Animating a box-shadow/text-shadow on a circular path?

Question

I'm trying to use CSS animations to create the effect of a light source pointing down on an object, casting a shadow and moving in a circular motion around it. I've created a snippet below to show where I've gotten to so far.

It's sort-of close but at the moment (because I only have 4 keyframes) it's like the light source is moving along a square path. I'd like it to look like it was moving along a circular path.

The only solution I can think of to come close is to add a bunch of more keyframes and create a (for the sake of simplicity) a dodecagon-shaped path, but is there a simpler solution? Is there a type of timing function I could use to ease it into a smoother path? Or could I use some sort of Sass function to automatically calculate the intermediate keyframes?

I should have noted that once I get this working with box-shadows, I'd also like to apply the same method to text-shadows.

.container {
  display: flex;
  align-items: center;
  justify-content: center;
  width: 100%;
  height: 100vh;
}

.circle {
  width: 200px;
  height: 200px;
  border-radius: 100%;
  background-color: teal;
  box-shadow: 50px 50px 5px darkgrey;
  animation: orbit-shadow 5s linear infinite;
}

@keyframes orbit-shadow {
  0% {
    box-shadow: 50px 50px 5px darkgrey;
  }
  25% {
    box-shadow: -50px 50px 5px darkgrey;
  }
  50% {
    box-shadow: -50px -50px 5px darkgrey;
  }
  75% {
    box-shadow: 50px -50px 5px darkgrey;
  }
  1000% {
    box-shadow: 50px 50px 5px darkgrey;
  }
}

<div class="container">
  <div class="circle"></div>
</div>

Answer 1

You have to consider rotation for this. Use a pseudo element to avoid rotating the main element:

.container {
  display: flex;
  align-items: center;
  justify-content: center;
  min-height: 100vh;
  position:relative;
  z-index:0;
}

.circle {
  width: 200px;
  height: 200px;
  margin:50px;
  border-radius: 100%;
  background-color: teal;
  position:relative;
}
.circle::before {
  content:"";
  position:absolute;
  z-index:-1;
  top:0;
  left:0;
  right:0;
  bottom:0;
  border-radius:inherit;
  box-shadow: 50px 50px 5px darkgrey;
  animation: orbit-shadow 5s linear infinite;
}

@keyframes orbit-shadow {
  100% {
    transform:rotate(360deg);
  }
}

body{
 margin:0;
}

<div class="container">
  <div class="circle"></div>
</div>

Or you simply rotate the element if you won't have any content:

.container {
  display: flex;
  align-items: center;
  justify-content: center;
  min-height: 100vh;
}

.circle {
  width: 200px;
  height: 200px;
  border-radius: 100%;
  background-color: teal;
  box-shadow: 50px 50px 5px darkgrey;
  animation: orbit-shadow 5s linear infinite;
}

@keyframes orbit-shadow {
  100% {
    transform:rotate(360deg);
  }
}

body{
 margin:0;
}

<div class="container">
  <div class="circle"></div>
</div>

Another idea:

.container {
  display: flex;
  align-items: center;
  justify-content: center;
  min-height: 100vh;
  position:relative;
  z-index:0;
}

.circle {
  width: 200px;
  height: 200px;
  margin:50px;
  border-radius: 100%;
  background-color: teal;
  position:relative;
}
.circle::before {
  content:"";
  position:absolute;
  z-index:-1;
  top:0;
  left:0;
  right:0;
  bottom:0;
  border-radius:inherit;
  background:darkgrey;
  filter:blur(5px);
  animation: orbit-shadow 5s linear infinite;
}

@keyframes orbit-shadow {
  0% {
    transform:rotate(0deg)   translate(50px);
  }
  100% {
    transform:rotate(360deg) translate(50px);
  }
}

body{
 margin:0;
}

<div class="container">
  <div class="circle"></div>
</div>

You can also do the same for text-shadow with a slightly different animation in order to not rotate the text:

.container {
  display: flex;
  align-items: center;
  justify-content: center;
  min-height: 100vh;
}

.circle {
  position:relative;
  font-size:40px;
  font-weight:bold;
}
.circle::before,
.circle::after{
  content:attr(data-text);
  position:relative;
  z-index:1;
}

.circle::before {
  position:absolute;
  top:0;
  left:0;
  right:0;
  bottom:0;
  color:transparent;
  text-shadow:0 0 5px darkgrey;
  animation: orbit-shadow 5s linear infinite;
}
/* the 50px is your offset */
@keyframes orbit-shadow {
  0% {
    transform:rotate(0deg)   translate(50px) rotate(0deg);
  }
  100% {
    transform:rotate(360deg) translate(50px) rotate(-360deg);
  }
}
body{
 margin:0;
}

<div class="container">
  <div class="circle" data-text="some text"></div>
</div>