@article {Hatch:2013:0836-1398:159,
title = "Gravitational clocks and apparent relativity",
journal = "Physics Essays",
parent_itemid = "infobike://pe/pe",
publishercode ="pe",
year = "2013",
volume = "26",
number = "2",
publication date ="2013-06-08T00:00:00",
pages = "159-173",
itemtype = "ARTICLE",
issn = "0836-1398",
eissn = "2371-2236",
url = "https://www.ingentaconnect.com/content/pe/pe/2013/00000026/00000002/art00001",
doi = "doi:10.4006/0836-1398-26.2.159",
keyword = "Kinetic Force, Selleri Transformation, Gravitational Force, Gravitomagnetic Force, General Relativity, Special Relativity, Lorentz Transformation",
author = "Hatch, Ronald R.",
abstract = "As was shown in a prior paper [R. R. Hatch, Phys. Essays 23, 540 (2010)], the conservation of momentum together with the increase of inertial mass with velocity requires that the orbit of a spacecraft around the earth be contracted in the along-velocity direction of the earth's
orbit around the sun. This length contraction effect combined with the effects of speed upon the clock rate results in an apparent Lorentz transformation between the earth's frame and the solar barycentric frame. However, the conservation of energy requires that some additional forces be present
which were not addressed in that paper. In the current paper, the forces are included in the analysis. Gravitomagnetic (referred to herein as kinetic) forces are developed which are consistent with both energy and momentum conservation. It is shown that these forces are consistent with a length
contracted orbit, which because of anisotropic light velocity appears as a circular orbit whose orbital frequency is decreased just as the frequency of electromagnetic radiation is decreased with the velocity of emitting atoms. The kinetic force effects are considered in two orthogonal planes,
in the plane normal to the earth's orbital velocity and in a plane containing earth's orbital velocity. The application to an arbitrary orbital plane is simply the sine/cosine combination of the two planes.",
}