Lets say you are somewhere near Saturn. How far away from the core would you need to be for your weight to be 100,000N? Do not enter your answer in scientific notation.

Answer 1

If you weigh 150 pounds, that's about equivalent to a mass of 68 kg.

The force due to gravity is found using Newton's Law of Universal Gravitation:

were G is the Gravitational Constant which is 6.67 x 10^-11 Nm²/kg² and we can let m₁ be your mass and m₂ can be the mass of Saturn. We can look up the mass of Saturn and see it is 5.683 x 10²⁶ kg so:

100000 = (6.67 x 10^-11)(68)(5.683 x 10²⁶)/r²

r² = (6.67 x 10^-11)(68)(5.683 x 10²⁶)/100000

r² = 2.578 x 10¹³

r = √2.578 x 10¹³ = 5076989 meters

You could round this to 5,000,000 meters or also answer in km by dividing by 1000 to get 5000 km

You would get a different answer if your mass was less so you may need to use a different mass. If so, just plug in your mass in place of 68 kg.