Abstract
We begin by studying the position of the orbital plane of an arbitrary satellite relative to the direction of the Sun, focusing on the notion of crossing time. We then turn more specifically to Sun-synchronous satellites for which this relative position provides the very definition of their orbit. We end the chapter with a more theoretical question, calculating the angle between the direction of the Sun and the plane of the orbit, and this will lead us to the study of solar eclipses, when the satellite is in the Earth’s shadow.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The time related to the hour angle is LAT. A Sun-synchronous satellite crosses the ascending node at the same LMT. If there is no difference between LAT and LMT here, it is because we have used a simplified scenario for the Earth orbit. However, for the calculation of the cycle C S, this could not be otherwise: we only want to know how many days it will be before the next crossing (to within a few minutes), whatever time of year it is. To treat an elliptical Earth orbit, we would have to specify the day we choose to begin the cycle.
- 2.
A satellite may carry instruments pertaining to different types of mission. For example, the Russian satellite Resurs-O1-4 carries the Russian imaging device MSU for remote-sensing and the French instrument ScaRaB to study the Earth radiation budget (which can be classified as meteorological). But it is the remote-sensing aspect that determined the choice of crossing time.
- 3.
The name derives from the late Latin eclipsis, which itself comes from the Greek ἡ ἔκλειψις, εως, meaning “defection.” The word contains the prefix εκ, meaning “outside of” and the verb λείπειν, meaning “to leave.” See the etymological note on the ellipse. The word “ecliptic,” referring to the orbital plane of the Earth around the Sun, is a more recent construction. If an eclipse is to occur, the Moon must cross this plane (a necessary but not sufficient condition).
- 4.
As an example, consider the most striking case. On 11 February or 1 November, the declination is the same, but the equation of time is very different, not being far from its extremal values:
$$\displaystyle{\delta = -14.{3}^{\circ }\quad \left \{\begin{array}{l} \mbox{ 11 February}\quad E_{\mathrm{T}} = +14\ \mbox{ min}\;, \\ \mbox{ 1 November}\quad E_{\mathrm{T}} = -16\ \mbox{ min}\;. \end{array} \right.}$$Consider Fig. 10.24 (upper). On 11 February, the 16:00 curve indicates an eclipse lasting \(\Delta t_{\mathrm{e}} = 21\) min, which corresponds to
$$\displaystyle{\mbox{ LAT = LMT $-E_{\mathrm{T}} = 16$:$00 - 0$:$14 = 15$:46}\;.}$$On 1 November, this same value of \(\Delta t_{\mathrm{e}} = 21\) min is obtained with the 15:30 curve, which corresponds to
$$\displaystyle{\mbox{ LAT = LMT $-E_{\mathrm{T}} = 15$:$30 + 0$:$16 = 15$:46}\;.}$$At LMT times differing by 30 min, but at the same LAT times, the two dates yield the same length of eclipse.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Capderou, M. (2014). Orbit Relative to the Sun: Crossing Times and Eclipse. In: Handbook of Satellite Orbits. Springer, Cham. https://doi.org/10.1007/978-3-319-03416-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-03416-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03415-7
Online ISBN: 978-3-319-03416-4
eBook Packages: EngineeringEngineering (R0)