The earth is known to be falling towards the sun as a result of intense gravity. The earth is known to have plenty of sideways momentum and due to this sideways momentum, the earth is often falling towards the sun and missing it.
The reason we are pulled to the center of the Earth and not into the much larger sun by gravity is that all objects with mass, like our Earth, do bend and curve the fabric of the universe referred to as spacetime.
At most, the gravity from the sun result in our planet moving in a curved, elliptical path. but, the planets are moving fast enough so that they are not pulled into the sun.
The sun has a more weaker gravity and as it loses mass, it causes the Earth to slowly move away from it.
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