File:Shell-diag-1.svg merupakan versi vektor bagi fail ini. Ia sepatutnya digunakan bagi menggantikan imej raster ini apabila ia mempunyai peleraian yang lebih besar dan lebih baik. File:Shell-diag-1.png → File:Shell-diag-1.svg Untuk maklumat lanjut, sila lihat Bantuan:SVG. Anda juga boleh melihat maklumat mengenai sokongan imej SVG MediaWiki. Dalam bahasa lain Alemannisch ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ မြန်မာဘာသာ ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ +/−

 

KeteranganShell-diag-1.png	A diagram illustrating the derivation of Newton's shell theorem. Shown is a thin shell with a test mass outside the shell (${\displaystyle r>R}$).
Tarikh	29 September 2006
Sumber	Karya sendiri
Pengarang	Jim Wisniewski

Dengan ini, saya selaku pemegang hak cipta karya ini, menerbitkannya di bawah lesen yang berikut:

Fail ini dilesenkan di bawah lesen Pengiktirafan-Perkongsian Serupa 2.5 Umum Creative Commons.

Anda bebas:

• untuk berkongsi – untuk menyalin, mengedar dan memindah hasil kerja
• untuk mencampur semula – untuk menyesuaikan karya

Di bawah syarat berikut:

• pengiktirafan – Anda mesti memberi penghargaan yang berpatutan, bekalkan pautan ke lesen, dan tunjukkan jika perubahan telah dibuat. Anda boleh lakukannya dalam sebarang cara yang munasabah, tetapi bukan dalam sebarang cara yang mencadangkan pemberi lesen mengendors anda atau penggunaan anda.
• perkongsian serupa – Jika anda mengubah, adun semula, atau menokok tambah bahan, anda mesti menyebarkan sumbangan anda di bawah lesen yang sama atau serasi dengan yang asal.

https://creativecommons.org/licenses/by-sa/2.5CC BY-SA 2.5 Creative Commons Attribution-Share Alike 2.5 truetrue

This image and the others in the same series (2, 3, 4) were generated from the MetaPost code presented below. The code is released under the same license as the images themselves.

% shell-diag.mp
% A diagram illustrating the derivation of Newton's shell theorem.  To be
% processed with MetaPost.

color bandshade, fillshade;
bandshade = 0.7 [blue, white];
fillshade = 0.9 white;

numeric dotsize, deg;
dotsize = 5 bp;
deg = length( fullcircle )/360;

freelabeloffset := 3/4 freelabeloffset;
labeloffset := 2 labeloffset;

def dot( expr P ) =
  fill fullcircle scaled dotsize shifted P withcolor black;
enddef;

def draw_circle( expr R, stroke ) =
  save p;
  pen p;
  p = currentpen;
  pickup p scaled stroke;
  draw fullcircle scaled 2R;
  pickup p;
enddef;

vardef anglebetween( expr a, b, rad, str ) =
  save endofa, endofb, common, curve, where;
  pair endofa, endofb, common;
  path curve;
  numeric where;
  endofa = point length( a ) of a;
  endofb = point length( b ) of b;
  if round point 0 of a = round point 0 of b:
    common = point 0 of a;
  else:
    common = a intersectionpoint b;
  fi;
  where = turningnumber( common--endofa--endofb--cycle );
  curve = (unitvector( endofa - common ){(endofa - common) rotated (90 * where)} ..
           unitvector( endofb - common )) scaled rad shifted common;
  draw thefreelabel( str, point 1/2 of curve, common ) withcolor black;
  curve
enddef;

def draw_angle( expr a, b, rad, str ) =
  begingroup
    save p;
    pen p;
    p = currentpen;
    pickup p scaled 1/2;
    draw anglebetween( a, b, rad, str );
    pickup p;
  endgroup
enddef;

def label_line( expr a, b, disp, str ) =
  begingroup
  save mid, opp;
  pair mid, opp;
  mid = 1/2 [a, b];
  opp = -disp rotated (angle( b - a ) - 90) shifted mid;
  draw thefreelabel( str, mid, opp );
  draw a -- b;
  endgroup
enddef;

