# Proper Motion of Stars: Solving Daniel's Calculation Problem

• Daniel P
In summary, at "Point 4 - Turn these velocities into Cartesian velocities" the results for vx, vy, and vz are all different.
Daniel P
Hi

I have a question about "proper motion of stars".
At this page (http://www.astronexus.com/a-a/motions-long-term) there are a lot of examples how you can measuring the proper motion of stars.

But at "Point 4 - Turn these velocities into Cartesian velocities" i have some different results.

vR = -5.19 Km/sec
vTA = -58.3 Km/sec
vTD = -106.6 Km/sec
α = 14.2612
δ = 19.1873

===========================================================================
should!

vx = ( vR * cos δ * cos α ) - (vTA*sin α ) - (vTD * sin δ * cos α ) = -57.7 Km/sec
vy = ( vR * cos δ * sin α ) + (vTA * cos α ) - (vTD * sin δ sin α ) = +31.5 Km/sec
vz = vR * sin δ + vTD* cos δ = -102.3 Km/sec

===========================================================================

My results: vx = +54.1, xy = +37.5 and xz = -102.4
You can see the results one and two don't agree with my calculation, the result three agrees (depents on the accuracy of "my" data!)

Thank you very much,
DANIEL

Last edited:
Did you see that α is in hours, not degrees? Did you convert it to degrees before taking the sin and cos?

Hi

now i have seen that i must convert α = 14.2612 Hours in degrees (=213.915°)! So far so good!

but if i calculate Vx = -5.19*COS(19.1873)*COS(213.915)-(-58.34*SIN(213.915))-(-106.6*SIN(19.1873)*COS(213.915)) = +45.7 instead -57.7 Km/sec.
and if i calculate Vy = -5.19*COS(19.1873)*SIN(213.915)+(-58.34*COS(213.915)-(-106.6*SIN(19.1873)*SIN(213.915)) = -47.7 instead +31.5 Km/sec

i calculate it with Excel!

query: http://www.astronexus.com/a-a/motions-long-term

thank you again, phyzguy!

You must have made a mistake. See below:
Code:
from pylab import *
alpha = 14.2612 * 15.0 * pi / 180.0
delta = 19.1873 * pi / 180.0
vR = -5.0
vTA = -58.3
vTD = -106.6
vx = (vR * cos(delta) * cos(alpha)) - (vTA * sin(alpha)) - (vTD * sin(delta) * cos(alpha))
vy = (vR * cos(delta) * sin(alpha)) + (vTA * cos(alpha)) - (vTD * sin(delta) * sin(alpha))
vz = vR * sin(delta) + vTD * cos(delta)
print vx, vy, vz

-57.6862773004 31.464877787 -102.321575814

Ohh ok now i have the right result! i forgot the ("Pi/180")
Tthank you very much!

## 1. What is proper motion of stars?

Proper motion of stars is the apparent movement of stars across the sky due to their actual motion through space. It is caused by the combination of the star's own motion, the Earth's orbit around the Sun, and the distance of the star from Earth.

## 2. How is proper motion measured?

Proper motion is measured by comparing the position of a star relative to distant background stars at different points in time. This can be done using specialized equipment such as telescopes and cameras, and the measurements are often recorded in units of arcseconds per year.

## 3. What is Daniel's calculation problem?

Daniel's calculation problem refers to a historical error made by astronomer John Flamsteed in the late 17th century. Flamsteed incorrectly calculated the proper motion of a star named 61 Cygni, leading to confusion and discrepancies in subsequent astronomical calculations.

## 4. How was Daniel's calculation problem solved?

Daniel's calculation problem was eventually solved by Friedrich Wilhelm Bessel in the early 19th century. Bessel used more accurate measurement techniques and data to correctly calculate the proper motion of 61 Cygni, resolving the discrepancy and providing a more accurate understanding of proper motion in general.

## 5. Why is proper motion important in astronomy?

Proper motion is important in astronomy because it provides crucial information about the motion and distances of stars in the sky. By studying proper motion, astronomers can better understand the structure and evolution of our galaxy, as well as the dynamics of individual stars and their potential impact on the surrounding space.