Vectors and coordinates

Chandra image of LP 944-20 before flare and during flare. Credit: Marshall Space Flight Center/NASA.{{free media}}

This problem set is devoted to a variety of vector situations and coordinates for evaluation.

## Contents

* 1 Problem 1
* 2 Problem 2
* 3 Problem 3
* 4 Problem 4
* 5 Problem 5
* 6 Problem 6
* 7 Problem 7
* 8 Problem 8
* 9 Hypotheses
* 10 See also
* 11 External links

## Problem 1[edit | edit source]

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

If the x-axis is the longitude of the Greenwich meridian, and ax equals ay, then RA equals?

If ax equals ay equals az, then the declination is?

The value of a is given by?

## Problem 2[edit | edit source]

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals ay equals az

If the x-axis is the longitude of the Greenwich meridian, and the object is at ax and 2ay, then RA equals?

ax and 2ay and 3az, then the declination is?

The value of a is given by?

## Problem 3[edit | edit source]

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals ay equals az

If the x-axis is the longitude of the Greenwich meridian, and the object is at 3ax and 4ay, then RA equals?

3ax and 4ay and 5az, then the declination is?

The value of a is given by?

## Problem 4[edit | edit source]

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals 2ay equals 3az

If the x-axis is the longitude of the Greenwich meridian, and the object is at 3ax and 4ay, then RA equals?

3ax and 4ay and 5az, then the declination is?

The value of a is given by?

## Problem 5[edit | edit source]

An object has RA 10h 10m 10s Dec -20° 20' 20" and r = 23 lyrs.

What are ax, ay, and az?

What are ℓ and b?

What are the ecliptic longitude and latitude?

What are J1855 and B1855?

What are J2100 and B2100?

## Problem 6[edit | edit source]

An object has coordinates: 125.678 -85.678 and r = 110 pc.

What are RA and Dec?

What are ax, ay, and az?

What are ℓ and b?

What are the ecliptic longitude and latitude?

What are J1800 and B1800?

What are J2075 and B2075?

## Problem 7[edit | edit source]

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), for ax equals 2ay equals 3az:

If the x-axis is the longitude of the Greenwich meridian, and the object is at a = 3ax and b = 4ay, then what is

a × b ? {\displaystyle a\times b?}

a ⋅ b ? {\displaystyle a\cdot b?}

## Problem 8[edit | edit source]

Standard basis, or unit, vectors are (i, j, k) for vector components of a (ax, ay, az).

Let ax equal 3ay equal 4az.

What are

[ 5 a x , 6 a y , 7 a z ] ⋅ [ 5 a x , 6 a y , 7 a z ] ? {\displaystyle [5a_{x},6a_{y},7a_{z}]\cdot [5a_{x},6a_{y},7a_{z}]?}

If a = [5a_x, 6a_y, 7a_z] and b = [8a_x, 9a_y, 10a_z], then

a × b ? {\displaystyle a\times b?}

## Hypotheses[edit | edit source]

Main article: Hypotheses

1. The square root of negative one is not needed in vector space.

## See also[edit | edit source]

* Angular momentum and energy
* Column densities
* Cosmic circuits
* Energy phantoms
* Furlongs per fortnight
* Planck's equation
* Radiation astronomy/Problem set
* Radiation dosage
* Radiation mathematics/Problem set
* Spectrographs
* Star jumping
* Synchrotron radiation problem set
* Telescopes and cameras
* Unknown coordinate systems
* Unusual units
* Vectors and coordinates

## External links[edit | edit source]

* International Astronomical Union
* NASA/IPAC Extragalactic Database - NED
* NASA's National Space Science Data Center
* Office of Scientific & Technical Information
* The SAO/NASA Astrophysics Data System
* Scirus for scientific information only advanced search
* SDSS Quick Look tool: SkyServer
* SIMBAD Astronomical Database
* SIMBAD Web interface, Harvard alternate
* Spacecraft Query at NASA
* Universal coordinate converter

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