What is the linear speed of Saturn in its orbit about the sun? Give your answer in meters per second. (Consider the orbit of Saturn to be a circle of radius 1.43×1012 m and that it takes 29.50 yr for one orbit around the sun.)
speed=2PI*radius/period
so you want period in seconds...
29.50yr(365.25 days/yr)(24hrs/day)(3600sec/hr)= period in seconds
To calculate the linear speed of Saturn in its orbit about the sun, we need to use the formula:
Linear Speed = Circumference / Time period
First, let's find the circumference of Saturn's orbit. Since the orbit is considered as a circle, we can use the formula for the circumference of a circle:
Circumference = 2 * π * Radius
Given that the radius of Saturn's orbit is 1.43×10^12 m, we can substitute this value into the formula:
Circumference = 2 * π * 1.43×10^12 m
Next, we need to determine the time period of Saturn's orbit. The question states that it takes 29.50 years for one orbit around the sun. However, we need to convert this time period into seconds to ensure consistency in units. Since 1 year consists of 365 days, and each day has 24 hours, and each hour has 60 minutes, and each minute has 60 seconds, we can calculate the time period in seconds as follows:
Time period = 29.50 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute
Now that we have the circumference and time period, we can substitute these values into the linear speed formula:
Linear Speed = (2 * π * 1.43×10^12 m) / (29.50 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute)
By simplifying this equation and performing the calculations, we can find the linear speed of Saturn in meters per second.