Earth is 149.6 billion meters from the sun and takes 365 days to make one complete revolution around the sun. mars is 227.9 billion meters from the sun and has an orbital period of 687 days. what is the ratio of earth’s centripetal acceleration to mars’s centripetal acceleration?

2.33

Explanation:

The basic equation for circular motion that relates to mass, radius, force , angular velocity and centripetal acceleration is ;

F=mv²r

You know that ;

F=manewton's laws of motion

Centripetal acceleration , ac=v²r where v is orbital speed and r is radius of orbit

Finding orbital speed in T period; v= 2πrT (1)

Express centripetal acceleration in terms of (1) above

ac=(2πrT)² r = 4π²rT²

Getting the ration of Earth's acceleration to Mars acceleration will be

(rE×Tm)÷(rM×Te)  

where rE=distance of Earth from the sun

Tm=orbital period of Mass

rM=distance of Mass from the sun

Te= orbital period of Earth

=(149.6×687²)÷(227.9×365²) = 2.33