Question

I imagined a 2D cross section of a 3D earth and having a 2D observer on that 2D cross section of the earth. they would still observe the acceleration due to gravity being 9.8m/s² because the 3D earth is still there but the 2D observer cannot see it and they would still observe gravity falling off in strength following the inverse square law. Wouldn't this mean that they observe the 2D earth to have a smaller mass because it is only 1 singular cross section of the 3D earth and (Mass = Density * Volume) the volume they would observe to contain their earth is much smaller than the full volume of the actual earth meaning a smaller observed mass. Since the formula for gravity between two objects is F=G∗m₁∗m₂/r². this mean that the 2D observer would assume that for a small amount of mass you get a large force of gravity also meaning a higher gravitational constant as every other variable is followed as it is in 3 dimension such as F the force experienced would be the same andr2r2following the inverse square law would be the same and the observed mass of objects in the 2D world would be less than a 3D observer in a 3D world would observe. Wouldn't the 2D observer also observe a much larger gravitational constant to give them the same values for the force?

Answer 1

In a 2D cross section of the earth, an observer would still experience the same acceleration due to gravity. However, they would perceive a smaller mass for the 2D earth due to the limited volume they can observe. This would result in a higher gravitational constant to maintain the same force of gravity.

Step-by-step explanation:

According to Newton's law of gravitation, the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. In the scenario described, the 2D observer on the 2D cross section of the earth would still observe the acceleration due to gravity as 9.8 m/s² because the 3D earth is still present and the force of gravity follows the inverse square law.

However, the 2D observer would perceive a smaller mass for the 2D earth because they can only observe a smaller volume of the actual earth. This would lead to a higher value for the gravitational constant in order to maintain the same values for the force of gravity.