Edit in JSFiddle

<div class="container" ng-controller="ctrl" ng-app>
    <div class="page-header">
        <h2>春分・秋分の日計算</h2>
    </div>
    <h4><input type="number" max="2099" min="1981" ng-model="year" ng-change="update();"/> 年の</h4>
    <h4>春分の日は「3月{{springEquinoxDay}}日」です。</h4>
    <p>springEquinox={{springEquinox}}</p>
    <h4>秋分の日は「9月{{autumnEquinoxDay}}日」です。</h4>
    <p>autumnEquinox={{autumnEquinox}}</p>
</div>

/**
 * AngularJSアプリケーションコントローラー
 */
function ctrl($scope) {
    var date = new Date();
    $scope.year = date.getFullYear();
    $scope.update = function() {
        $scope.springEquinox = getDayOfSpringEquinox($scope.year);
        $scope.springEquinoxDay = Math.round($scope.springEquinox);
        $scope.autumnEquinox = getDayOfAutumnEquinox($scope.year);
        $scope.autumnEquinoxDay = Math.round($scope.autumnEquinox);
    }
    $scope.update(); //初回アップデート
}


/**
 * @param year
 * @return 春分の日が3月の何日か（2099年までの正確な値）
 */
function getDayOfSpringEquinox(year) {
  var springEquinox = 99;
  if (year <= 2099) {
    var UNIT = 1000000;
    var yearDiff = year - 1980;
    springEquinox = (20843100 + (242194 * yearDiff)) / UNIT - (yearDiff / 4);
  }
  return springEquinox;
}


/**
 * @param year
 * @return 秋分の日が9月の何日か（2099年までの正確な値）
 */
function getDayOfAutumnEquinox(year) {
  var autumnEquinox = 99;
  if (year <= 2099) {
    var UNIT = 1000000;
    var yearDiff = year - 1980;
    autumnEquinox = (23248800 + (242194 * yearDiff)) / UNIT - (yearDiff / 4);
  }
  return autumnEquinox;
}