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.
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
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)
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.
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.
94 pounds (1/2 of my actual weight today).
In short, exactly half your weight today.
if it had twice the mass but the same diameter as it has now, your weight would double
109 Actually, no. 109 would probably be for Jupiter. For Earth, hundreds of Earth's surface could fit in the sun's radius.
Mars's gravitational pull is 38% that of Earth's, meaning you would weigh 38 pounds on that planet.
In the cavity at the center of the Earth, your weight would be zero, because you would be pulled equally by gravity in all directions. - The gravitational field of Earth at its center is zero.
It would go something like this. e = Earth's gravity m = Mercury's gravity e*0.38=m Just put whatever number in Earth's gravity and do the math.
If you are the only one living on earth it would last for your lifetime.
i will be twice as heavy
weight on jupiter=((mass of jupiter)*(Radius of earth)2/(mass of earth)*(Radius of jupiter)2)*weight on earth
Yes, in a way. If the radius of the Earth decreased but it's mass stayed the same, then the forces "pulling" on you (weight) would increase and you would be heavier. If the radius of the Earth increased and the mass stayed the same, then you would be lighter. You would actually weigh less on the top of Mount Everest than on the beach of Honolulu. BTW: This is not a good idea for a weight loss program.
If Earth had the same size but twice the mass you would weight twice as much
one-fourth of your weight on earth
It would double.
It would double.
Sara would weigh exactly the same as on Earth. The radius of the planet does not make any difference on ones weight. The mass of the planet is the crucial factor.
That would depend on the planet's radius. The strength of gravity depends on both the mass of the object in question and the distance from its center of mass. If the planet in question had the same radius as Earth, then the person would weigh 200 lbs as gravity would be twice as strong. If the planet had the same density as Earth it would have 1.26 times Earth's radius and gravity would be 1.26 times as strong and the person would weigh 126 lbs. If the planet had about 1.41 times Earth's radius then that person's would weight 100 lbs.
It is true that there is a change in weight the further you go from earth, but comparatively weight at sea level and Mt.Everest is insignificant since the radius of the earth is about 700 times greater than the height of Mt.Everest, therefore the weight would be insignificantly smaller.
Its kinda easy 6400-90kg=6310 divided by 625= 10.1 The weight of the earth would be around 10.1
That would be the radius of the earth which is:6,378.1 kilometers