On October 15, 2001, a planet was discovered orbiting around the ...

Question

On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD 68988? Express your answer in kilograms and in terms of our sun’s mass.

Accepted Answer

Welcome back everybody. We are taking a look at kepler five B orbiting around its parent star. And we are told a couple different things here, we're told that the distance between five B and its parent star is 7.58 times 10 to the six kilometers or 7. times 10 to the ninth meters. We're also told that the time it takes for one full revolution or its period is 3.55 days. And we are tasked with finding two things. One, what is the mass of our parent star? And then what is the mass of our parent star expressed as a factor of or sorry, a constant times the mass of our own sun. So we are actually going to use this formula right here that when we are looking at elliptical or circular orbit we have that are period is equal to two pi times the distance between the two bodies raised to the three halves all over the square root of Newton's gravitational constant times the mass of the parents. Start now our mass right here is what we desire to find. So I'm gonna have to isolate that. So first and foremost I'm actually gonna raise both sides to the power of two. That's going to get rid of the radicals. Get rid of the fractions, Make things a lot easier to work with and then I'll multiply both sides by M. This is going to give us that our mass is equal to four pi squared times r cubed. All over G times the period squared. Now that we know that let's go ahead and try to find the answer to part one. By just plugging in all the values that we know. So we have that the mass of our parent star is equal to four pi squared times 7.58 times 10 to the ninth. Our distance between our two bodies, all divided by Newton's gravitational constant of 6. times 10 to the negative 11th Times 3.55 times 24 times 30 600 since we need our period represented in terms of seconds. Plugging this into our calculator, we get that this is 2.73 times 10 to the 30th kg. Great. So that's the intro part one. Now, Part two. Pretty easy. We need to have our mass in terms of some constant times the mass of our own sun, meaning we're going to take the mass that we just found and divided by the mass of our sun to find that constant C. So we will have 2.73 times 10 to the 30th, divided by 1.99 times 10 to the 30th, meaning the mass of this parent star right here is equal to 1.37 times the mass of our own sun. So now we have found the answer to part A and part B corresponding to answer choice C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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