Many spacecraft have visited mars over the years. mars is smaller than the earth and has correspondingly weaker surface gravity. on mars, the free-fall acceleration is only 3.8 m/ s 2 . part a what is the orbital period of a spacecraft in a low orbit near the surface of mars? the radius of mars is 3.4× 10 6 m .

The equation to calculate the period (in seconds) of a body orbiting a massive body (in this specific case a spacecraft with mass orbiting Mars) is:  

(1)  

Where:  

is the radius of the orbit measured from the center of Mars to the satellite  

is the gravity constant with a value of  

is the mass of Mars, which is known to be  

Now, if we are told that the spacecraft is in a low orbit near the surface of Mars, we can assume the radius of the orbit is approximately equal to the radius of Mars :  

Having this stated, let’s begin with the solution:

Solving this equation being careful with the units, and taking into account we have:  

Finally:  

>>>>>This is the period of the orbit of the spacecraft around Mars  

not too sure thinking all accelerations are pointed down