Spacecraft have been sent to mars in recent years. mars is smaller than earth and has correspondingly weaker surface gravity. on mars, the free-fall acceleration is only 3.8m/s2 .what is the orbital period of a spacecraft in a low orbit near the surface of mars? assume the radius of the satellite's orbit is about the same as the radius of mars itself, rmars = 3.37

The orbital period of the spacecraft is about 5.9 × 10³ s ≈ 99 minutes

Let's recall Centripetal Force formula as follows:

where:

F = Centripetal Force ( Newton )

m = mass of object ( kg )

v = speed of object ( m/s )

R = radius ( m )

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

where:

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

Given:

free-fall acceleration = g = 3.8 m/s²

radius of Mars = R = 3.37 × 10⁶ m

Asked:

orbital period = T = ?

Solution:

Grade: High School

Subject: Physics

Chapter: Gravitational Fields