Weight of the whole earth with reference to an apple

[ffrancis]

I don't know the answer to this question but it may only require common sense:

Let's say an apple on the surface of the Earth weighs 0.25 Kg. Imagine the apple as the little Earth and the whole Earth on top of it. What is the weight of the Earth with reference to that apple?

I suspect the answer is 0.25 Kg also? If so, why? If not, then what is the correct answer and why?

 

[Dale]

First kg is a unit of mass, and weight is a force. So a .25 kg apple in Earth's gravitational field would weigh 2.45 N. Since forces are equal and opposite (Newton's 3rd law) the weight of the Earth in the gravitational field of the apple would also be 2.45 N.

 

[charng]

I can provide a more accurate and detailed response to this question. The weight of the Earth with reference to an apple would not be 0.25 Kg, as the Earth is much larger and more massive than an apple.

To calculate the weight of the Earth with reference to an apple, we would need to use the formula for gravitational force: F = (G x m1 x m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this scenario, the apple would be m1 and the Earth would be m2. We can assume that the distance between them is the radius of the Earth, which is approximately 6,371 kilometers. Using the mass of an average apple (0.25 Kg) and the mass of the Earth (5.972 x 10^24 Kg), we can calculate the weight of the Earth with reference to the apple.

Plugging in the values, we get F = (6.67 x 10^-11) x (5.972 x 10^24) x (0.25) / (6,371,000)^2 = 9.807 N. This means that the weight of the Earth with reference to an apple would be approximately 9.807 Newtons, which is significantly larger than the weight of the apple itself.

This calculation shows that even though the Earth is much larger and more massive than an apple, the gravitational force between the two objects is still significant. This is because the gravitational force is dependent on both the masses of the objects and the distance between them.

In conclusion, the weight of the whole Earth with reference to an apple is not 0.25 Kg, but rather approximately 9.807 N. This calculation highlights the importance of understanding the principles of gravity and how they apply to different objects in the universe.