What would be your weight if the earth had half its present radius and half its present mass?

Answer 1

You asked what would happen to your weight if the earth's mass doubled (due to a density increase) without changing in size.


There are three very useful equations in this context.


First, weight = mass * gravity.
Second, force = mass * acceleration.
Third, gravity = (g-constant (your mass * earth's mass))/distance between the masses squared.


It happens that the first two equations mean the same thing. For this to be true, weight would have to be a force (it is, and it's called "newtons"), and gravity would have to be an acceleration (that's also true).


So what we need to do here is figure out how much gravity the earth would have if its mass doubled. Since the earth does not change in size, in your problem, the distance doesn't either. We can then set distance = 1 in the third equation. Likewise, the gravitational constant doesn't change; that's why it's called a "constant".


So what do we have? It's clear that the gravity acting on you and earth doubles if we do nothing but double the earth's mass.


Since your weight = your mass times gravity, and gravity has doubled as we've shown, the answer is simple: YOUR WEIGHT WOULD DOUBLE TOO.

Answer 2

start with a = (G*m)/d^2, install arbritary numbers

G=10, m=10, d=10,then a= (10*10)/10^2=100/100 = 1

double mass (m) to 20 and distance(d) to 20

then a = (10*20)/20^2=200/400=0.5

say your mass = 50kg f=ma originally = 50*1 = 50n

after changes f=ma =50*0.5=25n

force(or weight) is halved

Answer 3

In order for that to happen, it would have to have (lose) half its mass, and that would have other causes and consequences. But if the Gravitational Constant or planetary density suddenly changed, and Earth's mass only exerted half as much gravity for its size, then:

- the Moon's orbit would change (if its velocity remained the same)

- artificial satellites would lose geostationary positions

- orbital and escape velocity would be lower

- everyone and everything would have less weight

- animals and people could jump higher

- objects would fall with slower acceleration (4.9 m/sec/sec)

Answer 4

As long as we stay above the surface, we can treat the Earth as if all its mass were in the center.

So the distance between you and the Earth's center of mass would decrease by a factor of two. The force of gravity depends on the square of the distance between the centers of the two masses. So if the mass didn't change, your weight would increase by a factor of 2 squared, or four.

However, you've also specified that the mass also decreases by a factor of two. The force of gravity is dependent on the masses of the two objects multiplied together. Your mass presumably didn't change, but the Earth's mass went DOWN by a factor of two, so the product is also reduced by a factor of two.

Combining these two, we get that overall your weight would double.

Answer 5

Assuming Earth's diameter didn't change (so, its density would have to double as well!), twice the mass would result in twice the weight.If Earth's density remains equal, its radius would increase, so the increase would be less than that. If you want the exact calculation in this case, you can calculate the increase in Earth's radius (it would be the cubic root of 2), and then divide the number 2 (for the double mass) by this factor squared. In summary, in this case the increase in weight would be by a factor of cubic root of 2.

Answer 6

94 pounds (1/2 of my actual weight today).

In short, exactly half your weight today.

Answer 7

if it had twice the mass but the same diameter as it has now, your weight would double