An artificial satellite is in a circular orbit around a planet of radius r = 5.25 ã 10^3 km at a distance d = 450.0 km from the planet's surface. the period of revolution of the satellite around the planet is t = 2.15 hours. what is the average density of the planet?

The average density of the planet is; 3020.68 kg/m³

We are given;

Radius; r = 5.25 × 10³ km = 5.25 × 10⁶ m

Distance; d = 450 km = 450 × 10³ m

Period; T = 2.15 hours = 7740 secs

The formula for the orbital velocity is;

V = √(GM/(r + d))

Formula for time period is;

T = 2π(r + d)/v

Thus;

T = 2π(r + d)/√(GM/(r + d))

T = 2π((r + d)^1.5)/√GM

Where G = 6.67 * 10⁻¹¹ N.m²/kg²

Plugging other relevant values gives us;

M = 1.83 * 10²⁴ kg

Formula for density is;

Density = mass/volume

Earth is spherical and as such, Volume = 4/3 πr³.

Thus;

Density = (1.83 * 10²⁴)/((4/3) * π * (5.25 × 10⁶)³

Density = 3020.68 kg/m³

Read more about Average Density at; link

d) physical means can be used to separate the components of air.