational Argument for the Expression-eix=cosx+isinx

Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Additional Notes on Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics
A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File
On Expansion of the Universe - PDF File

Designing a High Altitude Balloon

Design a gas balloon to carry an instrument package in the earth's atmosphere at an altitude of 90 km. Specify how large the balloon will have to be and the mass of gas it will require to maintain this altitude if:

  1. It uses helium (He).
  2. It uses hydrogen (H2).

Assume that the ideal gas law holds at the desired altitude, that the inflated balloon is spherical, and that the total payload mass (balloon + instrument package) is 10 kg.

Let's assume that:

  1. The buoyant force on the balloon is equal to the weight of the (fluid) atmosphere displaced.
  2. The ideal gas law holds in the form p = nkT
  1. where n is the number density in m-3, k is Boltzmann's constant (k = 1.38 X 10-23 j/K), T is the absolute temperature, and p is the pressure.

  2. Atmospheric conditions at an altitude of 90 km are:


    T = 187 K


    p = 1.38 x 10-3 Torr


    densityA = 3.42 x 10-6 kg/m3

    (ref.: U. S. Standard Atmosphere, 1976).


  1. In order for the balloon to stay aloft, we know that the buoyant force must equal the weight of the balloon and instrument package plus the weight of the (hydrogen or helium) gas inside the balloon. If densityAVBg is the weight of displaced atmosphere, then
  1. densityAVBg = (10 kg)g + densityGVBg


    densityAVB = 10 kg + densityGVB


    where densityG is the gas density inside the balloon, VB is volume of the balloon, and g is the local gravitational acceleration.

  2. We use the ideal gas law to obtain the gas density inside the balloon. For helium: p = nkT = (densityG/m)kT

    with m = 6.68 x 10-27 kg. Set p = 1.38 X 10-3 torr = 1.82 x 10-6 atm = 0.18 nt/m2, and T = 187 K, then solve for densityG:

    densityG = 4.66 x 10-7 kg/m3


    This number represents the density of helium at the pressure and temperature conditions stated for 90 km altitude. It is assumed to be the helium gas density inside the balloon as well.8

  3. We now use eq. 2 in eq. 1 to calculate the volume of the balloon:

    VB = 3.39 x 106 m3


    and we use eq. 3 with eq. 2 to calculate the mass of helium required:

    mHe = 1.58 kg


    If the balloon is assumed to be spherical, then

    VB = (4/3) pirB3.

    where rB is the balloon radius. Using the value of VB in eq. 3, we find that the radius of the balloon is

    rB = 93 m


    If hydrogen is used instead of helium, then we set mH2 = 1.67 x 10-27 kg in the ideal gas law, and repeat the above procedure to find

densityG = 1.16 x 10-7 kg/m3


VB = 3.03 x 106 m3


mH2 = 0.35 kg


rB = 90 m


8 Thus, the interior and exterior pressures are equal. This assumption is equivalent to saying that the balloon is inflated without stretching; i.e., that there is no tension in its material.

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