How does the gravitational force exerted by earth on the sun compare with the gravitational force exerted by the sun on earth?

Answer 1

The gravitational forces on two objects are equal. You attract the earth

with a force equal to your weight. Whatever you weigh on earth, that's

exactly how much the earth weighs on you.

Answer 2

The force of the Sun is a lot weaker. The Earth's gravity gives an acceleration of 9.806 metres/sec/sec at the surface.

The Sun is 330,000 times more massive but much further away, 149.6 million kilometres compared to the centre of the Earth which is 6378 kilometres away. So the Sun is 23,500 times further away. Therefore the Sun's force is 330,000/23,5002 as strong, which is 0.0006 times as strong, producing an acceleration of only 6 mm/sec/sec.

So if you were left behind from the Earth, in space and stationary, you would start accelerating towards the Sun at 6 mm/sec/sec. As you got closer the force and acceleration would increase and you would plunge into the Sun quicker than you might think, ten weeks later.

Comment : That's not exactly what the question is asking.

The answer is that the force between the Sun and Earth is much greater than the force on you, because the forces depend on the mass of you OR the Earth.

However, the gravitational acceleration is independent of the mass being accelerated.

(Of course, you and the Earth are virtually the same distance from the Sun.)

The Sun's gravity does raise tides on the Earth, but scientists usually say that there is no significant effect on people.

OK thanks for the improvement. It's true that an acceleration of 0.0006G is not going to be noticeable to the average person, which is why scientists say that - if that is what they say :). But you are right that the Sun produces the same acceleration on us and the Earth, but the force on the Earth is much more because it's more massive.

To compare the forces directly, the Sun's force on the Earth is 3.5 x 1022 Newtons, while its force on a 80 kg man is 0.47 Newtons. He does not notice it because he and the Earth and everything in it are in free fall and the force is exactly balanced by the acceleration.