At what altitude above the Earth's surface would your weight be two-thirds of what it is at the Earth's surface?

To solve this problem, we need to use the formula for gravitational force:

F = G * (m1 * m2) / r^2

where:

• F is the force of attraction between the two bodies,
• G is the gravitational constant,
• m1 and m2 are the masses of the two bodies,
• r is the distance between the centers of the two bodies.

We know that weight is the force of gravity on an object. So at the surface of the Earth, your weight is:

F1 = G * (m_earth * m_you) / r_earth^2

where:

• m_earth is the mass of the Earth,
• m_you is your mass,
• r_earth is the radius of the Earth.

We want to find the altitude (h) at which your weight is two-thirds of your weight at the surface of the Earth. So we set up the equation:

2/3 * F1 = F2 = G * (m_earth * m_you) / (r_earth + h)^2

We can cancel out the G, m_earth, and m_you from both sides to get:

2/3 = r_earth^2 / (r_earth + h)^2

Solving this equation for h gives us the altitude at which your weight would be two-thirds of what it is at the Earth's surface.