In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 x 10¹⁶ kg and a radius of 8.8 km. (b) What is the escape speed from the asteroid?

Video transcript

Everyone. Let's take a look at this practice problem dealing with escape velocity. So in this problem, a private space company plans to mine an asteroid in the near future. The asteroid being considered for mining has a mass of about three multiplied by 10 to the 17 kg in a diameter of around 15 kilometers. What would be the required speed needed to leave its surface? We're given four possible choices as our answers. Choice A is 21 m per second. Choice B is 23 m per second. Choice C is 73 m per second and choice D is 74 m per second. Now, since we're asked to find the speed that's required to leave its surface, we're gonna be calculating the escape velocity. Recall a formula for the escape velocity we have V is equal to the square root of two GM divided by R V is our escape speed. Um G is the gravitational constant M is the mass of the asteroid and R is the radius of the asteroid. Now, we weren't given the radius of the asteroid, but we was, we were given its diameter. So we'll need to calculate its radius. So we'll have R, it's equal to our diameter D divided by two. So we can plug in that value. So we have R is equal to the 15 kilometers divided by two. But I know that my units for the gravitational constant have meters in them. And my final answer also needs to be in meters per second. So I'm going to want to convert this kilometer into a meter. So I do that by multiplying this fraction by 1000 m divided by one kilometer. And this gives me a radius R equal to 7500 m. So now I have all the values that need to plug into my escape velocity formula will have V is equal to the square root of two for the gravitational constant. I'll have the 6.67 multiplied by 10 to the negative 11 that has units of Newton meter squared per kilogram squared that gets multiplied by the mass of the asteroid, which in this case was the three multiplied by 10 to the 17 kg. And then that gets divided by the radius that we just found, which is the 7500 m. But now I wanna plug in everything on the right hand side into my calculator. This turns out to be a speed of V equal to 73 meters per second. Here, I just kept two significant figures. This corresponds to answer C now, while this problem was a direct application of our escape velocity formula. We did have to remember that we needed to um use our radius instead of the diameter. And we also needed to convert that diameters kilometers units into meters. That's what appears in the gravitational constant, the units of meters. So I hope that this has been useful and I'll see you in the next video.