### Video Transcript

To three significant figures, the distance from Mars to the Sun is 142 million miles, and Mars’s average orbiting speed is 53979 miles per hour. Using this distance, and assuming that Mars’s orbit is circular, calculate the number of Earth days it would take to complete one full orbit. Part b: To four significant figures, the distance from Mars to the Sun is 141.6 million miles. How does this affect your answer to part a?

Let’s begin with part a. Here we have the Sun. And we’re told that Mars is 142 million miles away from the Sun. And we’re told that Mars’s orbit is circular. And we wanna know how many Earth days it would take to complete one full orbit if the orbiting speed is 53979 miles per hour.

We are told that the orbit is circular. So this is actually a distance. And that would be considered a circumference of a circle, the distance around the circle. So it would be the circumference with a radius of 142 million miles because Mars would be the point on the circle. The Sun would be considered the centre. So that distance between them would be considered 𝑟, the radius. The circumference of a circle is two times 𝜋 times the radius. So we have two times 𝜋 times 142 million giving us that the distance around the circle, the distance of the orbit, would be about 892212313.6 miles.

Now we are asked to find how many Earth days it would take to complete this distance. So we’re talking about speed and time and distance. We know that speed is equal to distance divided by time. And since we’re solving for the number of Earth days, we need to solve for time. So switching the positions of speed and time or multiplying both sides of the equation by time and then dividing both sides by speed, we get the equation which is equivalent to this: time is equal to distance divided by speed.

Well, we know the distance of this orbit. And in the question, we were given Mars’s average orbiting speed, 53979 miles per hour. So the time it would take would be 16528.87 hours. However, we wanna know the number of Earth days. And since we wanna get rid of hours and convert to days, since hours are on the numerator, we need to multiply with hours on the denominator. So there are 24 hours in one day. We get about 688.703 days. So it would take 688.7 Earth days to complete one full orbit.

Now for part b, we’re actually told that the distance from Mars to the Sun is really 141.6 million miles, not 142 million miles. So we’re told that this distance between Mars and the Sun is smaller. And that was the radius of our circle. So, essentially, if the radius is smaller, then the distance around the circle will be smaller because a smaller radius means a smaller circle. So the radius is smaller than the one we used. So the distance travelled will be less. So for travelling at the same speed, the time taken will be less. The number of Earth days to orbit the Sun will be less.