If Earths mass decreased to one half its original mass with no change in radius then what is your weight?

Answer 1

That would depend on what happened to the Earth's radius as well, since gravity depends on the mass of the object and the square of the distance between them. So if the mass were doubled and the radius of the Earth also doubled, the force of gravity would actually go down by half!

Answer 2

Your weight would be half of your original weight. Weight is determined by the force of gravity pulling on an object, which is directly proportional to the mass of the object. If the Earth's mass is halved, the force of gravity pulling on you would also be reduced by half.

Answer 3

From the Law of Gravity, F=(GmM)/rr where M is the mass of Earth and m the human mass, G=6.67*10^(-11) r is Earth's radius The force F is F=mg also mg=weight where g is the acceleration due to gravity and m the human mass Putting them together, we get that the acceleration due to gravity g, is g=GM/rr From this, we get that if the mass of the Earth was doubled, then the acceleration due to gravity would be doubled. So, F=m2g this means that the human weight would be doubled as well I think the derivation is correct.

Answer 4

The formula for the gravitational force is F = G my me / R2 .

F = your weight

G = gravitational constant

my = your mass

me = earth's mass

R = distance between your center of mass and earth's center of mass

G and my don't change in this discussion, so we'll represent them by 'K'.

Original weight = K me / R2

New weight = K (2me ) / (2R)2

= K (2/4) me / R2 = 1/2 of original weight.

Your weight would decrease by 1/2.

Answer 5

If the mass of the earth suddenly doubled, while its radius and relative density distribution remained constant,
The weight of you and me and every person and object on earth would also double.

Answer 6

Let's take the changes one at a time, so you can see the effect of each one:

-- If the mass of the Earth suddenly doubled, your weight would also double.

-- If the Earth's radius suddenly doubled, so that you were suddenly twice as far away

from its center, your weight would become 1/22 = 1/4 of its original value.

So if both of these impossible things happened at the same time, your weight

would suddenly multiply by (2) x (1/4) = 1/2 of where it started out.

Answer 7

I suppose with "relative mass" you mean, assume the density is the same.

Surface area is proportional to the square of the radius, so the radius would increase by a factor square root of 2, or 20.5 - about 1.414. Volume, and therefore (assuming the same density) mass, is proportional to the cube of the radius, therefore, it will increase by a factor of 2 times the square root of 2, or 21.5 - about 2.818. Now you can use the formula of universal gravitation, with those numbers (mass increases by a factor 2.818, distance increases by a factor 1.414). Clearly, the force (weight) will increase by a factor square root of 2.

Answer 8

The person's distance from the center of the earth would be reduced to 1/2 of its

present distance, so the force of gravity between the earth and the person would

increase by the factor of (2)2 = 4. He would weigh four times his present weight.

Answer 9

Then (assuming Earth's diameter didn't change), weight would also double.

Then (assuming Earth's diameter didn't change), weight would also double.

Then (assuming Earth's diameter didn't change), weight would also double.

Then (assuming Earth's diameter didn't change), weight would also double.

Answer 10

Fundamentally, the object's weight would double (2x higher). However, if the Earth's diameter did change, then your distance to it's core which is where the Earth's mass is centered would also change. Gravity is diretly proportional to mass, however it is also inversely dependent upon the square of the distance between the two masses. The distribution of mass within the Earth also has some effect on what you weigh depending on where on Earth you stand, but ignoring this small efect, taking the reverse of the question - if the Earth were the same mass but double the diameter, your weight would be 1/4th of what it is now.