Diameter of Earth-like planet / gravitational force

[chris2112]

I kind of have a stupid question. How much more massive would the Earth have to be for the average person to weigh about 50 more pounds? How much bigger could the Earth's diameter be? Thanks.

 

[Drakkith]

There isn't a single number. Decreasing the radius of the Earth while keeping the mass the same would increase the weight of a person on the surface. You could also keep the Earth the same radius but increase the mass to get the same effect. Or any combination of the two.

 

[marcus]

I kind of have a stupid question. How much more massive would the Earth have to be for the average person to weigh about 50 more pounds? How much bigger could the Earth's diameter be? Thanks.

Let's say average weight for women is 145 pounds and for men 185 pounds and average "person" weighs 165 pounds.

Lets say "earth-like" means roughly same DENSITY because roughly same chemical composition---iron core, rocky mantle, crust etc etc.

So you want the size for which the 165 pound person will weigh 50 more pounds, or 215. So you want gravity to be stronger by a factor of 215/165.

So you want the RADIUS to increase by that same factor.

So calculate what 215/165 is. About 1.3.

So with those assumptions (about "average person" and "earth-like") the answer is that the radius would need to be about 30% bigger.
IOW the diameter would need to be about 30% bigger.

 

[DaveC426913]

marcus, I am not following your logic. Ifd the radius increased by 30%, the mass would increase by 2.2. Are you accounting for that?

 

[Bandersnatch]

marcus, I am not following your logic. Ifd the radius increased by 30%, the mass would increase by 2.2. Are you accounting for that?

You'd also be 30% farther away from the centre of the gravitational field. Marcus is correct.

 

[TEFLing]

G ~ M/R^2
Surface gravityp ~ M/R^3
Density

G ~ p x R

 

[marcus]

True, TEFL. The surface gravity is proportional to the density times the radius.

BTW at the top of the blank space where we write replies there is this line of symbols B I U ... Σ
and if you click on the the Σ you get a convenient menu of symbols including the lowercase Greek rho (ρ) which is normally used for density.

There's also an x² symbol you can click on to write superscripts. So your second equation could be written ρ ~ M/R³

You may have discovered this already, but in case not I wanted to mention it. Very handy.

I do write the ^ for superscripts when I want to use the google calculator, to be able to paste the formula into the google window and have it evaluate it. The calculator likes to have exponents written in the x^2 form. But for purely human consumption it looks better to use the PF symbols gadget.