Well, the mass of the Sun is about 300,000 times greater than the mass of the Earth. The radius of the Sun is about 100 times greater than the radius of the Earth. This means, I believe, that the gravity at the surface of the Sun might be about 30 times greater than the gravity at the surface of the Earth.
Gravity always pulls us towards the center of a particular gravity well. Any massive object creates its own gravity well around itself, and the "bottom" of the gravity well is at the center of the massive object itself. The closer you come to the center of a massive object, the more strongly its gravity will act upon you.
Here is the implications of that. Consider the Moon. The mass of the Moon is only about 1/80 of the mass of the Earth. You might think that that should mean that you would only weigh 1/80 as much on the Moon as you do on the Earth. Suppose a person weighs 80 kilograms, a fairly average weight for a grown man who isn't too overweight. If the mass of the Moon is only 1/80 of the mass of the Earth, you'd expect the man who weighs 80 kilograms on the Earth to weigh just 1 kilogram on the Moon!
However, that is not the case. A man who weighs 80 kilograms on the Earth will weigh about 13 kilograms on the moon. The reason for this is that the Moon is considerably smaller than the Earth, and therefore the distance from the Moon's surface to its center is smaller than the distance from the Earth's surface to its center. Simply because an astronaut on the Moon is closer to the Moon's center of gravity than we Earthlings ever get to the Earth's center of gravity, the astronaut simply feels a lot more of the Moon's gravity than we Earthlings feel of the gravity of the Earth
How much would we weigh if we could burrow all the way into the Earth's center? I believe the radius of the Earth is about 6,000 kilometers, which means that the center of the Earth is about 6000 kilometers away, straight down into the Earth. Gravity increases with the square of the distance, or so I believe, and 6,000 squared is actually 36 million!!! Does that mean we would weigh 36 million times more at the center of the Earth than we weigh at its surface? People, I have no idea if this is the correct way of counting and calculating.
But I am sure of two things. One, we would indeed weigh a heck of a lot more at the center of the Earth than we do here at its surface. And two, don't worry about the gravity of the Sun. It will not lift us off the Earth and send us plunging into the Sun. Sure, the Sun contains 300,000 times more mass than the Earth, but the mass center of the Sun is 150 million kilometers away, a very safe distance indeed! So, no worries, people, the Sun is not a body snatcher!
Ann
