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

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)