Asteroid 253 Mathilde is one of several that have been visited by space probes. This asteroid is roughly spherical with a diameter of 53 km. The free-fall acceleration at the surface is 9.9 ✕ 10⁻³ m/s². What is the asteroid's mass?

Video transcript

Hi, everyone in this practice problem. We're being asked to find the mass of the moon. We will have the moon of Jupiter with a radius of 3270 kilometer and a freefall acceleration at its surface of 1.79 m per second square. We're being asked to determine the mass of the moon and the options given are a 8.77 times 10 to the power of 23 kg. B 8.77 times 10 to the power of 20 kg. C 2.87 times 10 to the power of 23 kg and D 2.87 times 10 to the power of kg. So we will consider the moon as a solid sphere and also symmetric in its mass distribution. We wanna next apply Newton's law of gravity to the moon which will then give us um the acceleration due to gravity on the surface of the moon to be equals to g multiplied by mass of the moon divided by R squared. So uh according to Newton's law of gravity of the moon, the acceleration due to gravity on the surface of the moon or G moon well equals to capital G or the gravitational constant multiplied by M or the mass of the moon and moon divided by R squared. In this case, we are interested to find the mass of the moon. So I'm gonna rearrange the equation to get an equation for mass. So mass will equals to G moon multiplied by R squared divided by the gravitational constant big capital G. We are given what the G of the moon is and also are squared and the G is just a constant. So we can uh substitute everything into this equation. So that M moon will equals to 1. meters per second squared. Four G moon multiply that by R square which is 3270 kilometer, we wanna subs uh we wanna convert that into a meter by multiplying it with m divided by one kilometer squared and then divide everything with the constant, which is just going to be 6.67 times 10 to the power of negative 11 Newton multiplied by a meter squared divided by kilograms squared. Awesome. So um calculating all of this, you will get a moon or the mass of the moon to then be equals to 2.87 times 10 to the power of 23 kg. So the mass of the Jupiter's moon is going to equal to 2.87 times 10 to the power of 23 kg, which will correspond to option C in our answer choices. So answer C will be the answer to this particular practice problem. And if you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics, but that'll be it for this one. Thank you.