Question Video: Calculating the Orbital Speed of a Satellite Physics • 9th Grade

Nilesat 201 is a communications satellite that orbits Earth at a radius of 35,800 km. What is the orbital speed of Nilesat 201? Assume that the satellite follows a circular orbit. Use a value of 5.97 × 10²⁴ kg for the mass of Earth and 6.67 × 10⁻¹¹ m³/kg ⋅ s² for the universal gravitational constant. Give your answer in scientific notation to two decimal places.

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Video Transcript

Nilesat 201 is a communications satellite that orbits Earth at a radius of 35,800 kilometers. What is the orbital speed of Nilesat 201? Assume that the satellite follows a circular orbit. Use a value of 5.97 times 10 to the 24 kilograms for the mass of Earth and 6.67 times 10 to the negative 11 meters cubed per kilogram second squared for the universal gravitational constant. Give your answer in scientific notation to two decimal places.

Here, we want to find the orbital speed of a satellite in the special case of circular orbit. So we’ll use the orbital speed formula 𝑉 equals the square root of 𝐺 times 𝑀 divided by 𝑟, where 𝑉 is orbital speed. 𝐺 is the universal gravitational constant. 𝑀 is the mass of the large body being orbited. Here, that’s Earth. And 𝑟 is orbital radius, which extends between the Earth’s and the satellite’s centers of gravity.

We’ve been given values for 𝐺, 𝑀, and 𝑟. But before we substitute them into the formula, all of these terms should be expressed in base SI units. 𝐺 is expressed in meters, kilograms, and seconds, so it’s good to go, as well as mass in kilograms. But the kilometer is not the base SI unit of distance, so we’ll need to convert it into plain meters. Recall that one kilometer is equal to 1,000 meters. So we’ll multiply 𝑟 by this conversion factor: 1,000 meters divided by one kilometer, which is just equal to one. And we can cancel units of kilometers. So now we have 𝑟 equals 35,800,000 meters. The units are correct, but let’s write this in scientific notation.

𝑟 equals 3.58 times 10 to the seven meters. Now, copying the formula below, let’s substitute in these values. 𝑉 equals the square root of 6.67 times 10 to the negative 11 meters cubed per kilogram second squared times 5.97 times 10 to the 24 kilograms divided by 3.58 times 10 to the seven meters, which comes out to about 3,335 meters per second. Finally, in scientific notation, to two decimal places, we have found that the orbital speed of Nilesat 201 is 3.34 times 10 to the three meters per second.

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