On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 km above the earth's surface. Assume a circular orbit. (a) How many hours does it take this satellite to make one orbit?

Video transcript

Welcome back everybody. We are taking a look at an event that happened on February nine in 2009. What happened is that US and Russian satellites collided in orbit. Now they collided in orbit at a height of km above Earth's surface. And we are asked to find assuming circular orbit here. What the orbital period was of the two colliding satellites right before they collided. Right? So we know according to capitalist law that the period is equal to the square root of four pi squared times the radius of orbit cubed all over Newton's gravitational constant times the mass of our planet, which in this case is Earth. But we have everything here except this little r value. What is the radius of orbit? Well, the radius of the orbit is going to be the distance between the satellite and the center of earth, meaning, as you can see by my little diagram here, our radius of orbit is going to be equal to the radius of Earth plus the height of the collision off of the surface of the earth. So let's go ahead and find that radius of orbit first. We have that. The radius of Earth can just look it up is 6.37 times 10 to the six m plus 790 kilometers or 7.9 times 10 to the fifth meters. This gives us a radius of orbit of 7. times 10 to the six m. Now that we have that we can go ahead and find our orbital period here are orbital period is equal to four pi squared Times 7.16 times 10 to the six cute all over our gravitational constant of 6.67 times 10 to the negative 11 times the mass of the Earth, which is just another thing you can look up, but I'll give it to you. It's 5.97 times 10 to the 24th. Plugging this into our calculator, we get 6033 seconds, which we need to divide by 60 to get minutes and we get 101 minutes as our final answer corresponding to answer choice. A thank you all so much for watching. Hope This video helped. We will see you all in the next one.