A new planet is discovered that has twice the earths mass and twice the earths radius. On the surface of this new planet, a person who weighs 500 N on Earth would experience a gravitational force of what
The gravitational force experienced by a person on the surface of a planet can be calculated using the formula:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2)
m1 is the mass of the person
m2 is the mass of the planet
r is the radius of the planet
Given that the mass of the person is the same on Earth and the new planet, and the radius and mass of the new planet are both twice that of Earth, we can set up the following equation:
F1 / F2 = (G * m1 * m2) / r1^2 / (G * m1 * m2) / r2^2
Simplifying the equation, we get:
F1 / F2 = r2^2 / r1^2
Since r2 = 2r1, we can substitute that in:
F1 / F2 = (2r1)^2 / r1^2
F1 / F2 = 4
Therefore, a person who weighs 500 N on Earth would experience a gravitational force of 500 N / 4 = 125 N on the surface of this new planet.