Question Video: Finding the Orbital Velocity from the Radius and Period for Circular Orbits | Nagwa Question Video: Finding the Orbital Velocity from the Radius and Period for Circular Orbits | Nagwa

Question Video: Finding the Orbital Velocity from the Radius and Period for Circular Orbits Physics • First Year of Secondary School

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A satellite orbits Earth at an orbital radius of 10,000 km. Its orbital period is 2.8 hours. How fast is the satellite moving? Give your answer to the nearest kilometer per second.

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Video Transcript

A satellite orbits Earth at an orbital radius of 10,000 kilometers. Its orbital period is 2.8 hours. How fast is the satellite moving? Give your answer to the nearest kilometer per second.

To answer this question, let’s consider what exactly is being asked here. We want to know how fast this satellite is moving, which means we want to figure out the satellite’s speed. And to find it, we’re only given two other numbers: the orbital radius of the satellite around Earth, 10,000 kilometers, which is the distance from the satellite to the center of the Earth, and its orbital period of 2.8 hours, which is how long it takes to complete one full orbit.

Now, using these two values, the radius and period, we need to find the speed. To do this, let’s look at the definition of speed. Speed is equal to the distance an object travels over the time it takes to travel that distance, which, in this case, would be the distance the satellite travels over the orbital period.

We have to be careful here though. The distance the satellite travels is not the radius. The radius is just the distance between the satellite and the center of the Earth. We want to find the distance the satellite travels through one complete circular orbit. We can find this using the orbital radius in the equation for the circumference of a circle, two 𝜋𝑟, where 𝑟 is the radius of the circle we’re looking at.

Now, the circumference of a circle is the length of its perimeter, which means it is the same as the distance of a complete orbit around that circle, making the distance two 𝜋 times 10,000 kilometers.

This means all we have to do now is substitute in the orbital period and we’re done, right? Well, not quite. We need the answer for speed in kilometers per second, not kilometers per hour. So we’ll need to convert the orbital period from hours to seconds. There are 60 minutes in one hour and 60 seconds in one minute. So multiplying this first relation by 2.8 hours, the units of hours cancel. And 2.8 times 60 minutes is equal to 168 minutes. Multiplying this by the next relation then, the minutes cancel, and 60 seconds times 168 is 10,080 seconds.

Now that we have this number, we can substitute it into the equation we have for speed, making our equation two 𝜋 times 10,000 kilometers divided by 10,080 seconds. Calculating through and paying attention to our units, we find the answer to be 6.23 kilometers per second. Rounding this then to the nearest kilometer per second, we find that the answer to how fast this satellite is moving is six kilometers per second.

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