Light will travel more slowly in a material with a higher index of refraction
the weight of the balloon is .030 * 10 = 0.3 N
the weight of the gas of volume v is 0.54*10 N
The lifting force of a volume of v m³ of displaced air is 1.29v N
so, we need
1.29*10*v = 0.3 + 0.54*10*v
or
1.29v = 0.03+0.54v

Explanation:
The acceleration due to gravity g is defined as

and solving for R, we find that

We need the mass M of the planet first and we can do that by noting that the centripetal acceleration
experienced by the satellite is equal to the gravitational force
or

The orbital velocity <em>v</em> is the velocity of the satellite around the planet defined as

where <em>r</em><em> </em>is the radius of the satellite's orbit in meters and <em>T</em> is the period or the time it takes for the satellite to circle the planet in seconds. We can then rewrite Eqn(2) as

Solving for <em>M</em>, we get

Putting this expression back into Eqn(1), we get