def draw_thinshell( expr R, r, theta, dtheta, thetarad, phirad ) =
  begingroup
    save M, m;
    pair M, m;
    M = (0, 0);
    m = (r, 0);
    
    save circ;
    path circ;
    circ = fullcircle scaled 2R;
    
    save thetapt, dthetapt;
    pair thetapt, dthetapt;
    thetapt   = point (theta * deg) of circ;
    dthetapt  = point ((theta + dtheta) * deg) of circ;
    
    save upper, lower, band;
    path upper, lower, band;
    upper = subpath (0, 4) of circ;
    lower = subpath (4, 8) of circ;
    band = buildcycle( upper, (xpart thetapt,  R) -- (xpart thetapt,  -R),
                       lower, (xpart dthetapt, R) -- (xpart dthetapt, -R) );
    
    % draw figures
    save p;
    pen p;
    p = currentpen;
    pickup p scaled 1/2;
    fill band withcolor bandshade;
    draw band;
    pickup p;
    
    save near, far;
    pair near, far;
    if theta < 90:
      near = 3/4[ulcorner band, llcorner band];
      far  = right shifted near;
    else:
      near = 3/4[urcorner band, lrcorner band];
      far  = left shifted near;
    fi;
    draw thefreelabel( btex $dM$ etex, near, far );
    
    dot( M );
    %label.llft( btex $M$ etex, M );
    
    dot( m );
    label.lrt( btex $m$ etex, m );
    
    draw M -- thetapt;
    label_line( M, m, right, btex $r$ etex );
    label_line( m, thetapt, right, btex $s$ etex );
    if R <> r:
      label_line( M, dthetapt, left, btex $R$ etex );
    else:
      draw M -- dthetapt;
    fi;
    
    draw_angle( m -- M, m -- thetapt, phirad, btex $\phi$ etex );
    draw_angle( M -- m, M -- thetapt, thetarad, btex $\theta$ etex );
    draw_angle( M -- thetapt, M -- dthetapt, R, btex $d\theta$ etex );
  endgroup
enddef;

def draw_thickshell( expr Ra, Rb, r ) =
  begingroup
    save m;
    pair m;
    m = (r, 0);
    
    fill fullcircle scaled 2Rb withcolor fillshade;
    fill fullcircle scaled 2r  withcolor bandshade;
    unfill fullcircle scaled 2Ra;

    dot( origin );
    dot( m );
    label.lrt( btex $m$ etex, m );
    label_line( origin, m, right, btex $r$ etex );
    
    draw_circle( Rb, 2 );
    if Ra > 0:
      draw_circle( Ra, 2 );
      label_line( origin, dir( 100 ) scaled Rb, left,  btex $R_b$ etex );
      label_line( origin, dir( 80 )  scaled Ra, right, btex $R_a$ etex );
    else:
      label_line( origin, dir( 90 )  scaled Rb, left,  btex $R_b$ etex );
    fi;
  endgroup
enddef;

% Thin shell, r > R
beginfig(1)
  numeric R;
  R = 1 in;
  draw_thinshell( R, 3R, 50, 15, 1/4 in, 3/4 in );
  draw_circle( R, 2 );
endfig;

% Thin shell, r < R
beginfig(2)
  numeric R;
  R = 1 in;
  draw_thinshell( R, 0.7R, 125, 15, 1/8 in, 1/3 in );
  draw_circle( R, 2 );
endfig;

% Thick shell
beginfig(3)
  numeric Ra, Rb, r;
  Ra = 0.8 in;
  Rb = 1.3 in;
  r = 1 in;

  draw_thickshell( Ra, Rb, r );
endfig;

% Solid sphere
beginfig(4)
  numeric Ra, Rb, r;
  Ra = 0;
  Rb = 1.3 in;
  r = 1 in;
  
  draw_thickshell( Ra, Rb, r );
endfig;

end