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Geoid and Ellipsoid01:28

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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...
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Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Influence of Earth's Curvature and Atmospheric Refraction on Leveling01:26

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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...
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Relative Motion Analysis using Rotating Axes01:25

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
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Equations of Motion: Normal and Tangetial Components01:10

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Describing the motion of a particle along a curvilinear path involves understanding its components in terms of normal and tangential aspects. The normal component aligns with the radial direction of the curve at a specific point, reflecting changes in the trajectory of the velocity vector. In contrast, the tangential component is tangential to the curve at that point and signifies the rate at which speed alters along the path.
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Related Experiment Video

Updated: Dec 30, 2025

Assessment of Static Graviceptive Perception in the Roll-Plane using the Subjective Visual Vertical Paradigm
06:30

Assessment of Static Graviceptive Perception in the Roll-Plane using the Subjective Visual Vertical Paradigm

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Attitude Sensor from Ellipsoid Observations: A Numerical and Experimental Validation.

Dario Modenini1, Alfredo Locarini1, Marco Zannoni1

  • 1Department of Industrial Engineering, University of Bologna, 47121 Forlì, Italy.

Sensors (Basel, Switzerland)
|January 17, 2020
PubMed
Summary
This summary is machine-generated.

A new infrared horizon sensor for small satellites accurately determines attitude using Earth limb ellipse fitting. This novel sensor achieves root-mean-square errors of less than a hundredth of a degree.

Keywords:
attitude determinationellipsoidhorizon sensor

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Area of Science:

  • Spacecraft Attitude Determination
  • Satellite Navigation Systems
  • Infrared Sensor Technology

Background:

  • Accurate attitude determination is crucial for small satellite missions.
  • Existing horizon sensors face challenges with atmospheric effects and size limitations.
  • Novel sensor designs are needed to enhance precision and robustness.

Purpose of the Study:

  • To present the preliminary design and validation of a novel, high-accuracy horizon sensor for small satellites.
  • To introduce an attitude determination algorithm based on Earth limb ellipsoid observations.
  • To evaluate the sensor's performance through simulation and experimental validation.

Main Methods:

  • Utilizing a multi-head infrared sensor to capture Earth limb images.
  • Applying ellipse fitting to imaged limb arcs for attitude computation.
  • Developing a dimensionless algorithm exploiting projective geometry for a closed-form solution.
  • Employing a numerical simulator for low Earth orbit scenarios with atmospheric presence.
  • Conducting experimental validation with a miniature infrared camera testbed.

Main Results:

  • The proposed sensor concept achieves root-mean-square (rms) errors of a few hundredths of a degree or less in determining the local nadir direction.
  • The algorithm's dimensionless framework reduces sensitivity to limb shift caused by atmospheric radiance.
  • Numerical simulations and experimental tests confirm the sensor's high accuracy and reliability.
  • The closed-form solution provides an efficient method for attitude matrix computation.

Conclusions:

  • The novel infrared horizon sensor offers a high-accuracy solution for small satellite attitude determination.
  • The ellipsoid observation-based method provides a robust and less atmospherically sensitive approach.
  • The validated sensor design is suitable for enhancing the navigational capabilities of small satellites.