TI-65: Relativity Applications
Introduction
The programs on today's blog entry were programmed on the Texas Instruments TI-65 calculator. One of the features of the TI-65 is the set of physical constants.
The programs call up the speed of light, c = 299,792,458 m/s, by the [ 3rd ] [ 2 ] key combination. If you are using a TI-58, TI-59, or TI-66, where there are no physical constants, please store 299792458 in a memory register first, and replace the key sequence by recalling that register.
These programs will use the shortcut:
cos(arcsin x) = √(1 - x^2) for all -1 ≤ x ≤ 1
This allows us to cut down on the number of bytes required.
Redshift vs. Blueshift
f0 = fs * √((1 - v/c) / (1 + v/c))
v = velocity of the source/star in m/s
blueshift: v < 0
redshift: v > 0
fs = frequency given off by the source/star in Hz
f0 = observed frequency in Hz
v/c is stored in register 0.
Program
Keys:
LBL F1
1
-
(
R/S
÷
[c]
)
STO 0
=
÷
(
1
+
RCL 0
)
=
√
×
R/S
=
RTN
Key Codes:
2nd 53.53
1
49
16
51
28
3rd 46
17
12.0
39
28
16
1
59
13.0
17
39
33
38
51
39
2nd 52
Instructions:
1. Press [ F1 ].
2. Enter v when execution stops, press [ R/S ].
3. Enter fs when execution stops, press [ R/S ].
4. f0 is calculated.
Example:
v = 210,000,000 m/s
fs = 450 * 10^6 Hz (450 [ EE ] 6)
Result: f0 = 1.888581542E8 Hz (188.8581542 * 10^6)
Relativistic Doppler Effect
f0 = (fs * √(1 - v^2/c^2)) / (1 - v/c * cos Θ)
v = velocity of the source
Θ = direction of source's motion relative to the observer (angle from the observer's perspective)
fs = frequency given off by the source/star in Hz
f0 = observed frequency in Hz
Program
Key:
LBL F2
(
R/S
÷
[c]
)
STO 0
INV SIN
COS
×
R/S
=
÷
(
1
-
RCL 0
×
R/S
COS
)
=
RTN
Key Code:
2nd 53.54
16
51
28
3rd 46
17
12.0
-22
23
38
51
39
28
16
1
49
13.0
38
51
23
17
39
2nd 52
Instructions:
1. Press [ F2 ].
2. Enter v when execution stops, press [ R/S ].
3. Enter fs when execution stops, press [ R/S ].
4. Enter Θ when the execution stops, press [ R/S ].
5. f0 is calculated.
Example:
v = 196 * 10^6 m/s
fs = 500 * 10^6 Hz
Θ = 40° (degrees mode)
Result: f0 = 7.579362482 * 10^8 Hz = 757.9362482 * 10^6 Hz
Time Dilation
t' = t0 * √(1 - (v/c)^2)
t0 = source's time
v = velocity of source in m/s
t' = observer's time
Key:
LBL 0
R/S
÷
[ c ]
=
INV SIN
COS
×
R/S
=
RTN
Key Codes:
2nd 53.0
51
28
3rd 46
39
-22
23
38
51
39
2nd 52
Instructions:
1. Press [ SBR ] [ 0 ].
2. Enter v, press [ R/S ].
3. Enter t0 when execution stops, press [ R/S ].
4. t' is calculated.
Example:
v = 164 * 10^6 m/s
t0 = 1.5 yr
Result: t' = 1.255654687 yr
Source:
"Sinclair Enterprise Programmable: Physics Engineering Electronics Program Library" Sinclair Radionics Inc. New York, NY and St. Ives, Huntingdon, Cambridgeshire UK. 1976
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
