没有合适的资源?快使用搜索试试~ 我知道了~
首页火星地心坐标系的定义及其之间的关系
火星地心坐标系的定义及其之间的关系
5星 · 超过95%的资源 需积分: 10 30 下载量 117 浏览量
更新于2023-03-03
评论 2
收藏 2.72MB PDF 举报
这是国外的一篇关于我们地球的近邻——火星(Mars)的坐标系的文档,非常有用,解释的很到位,唯一的确定是英文版本,但是只要你有耐心,绝对能读懂。
资源详情
资源评论
资源推荐
Interoffice Memorandum
343B-2006-004
August 15, 2006
To: Distribution
From: P. Daniel Burkhart
Subject: MSL Update to Mars Coordinate Frame Definitions
This memo is an update to the MSP’01 (later Mars Odyssey) mission planning memo
written in July, 1999 by Robert Mase des cribing Mars centered coordinate frame
definitions and relationships.
1
The text of the original memo is unchanged except
where specific Mars Odyssey references were changed. The text is included here to
create a stand-alone reference, as opposed to supplying a supplement to the Mars
Odyssey memo.
Introduction
The purpose of this memo is to update the planetary constants that have changed
in the Mars Odyssey memo on the definition of Mars coordinate frames. This up-
date is specifically for Mars Science Laboratory (MSL) for consistency with the MSL
Planetary Constants and Models document.
2
Since the Mars Odyssey update, this
memo has become the standard reference for Mars coordinate frames for subsequent
missions. The focus here will be on Mars centered coordinate systems, and only a
subset of those systems will be described. This memo is not intended to be a generic
reference on the subject, merely an update to certain coordinate frame definitions
that are of interest to Mars missions.
The first part of this memo will briefly define the terminology that is customarily
utilized in the description of these systems. The definitions presented are either based
on or taken verbatim from the reference material. Then, several specific Mars relative
coordinate systems will be carefully defined. The process used to define these systems
remains unchanged from the MO document, however, certain quantities associated
with those systems will be updated. Finally, the relationships between the systems
of interest will be calculated.
Basic Definitions
Any treatment of astrodynamic quantities will involve the use of coordinate systems.
A coordinate system is simply a means of relating points in three dimensional space,
MSL Update to Mars Coordinate Frame Definitions
and their motion as ordered triples (ex. X,Y,Z). The system is fully specified by three
fundamental characteristics: frame, center and type.
Frame
A coordinate frame represents an associated set of Cartesian axes: X,Y,Z which
are themselves specified by four additional items: reference body, reference plane,
reference direction, and reference time.
The reference body can be any body in the solar system. For the applications
of this memo, the reference body will be either the Earth or Mars. Note that the
specification of a reference body name in the coordinate frame definition says nothing
about where the frame is actually centered. For example, we will later define an Earth
equator frame centered at Mars.
The reference plane along with the reference body define the X-Y plane of the
frame. Two pertinent examples of reference planes are the Earth equator plane and
the Earth orbit plane. Because a plane is defined by its unit normal, the Z-axis
defines the X-Y reference plane. For an equator plane, the Z-axis will generally be
along the axis of rotation of the planet. For an orbit plane, the Z-axis will be in the
direction of the orbital angular momentum vector.
The reference direction is an arbitrary, although usually physically meaningful,
direction in the X-Y plane that defines the direction of the X-axis. Typically, such
a direction is obtained from the line of no des that result from the intersection of the
reference plane with some other known plane. For example, the X-axis of the Earth
equator plane may be the vernal equinox, which is the ascending node of the Earth
orbit plane on the Earth equator plane. This system is called the Earth Equator and
Equinox plane for obvious reasons. In another c ase, the X-axis of the Mars equator
plane may be the ascending node of the Mars equator plane on the Earth equator
plane, illustrating the fact that the two planes do not necessarily have to have the
same reference body name. This system is called the Mars Equator and IAU-vector
plane since the X-axis definition is that specified by the International Astronomical
Union (Ref 2). A frame with a body-fixed X-axis will rotate as the body rotates.
Such a system would typically utilize the intersection of the body’s prime meridian
with the equator plane to define the direction of the X-axis. Such a system is defined
for Mars and is called the Mars Equator and Prime Meridian plane.
The reference time is a specification of when the frame being described has, had or
will have a physical existence. It is necessary to specify a reference time, because the
reference planes that describe the coordinate frames are likely to be in some state of
motion due to the fact that the bodies they are associated with are continually being
subjected to the perturbing forces of the physical universe.
For the Earth, the plane of the ecliptic and the plane of the equator are used as
planes of refe rence, and their intersection, the equinox, is in a state of motion due to
their motion. The motion of the ecliptic plane is due to the the gravitational action
of the planets on the Earth’s orbit and makes a contribution to precession known as
2
MSL Update to Mars Coordinate Frame Definitions
planetary precession. The motion of the equator is due to the torque of the Sun,
Moon, and planets on the oblate Earth. This motion can be divided up into two
parts, lunisolar precession, which is the smooth, long-period motion of the mean
pole of the equator about the pole of the ecliptic, with a period of about 26, 000
years, and nutation, which is the short-period motion of the true pole around the
mean p ole with a variety of periods up to 18.6 years. The combination of lunisolar
and planetary precession is called general precession.
Precession and nutation taken together represent the true motion of a reference plane,
as well as its Z-axis, which manifests as a cyclic behavior about a mean motion that
would be obtained if precession were considered alone. Thus the Earth True Equator
plane reflects the effects of prec ession and nutation, whereas the Earth Mean Equator
plane reflects the effect of precession alone.
