A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.17 hours. What is density of the planet

Explanation:

Lets consider

Circumference of orbit = T

as it is mentioned in the question that a satellite is in orbit that is very close to the surface of planet. so

circumference of orbit = circumference of planet

Time period = T

radius of planet = R

orbital velocity = V

gravitational constant = G

mass of planet = m

Solution:

Time period for a uniform circular motion of orbit is,

T =

where p = density

T = 2.17 hours = 7812 sec

(7812)² = [( 3×3.14)/6.67××ρ)]

ρ = 6.28/6.67××6.10×

ρ = 6.28/40.687×

ρ = 0.1543×kg/m³

ρ = 15.43×kg/m³

increase masses, decrease separation

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.)