Re: how do u find your weight in kilograms on each planet in the solar system?

First of all, you have misused the term "weight", or you have asked for the wrong units. "Weight" is a force, and kilograms measure mass, so your question, as asked, has no answer. So, I suppose what you are asking is "What is my weight on each planet?" Assuming that is the question you are asking, I will now try to answer it!!

As I said above, weight is a force, and force can be calculated by the equation
w = f = m g
where w is the weight, f is the force, m is the mass of the object, and g is the acceleration due to gravity. The units of force are thus kilogram meters per second squared, or kg m / s², and we call that unit a "Newton". So if you know what your mass is and if you know the acceleration of gravity on each planet's surface, you can calculate your weight on each planet.

Let's say you know your weight in pounds. The conversion factor from pounds to kilograms is 1/2.2 or 0.454, so multiply your weight (in pounds) times 0.454 and you obtain your mass in kilograms. "Pounds" is actually a force, but this conversion assumes you are on the surface of the earth. However, if you actually know your weight in Newtons then you divide by 9.8 (which is the acceleration of gravity at the surface of the earth) to obtain your mass in kilograms.

Let's now assume you know your mass in kilograms. There are two ways to find the acceleration of gravity on each planet's surface: look it up, or calculate it!! To look it up you will need a general astronomy book or some astronomy reference book. To calculate, you will need to look up the mass of each planet and its radius, so again you will need a general or reference astronomy book. If you can find the acceleration of gravity on each planet in the units "meters per second squared" then all you have to do is multiply that times your mass (in kilograms) to obtain your weight in Newtons. However, if you can only find the mass and radius of each planet, here is how you calculate the acceleration of gravity at the surface:

Newton's law of gravitational force is
F_g = GmM/r²
where F_g is the gravitational force (the weight), G is the universal gravitational constant, m is your mass, M is the mass of the planet, and r is the radius of the planet at its surface. Since
w = f = m g
we can equate f with F_g, so we obtain
m g = GmM/r²
and if we divide both sides by the mass m (your mass) we obtain
g = GM/r²
where g is the gravitational acceleration we're looking for. The value for G is about 6.67 x 10^-11 Newton meters squared per kilogram squared (N m² / kg² ), so with the planet's mass and surface radius you can now calculate the gravitational acceleration at the surface of the planet, and multiply that times your mass to obtain your weight.

Here's an example. Let's say your mass is 50 kilograms (a reasonable number, and your weight in pounds would be 110 pounds). The mass of the earth is about 5.98 x 10²⁴ kg, and the radius of the earth is about 6.37 x 10⁶ meters. If you work out the equation for the gravitational acceleration you obtain 9.8 Newtons per kilogram (which is also meters per second squared), and if you then multiply that times your mass you get your weight as 490 Newtons (which, as you know from above, is also kilogram meters per second squared).

Have fun working out your weight on the other planets!!!!

John Link, MadSci Physicist