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When the Earth is closer to the Sun it is in a slightly stronger gravitational field.

According to "General Relativity" this means time will be slowed down compared with when it's further away. However, the effect will be very small.

There is another small effect because the Earth orbits faster when closer to the Sun. This is part of "Special Relativity". Again the effect is to slow down time relative to when the Earth is further from the Sun.

Any gravity well will "slow down" time, just not perceptible for those in the well. Without getting too technical, space and time are essentially the same, or are at least interwoven. Gravity warps this fabric.

An easier way to imagine this is to think in terms of a black hole. As light and matter fall into the gravity well of a black hole, time will slow. Picture a space ship falling into the gravity well. The astronaut inside the ship will perceive the passage of time normally, all the way to the event horizon. If the ship is able to somehow stop and orbit at this point, time for the astronaut will appear unchanged. But, to an observer outside the gravity well, the astronaut will appear to move more slowly, as if time is slowing down the closer the ship gets to the event horizon.

The gravity wells of Earth and the Sun are similar to that of a black hole, just nowhere near as intense.

For further information, study the relativistic affects of gravity. Space and time here limit how much this can be discussed. (No pun intended. Or, is there?)

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