It has been proposed that we could explore mars using inflated balloons to hover just above the surface. the buoyancy of the atmosphere would keep the balloon aloft. the density of the martian atmosphere is 0.0154kgm3 (although this varies with temperature). suppose we construct these balloons of a thin but tough plastic having a density such that each square meter has a mass of 5.00 g. we inflate them with a very light gas whose mass we can ignore.

(a) what should be the radius and mass of these balloons so they just hover above the surface of mars?
(b) if we released one of the balloons from part (a) on earth, where the atmospheric density is 1.20kgm3, what would be its initial acceleration assuming it was the same size as on mars? would it go up or down?
(c) if on mars these balloons have five times the radius found in part (a), how heavy an instrument package could they carry?

Answer: a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same sign as the  -4.0  µc charge.======electricstatic force between two point charges  is given by    where k is coulomb's constant,  8.99×10⁹  n·m²/c², q₁ and q₂ are the point charges, and r is the distance between the two point charges.assign positive to q₁let q₁ =  6.0 µc, q₂ = -4.0  µc, q₀ represent the charge at the origin, and q₃ represent this new charge to place.the charge at the origin q₀ would experience the following force f₀₁ from q₁, with r = 6.0 m (note that 1  µc = 10⁻⁶ c)    the force from q₂    the force from q₃    the net force on the origin charge, q₀, has to be zero for no electrostatic forcehaving an equation where k and q₀ can be divided out of the equation will allow us to solve for q₃    isolating:     a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same as the  -4.0  µc charge

We can infer that star y is closer but other factors must be considered include the heat of the star, the mass, and the brightness of the star. even though star x seems dimmer it may just be less bright or contains less heat.

Iwould think it would be 2.6