Yes, the gravity of the sun causes all celestial bodies to orbit around.
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Sort of. The mass of the sun pulls the earth towards it. It's the same relationship between the earth and the moon.
No. The sun's gravity keeps the planets, including Earth, in orbit around the sun.
The sun does indeed keep the orbits of the planets and other celestial objects in place because of its gravity.
The Sun's gravity keeps planets in an oval-shaped orbit known as an ellipse. This shape is due to the gravitational pull exerted by the Sun on the planets, causing them to move in a curved path rather than a perfect circle.
The gravitational force between the planets and the sun keeps them in orbit. The planets have enough velocity to counteract the pull of gravity, creating a stable orbit around the sun. This balance of gravitational force and velocity keeps the planets in their respective orbits.
Objects are held in their orbits by the force of gravity. The Moon moves round the Earth but is continuously being accelerated towards the Earth by the mutual force of gravity. Because the Moon is lighter, it moves more noticeably. The acceleration caused by the force makes the Moon continuously curve towards the Earth but its high speed prevents it falling inwards. That is how an orbit happens.
The force that holds the planets in orbit around the sun is gravity. The gravitational pull of the sun keeps the planets in their respective orbits, balancing the centripetal force that would otherwise cause them to drift away.
The question probably means "What keeps the planets in orbit around the Sun?" The answer to that is : The Sun's gravitational attraction provides the force needed to keep the planets in orbit. This force doesn't pull the planets any closer to the Sun, but it stops the planets moving away (at a tangent to their orbits) due to their own velocities.