• Journal of Astronomy and Space Sciences
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• v.22 no.3
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• pp.249-262
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• 2005

Optimization problems are formulated to calculate optimal impulses for deflecting Earth-Crossing Objects using a Nonlinear Programming. This formulation allows us to analyze the velocity changes in normal direction to the celestial body's orbital plane, which is neglected in many previous studies. The constrained optimization in the three-dimensional space is based on a patched conic method including the Earth's gravitational effects, and yields impulsive ${\Delta}V$ to deflect the target's orbit. The optimal solution is dependent on relative positions and velocities between the Earth and the Earth-crossing objects, and can be represented by optimal magnitude and angle of ${\Delta}V $ as a functions of a impulse time. The perpendicular component of ${\Delta}V $ to the orbit plane can sometimes play un-negligible role as the impulse time approaches the impact time. The optimal ${\Delta}V $ is increased when the original orbit of Earth-crossing object is more similar to the Earth's orbit, and is also exponentially increased as the impulse time reaches to the impact time. The analyses performed in present paper can be used to the deflection missions in the future.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.28 no.2
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• pp.247-254
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• 2010

In this paper, a new approach has been studied correcting the geometric distortion of SPOT 4 imagery. Two new equations were induced by the relationship between satellite and the Earth in the space. line-of-sight (LOS) vector adjustment model for SPOT 4 imagery was implemented in this study. This model is to adjust LOS vector under the assumption that the orbital information of satellite provided by receiving station is uncertain and this uncertainty makes a constant error over the image. This model is verified using SPOT 4 satellite image with high look angle and thirty five ground points, which include 10 GCPs(Ground Control Points) and 25 check points, measured by the GPS. In total thirty five points, the geometry of satellite image calculated by given satellite information(such as satellite position, velocity, attitude and look angles, etc) from SPOT 4 satellite image was distorted with a constant error. Through out the study, it was confirmed that the LOS vector adjustment model was able to be applied to SPOT4 satellite image. Using this model, RMSEs (Root Mean Square Errors) of twenty five check points taken by increasing the number of GCPs from two to ten were less than one pixel. As a result, LOS vector adjustment model could efficiently correct the geometry of SPOT4 images with only two GCPs. This method also is expected to get good results for the different satellite images that are similar to the geometry of SPOT images.