Both of these influences are related to the concept of inertial and non-inertial reference
frames. An inertial frame is one in which the Cartesian axes are in a state of
rest or uniform (unaccelerated) motion. Since rotation always involves acceleration,
rotating systems cannot be considered inertial. A non-inertial system is one which
is undergoing some sort of non-uniform (accelerated) motion and is most commonly
thought of as one in which the axes are rotating. A body-fixed frame is a specialized
typ e of noninertial frame, though it is certainly not the only such frame.
The most common type of motion for axes in a non-inertial frame is rotation, although
precession and nutation are also examples. The reference time defining the orientation
of the axes is taken to be the same time at which a state is to be related to the
frame. This reference time is considered to be “of-date ”. One example of a non-
inertial frame is the Earth Mean Equator and Equinox of Date, which refle cts only
the precession of the Earth’s pole. However, it is noteworthy that this system is
not too different from an inertial system since precession is a long period motion.
Another non-inertial frame is the Earth True Equator and Equinox of Date, which
reflects both the precession and nutation of the Earth pole, the latter of which is of
short period and more rapid. Finally there are the body-fixed frames such as the
Earth True Equator and Prime Meridian of Date, which is non-inertial because, in
addition to precession and nutation, it reflects the daily rotation of the X-axis which
is tied to the Prime Meridian.
In order to specify an inertial frame, it is typical, though not essential, to begin with
a mean equator or mean orbit plane (i.e. one which considers only precession) and
freeze it at a particular instant of time. This moment, or reference time, is called
the epoch of the reference plane and represents a snapshot of the position of the
plane at that instant in time. The standard reference epoch is 01-Jan-2000 12:00:00
ET, commonly called J2000. This is the beginning of the Julian year 2000, and
corresponds to a Julian date of 2451545.0. The fundamental inertial frame definition
uses the Earth as the reference body, its mean equator as the reference plane, the
vernal equinox of its mean orbit as the reference direction, and J2000 as the reference
epoch. Hence, this frame is called the Earth Mean Equator and Equinox of Epoch
J2000 or simply EME2000.
3
MSL Update to Mars Coordinate Frame Definitions
Center
The center of a coordinate frame is the origin of the system. It may be at the center
of any of the nine planets, their natural satellites, comets, the Sun, the solar system or
any planet system barycenter, at a topographic location on any of these b odies, or at
a spacecraft. The reference body name used in the frame definition is not necessarily
related to the body center, although frequently the reference body is chosen as the
frame center. One such system would be the Mars-centered Mars Mean Equator and
Equinox of Date. Another example that is widely used for interplanetary navigation
is a Sun-centered Earth Mean Equator and Equinox of Epoch J2000. In this case,
the inertial frame is related to the Earth, while the system is centered at the Sun.
Typ e
Given a center and a coordinate frame, there are then several types of coordinates
commonly used to represent state vectors. They are all equivalent, and each requires
the specification of six parameters to specify both the p osition and velocity of a point
in the frame. Because this memo is of a limited scope, only cartesian and spherical
coordinates will be discussed here.
Cartesian coordinates consist of the X, Y, and Z triple to specify p osition and
the time derivatives of these to specify velocity. These are most useful during the
process of numerical integration of a trajectory, although they may give little insight
into the overall characteristics of the trajectory.
Spherical coordinates utilize a distance (radius or altitude), and two angles (dec-
lination and right ascension, or latitude and east longitude) to specify position, and
speed, flight path azimuth and flight path angle to specify velocity. Generally dec-
lination and right ascension are used with an equator plane when the X-axis is not
rotating diurnally, such as an equinox X-axis. One example is the Earth-centered
Earth Mean Equator and Equinox of Epoch J2000. In this case right ascension is
measured along the mean equator, positive East (in the right-handed sense) from the
equinox. Declination is measured from the mean equator plane positive to the North.
Latitude and longitude are commonly used for an equator plane with an X-axis that
rotates diurnally, such as a Prime Meridian based system. These coordinates are
useful in relating the motion of a spacecraft to a central body. An example is the
Earthcentered Earth Mean Equator and Prime Meridian of Date. In this case, East
longitude is measured along the mean equator p ositive East from the Prime Meridian.
Latitude is measured from the mean equator positive North.
In addition, latitude and longitude are sometimes used when the reference plane is
in a body’s orbit, even though the X-axis of such a system is not generally rotating
diurnally. One example is Sun-centered Earth Mean Orbit and Equinox of Epoch
J2000 spherical coordinates, sometimes referred to as Celestial coordinates. In this
case Celestial Longitude is measured in the plane of the ecliptic positive East (in the
right-handed sense) from the equinox. Latitude is measured from the ecliptic plane
positive to the North.
4
剩余18页未读,继续阅读
cangtian001
- 粉丝: 0
- 资源: 2
上传资源 快速赚钱
- 我的内容管理 收起
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
会员权益专享
最新资源
- 27页智慧街道信息化建设综合解决方案.pptx
- 计算机二级Ms-Office选择题汇总.doc
- 单链表的插入和删除实验报告 (2).docx
- 单链表的插入和删除实验报告.pdf
- 物联网智能终端项目设备管理方案.pdf
- 如何打造品牌的模式.doc
- 样式控制与页面布局.pdf
- 武汉理工Java实验报告(二).docx
- 2021线上新品消费趋势报告.pdf
- 第3章 Matlab中的矩阵及其运算.docx
- 基于Web的人力资源管理系统的必要性和可行性.doc
- 基于一阶倒立摆的matlab仿真实验.doc
- 速运公司物流管理模式研究教材
- 大数据与管理.pptx
- 单片机课程设计之步进电机.doc
- 大数据与数据挖掘.pptx
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功
评论2