(This answers tries to address good practices, but doesn't consider the question of "standard c". This answer is also specific to POSIX)

Standard constants

Use M_PI from math.h, or define PI as M_PI.

Comments

You could explain what the value -.83 represents. Is it an angle? If so, is it in radians or degreses, and what does it measure. Maybe include a Wikipedia link.

Listen to compiler warnings

These are from clang 15. See for yourself on godbolt. These are the ones I'd consider important:

<source>:39:9: warning: variable 'length' is used uninitialized whenever 'if' condition is false [-Wsometimes-uninitialized]
    if (fp) {

Very important.

<source>:70:15: warning: implicit conversion loses integer precision: 'unsigned long' to 'int' [-Wshorten-64-to-32]
    len_rep = strlen(trg);

Follow the return type of strlen and use size_t for pointer-sized things.

<source>:155:29: warning: cast from 'const char *' to 'char *' drops const qualifier [-Wcast-qual]
    char *template = (char*)insert;

Declare insert as char *, not const char *, so the signature doesn't tell lies.

<source>:212:16: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float N1 = floor(275*month/9);
<source>:218:24: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float lngHour = lng/15.0;

Be consistent and use either float or double consistently. Use floorf and 15.0f for floats.

<source>:296:1: warning: non-void function does not return a value in all control paths [-Wreturn-type]
}

This is about days_in_month. Think about what happens if the argument is 42.

(This answers tries to address good practices, but doesn't consider the question of "standard c". This answer is also specific to POSIX)

Standard constants

Use M_PI from math.h, or define PI as M_PI.

Comments

You could explain what the value -.83 represents. Is it an angle? If so, is it in radians or degrees, and what does it measure? Maybe include a Wikipedia link.

Listen to compiler warnings

These are from clang 15. See for yourself on godbolt. These are the ones I'd consider important:

<source>:39:9: warning: variable 'length' is used uninitialized whenever 'if' condition is false [-Wsometimes-uninitialized]
    if (fp) {

Very important.

<source>:70:15: warning: implicit conversion loses integer precision: 'unsigned long' to 'int' [-Wshorten-64-to-32]
    len_rep = strlen(trg);

Follow the return type of strlen and use size_t for pointer-sized things.

<source>:155:29: warning: cast from 'const char *' to 'char *' drops const qualifier [-Wcast-qual]
    char *template = (char*)insert;

Declare insert as char *, not const char *, so the signature doesn't tell lies.

<source>:212:16: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float N1 = floor(275*month/9);
<source>:218:24: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float lngHour = lng/15.0;

Be consistent and use either float or double consistently. Use floorf and 15.0f for floats.

<source>:296:1: warning: non-void function does not return a value in all control paths [-Wreturn-type]
}

This is about days_in_month. Think about what happens if the argument is 42.

Includes

You forgot #include <stdio.h> for FILE

Standard constants

Use M_PI from math.h, or define PI as M_PI.

Comments

You could explain what the value -.83 represents. Is it an angle? If so, is it in radians or degreses, and what does it measure. Maybe include a Wikipedia link.

Listen to compiler warnings

These are from clang 15. See for yourself on godbolt. These are the ones I'd consider important:

<source>:39:9: warning: variable 'length' is used uninitialized whenever 'if' condition is false [-Wsometimes-uninitialized]
    if (fp) {

Very important.

<source>:70:15: warning: implicit conversion loses integer precision: 'unsigned long' to 'int' [-Wshorten-64-to-32]
    len_rep = strlen(trg);

Follow the return type of strlen and use ssize_t for pointer-sized things.

<source>:155:29: warning: cast from 'const char *' to 'char *' drops const qualifier [-Wcast-qual]
    char *template = (char*)insert;

Declare insert as char *, not const char *, so the signature doesn't tell lies.

<source>:212:16: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float N1 = floor(275*month/9);
<source>:218:24: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float lngHour = lng/15.0;

Be consistent and use either float or double consistently. Use floorf and 15.0f for floats.

<source>:296:1: warning: non-void function does not return a value in all control paths [-Wreturn-type]
}

This is about days_in_month. Think about what happens if the argument is 42.

(This answers tries to address good practices, but doesn't consider the question of "standard c". This answer is also specific to POSIX)

Standard constants

Use M_PI from math.h, or define PI as M_PI.

Comments

You could explain what the value -.83 represents. Is it an angle? If so, is it in radians or degreses, and what does it measure. Maybe include a Wikipedia link.

Listen to compiler warnings

These are from clang 15. See for yourself on godbolt. These are the ones I'd consider important:

<source>:39:9: warning: variable 'length' is used uninitialized whenever 'if' condition is false [-Wsometimes-uninitialized]
    if (fp) {

Very important.

<source>:70:15: warning: implicit conversion loses integer precision: 'unsigned long' to 'int' [-Wshorten-64-to-32]
    len_rep = strlen(trg);

Follow the return type of strlen and use size_t for pointer-sized things.

<source>:155:29: warning: cast from 'const char *' to 'char *' drops const qualifier [-Wcast-qual]
    char *template = (char*)insert;

Declare insert as char *, not const char *, so the signature doesn't tell lies.

<source>:212:16: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float N1 = floor(275*month/9);
<source>:218:24: warning: implicit conversion loses floating-point precision: 'double' to 'float' [-Wimplicit-float-conversion]
    float lngHour = lng/15.0;

Be consistent and use either float or double consistently. Use floorf and 15.0f for floats.

<source>:296:1: warning: non-void function does not return a value in all control paths [-Wreturn-type]
}

This is about days_in_month. Think about what happens if the argument is 42.