.. index:: Fundamental Constants
There is a bound variable called CONSTANT which contains some basic fundamental
constants about the universe that you may find handy in your math operations.
.. versionadded:: 0.18
Prior to kOS version 0.18, ``constant`` was a function call, and
therefore to say ``constant:pi``, you had to say ``constant():pi``.
The function call ``constant()`` still exists and still works, but
the new way without the parentheses is preferred going forward,
and the way with the parentheses may become deprecated later.
For the moment, both ways of doing it work.
.. global:: Constant:G
Newton's Gravitational Constant, 6.67384E-11::
PRINT "Gravitational parameter of Kerbin is:".
PRINT constant:G * Kerbin:Mass.
.. global:: Constant:E
Natural Log base "e"::
PRINT "e^2 is:".
PRINT constant:e ^ 2.
.. global:: Constant:PI
Ratio of circumference of a circle to its diameter
.. global:: Constant:C
Speed of light in a vacuum, in meters per second.
.. note::
In Kerbal Space Program, all physics motion is purely Newtonian.
You can go faster than the speed of light provided you have enough
delta-V, and no time dilation effects will occur. The universe
will behave entirely linearly even at speeds near *c*.
This constant is provided mainly for the benefit of people who are
playing with the mod "RemoteTech" installed, who may want to perform
calculations about signal delays to hypothetical probes. (Note that
if the probe already has a connection, you can
:ref:`ask Remotetech directly <remotetech>` what the signal delay is.
.. global:: Constant:AtmToKPa
A conversion constant.
If you have a pressure measurement expressed in atmospheres of pressure,
you can multiply it by this to get the equivalent in kiloPascals
(kiloNewtons per square meter).
.. global:: Constant:KPaToATM
A conversion constant.
If you have a pressure measurement expressed in kiloPascals (kiloNewtons
per square meter), you can multiply it by this to get the equivalent
in atmospheres.
.. global:: Constant:DegToRad
A conversion constant.
If you have an angle measured in degrees, you can multiply it by
this to get the equivalent measure in radians. It is exactly
the same thing as saying ``constant:pi / 180``, except the result is
pre-recorded as a constant number and thus no division is performed
at runtime.
.. global:: Constant:RadToDeg
A conversion constant.
If you have an angle measured in radians, you can multiply it by
this to get the equivalent measure in degrees. It is exactly
the same thing as saying ``180 / constant:pi``, except the result is
pre-recorded as a constant number and thus no division is performed
at runtime.
.. index:: Mathematical Functions
.. function:: ABS(a)
Returns absolute value of input::
PRINT ABS(-1). // prints 1
.. function:: CEILING(a)
Rounds up to the nearest whole number::
PRINT CEILING(1.887). // prints 2
.. function:: FLOOR(a)
Rounds down to the nearest whole number::
PRINT FLOOR(1.887). // prints 1
.. function:: LN(a)
Gives the natural log of the provided number::
PRINT LN(2). // prints 0.6931471805599453
.. function:: LOG10(a)
Gives the log base 10 of the provided number::
PRINT LOG10(2). // prints 0.30102999566398114
.. function:: MOD(a,b)
Returns remainder from integer division.
Keep in mind that it's not a traditional mathematical Euclidean division where the result is always positive. The result has the same absolute value as mathematical modulo operation but the sign is the same as the sign of dividend::
PRINT MOD(21,6). // prints 3
PRINT MOD(-21,6). // prints -3
.. function:: MIN(a,b)
Returns The lower of the two values::
PRINT MIN(0,100). // prints 0
.. function:: MAX(a,b)
Returns The higher of the two values::
PRINT MAX(0,100). // prints 100
.. function:: RANDOM()
Returns a random floating point number in the range [0,1]::
PRINT RANDOM(). //prints a random number
.. function:: ROUND(a)
Rounds to the nearest whole number::
PRINT ROUND(1.887). // prints 2
.. function:: ROUND(a,b)
Rounds to the nearest place value::
PRINT ROUND(1.887,2). // prints 1.89
.. function:: SQRT(a)
Returns square root::
PRINT SQRT(7.89). // prints 2.80891438103763
.. index:: Trigonometric Functions
.. function:: SIN(a)
:parameter a: (deg) angle
:return: sine of the angle
::
PRINT SIN(6). // prints 0.10452846326
.. function:: COS(a)
:parameter a: (deg) angle
:return: cosine of the angle
::
PRINT COS(6). // prints 0.99452189536
.. function:: TAN(a)
:parameter a: (deg) angle
:return: tangent of the angle
::
PRINT TAN(6). // prints 0.10510423526
.. function:: ARCSIN(x)
:parameter x: (scalar)
:return: (deg) angle whose sine is x
::
PRINT ARCSIN(0.67). // prints 42.0670648
.. function:: ARCCOS(x)
:parameter x: (scalar)
:return: (deg) angle whose cosine is x
::
PRINT ARCCOS(0.67). // prints 47.9329352
.. function:: ARCTAN(x)
:parameter x: (scalar)
:return: (deg) angle whose tangent is x
::
PRINT ARCTAN(0.67). // prints 33.8220852
.. function:: ARCTAN2(y,x)
:parameter y: (scalar)
:parameter x: (scalar)
:return: (deg) angle whose tangent is :math:`\frac{y}{x}`
::
PRINT ARCTAN2(0.67, 0.89). // prints 36.9727625
The two parameters resolve ambiguities when taking the arctangent. See the `wikipedia page about atan2 <http://en.wikipedia.org/wiki/Atan2>`_ for more details.