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Standard Gravitational Parameter

In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the ... more

Langarian point (radius around M2 in the absense of M1)

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Orbital Period - as a function of central body's density

The orbital period is the time taken for a given object to make one complete orbit around another object.

When mentioned without further ... more

Mean anomaly - function of gravitational parameter

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Orbit Equation

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... more

Thermal de Broglie wavelength (Massless particles)

The thermal de Broglie wavelength is the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature. We can take the ... more

Leaning ( for bikes and motorcycles)

Bikes must lean during a turn to balance the relevant forces: gravitational, inertial, frictional, and ground support. The angle of lean can be ... more

Mass Ratio - Rockets

In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than ... more

Centripetal Force

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.


then we calculate the number of hours worked in the 20 years.


Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.


The efficiency is the resulting potential energy divided by the consumed energy.


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