1) The buoyant force acting on an object submerged in a fluid can be described as:

where

indicates the fluid's density,

represents the volume of the fluid displaced, and

signifies the gravitational acceleration.
2) To determine the volume of the displaced fluid, we note that the titanium object is entirely submerged in the fluid (air), thus this volume matches the volume of 1 Kg of titanium, which has a density of

. Using the correlation between density, volume, and mass, we derive

3) We can now revisit the equation in step 1) to compute the buoyant force. Given that the air density is

, this provides us with

4) The weight of 1 Kg of titanium is:

Therefore, the buoyant force is negligible when compared to the weight.
The formula used is known as the Law of Universal Gravitation. The gravitational constant G is 6.67×10⁻¹¹ Nm²/kg². The Earth's mass is <span>5.972 ×10</span>²⁴ kg. The mass of the rocket is negligible in comparison to Earth’s mass, hence it is unnecessary for our calculations. Plugging in the values:
F = (6.67×10⁻¹¹ Nm²/kg²)(5.972 ×10²⁴ kg)/(4000 miles*(1.609 km/1 mile))²
F = 9616423.08 N
The work done is given by
W = Fd
W = (9616423.08 N)(2000 miles*1.609 km/mile)
W = 9.095×10¹⁰ Joules