Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Geoid and Ellipsoid

Geoid and Ellipsoid

The Earth's shape is best described as an ellipsoid, a slightly flattened sphere created by rotating an ellipse around its minor axis. This flattening results in the polar axis being about 21 kilometers shorter than the equatorial axis. In contrast, the geoid represents the Earth's gravitational shape and aligns with the mean sea level (MSL). The geoid is an irregular equipotential surface where gravity is perpendicular at every point. Variations in Earth's mass distribution cause geoid...

Trigonometric Substitution

Trigonometric Substitution

Trigonometric substitution is a technique used to simplify integrals that contain square root expressions involving quadratic forms. It is particularly effective when the integrand includes terms resembling those found in standard geometric equations, such as circles or ellipses.Molniya satellites follow highly elliptical orbits, repeatedly sweeping out the same regions of space as they revolve around Earth. To estimate the area enclosed by such an orbit, the path is modeled as an ellipse...

Application of Linearization and Approximation

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

$Influence of Earth's Curvature and Atmospheric Refraction on Leveling$ 01:26

Influence of Earth's Curvature and Atmospheric Refraction on Leveling

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance. Over a...

Circular Orbits and Critical Velocity for Satellites

Circular Orbits and Critical Velocity for Satellites

The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial satellites in orbit. One can examine the circular orbit, the simplest kind of orbit, to understand the relationship between the speed and the period of planets and satellites with respect to their positions and the bodies that they orbit.
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...

Simple Harmonic Motion and Uniform Circular Motion

Simple Harmonic Motion and Uniform Circular Motion

While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic motion is an oscillatory motion in a system where the net force can be described by Hooke's law, while uniform circular motion is the motion of an object in a circular path at constant speed.
There is an easy way to produce simple harmonic motion by using uniform circular motion. For instance, consider a ball attached to a uniformly rotating...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Europa's differentiated internal structure: inferences from four Galileo encounters.

Science (New York, N.Y.)·1998

Same author

Distribution of rock, metals, and ices in Callisto.

Science (New York, N.Y.)·1998

Same author

Europa's differentiated internal structure: inferences from two Galileo encounters.

Science (New York, N.Y.)·1997

Same author

Gravitational evidence for an undifferentiated Callisto.

Nature·1997

Same author

Gravity field of venus: a preliminary analysis.

Science (New York, N.Y.)·1979

Same author

Mars gravity: high-resolution results from viking orbiter 2.

Science (New York, N.Y.)·1979

Search research articles

Related Experiment Video

Updated: Jul 12, 2026

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Published on: July 30, 2020

Lunar Shape via the Apollo Laser Altimeter.

W L Sjogren, W R Wollenhaupt

Science (New York, N.Y.)

|January 19, 1973

Summary

Apollo missions precisely measured lunar elevations, revealing significant differences between the near and far sides. Combined data indicate the Moon

Area of Science:

Lunar geology and geophysics
Planetary science
Geodesy

Background:

Accurate lunar topography is crucial for understanding planetary evolution.
Previous lunar elevation data had limitations in accuracy and coverage.

Purpose of the Study:

To determine precise elevation differences across the Moon using laser altimetry.
To refine models of the Moon's shape and internal structure.

Main Methods:

Utilized laser altimeter data from the Apollo 15 and Apollo 16 missions.
Compared altimetry results with existing lunar map data.
Analyzed discrepancies to model the Moon's gravitational field and center of mass.

Main Results:

Revealed significant elevation discrepancies between lunar hemispheres.

More Related Videos

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Published on: May 10, 2020

Related Experiment Videos

Last Updated: Jul 12, 2026

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Published on: July 30, 2020

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Published on: May 10, 2020

Identified regional elevation variations in Mare Nubium and Mare Tranquillitatis.

Established a best-fit spherical model for the Moon with a radius of 1737.7 km.

Determined a 2 km offset of the center of mass towards Earth and 1 km eastward.

Conclusions:

The Moon exhibits substantial topographic asymmetry between its near and far sides.
Laser altimetry provides unprecedented accuracy for lunar surface mapping.
The Moon's center of mass is offset from its geometric center, indicating internal density variations.