Pluto travels in a fairly elliptical orbit around the Sun. At its closest distance of 4.43×1094.43\times10^9 km, its orbital speed is 6.12 km/s. At its farthest, its orbital speed reduces to just 3.71 km/s. How far is it from the Sun at this point (in km)?

7.31×1097.31\$$times10^97.31×109 km$$

Pluto travels in a fairly elliptical orbit around the Sun. At its closest distance of 4.43 × 10 9 4.43\times10^9 km, its orbital speed is 6.12 km/s. At its farthest, its orbital speed reduces to just 3.71 km/s. How far is it from the Sun at this point (in km)?

Alright, guys. Let's get some more practice with this stuff. So we're told some information about Pluto's orbit, and we're supposed to be finding out how far is it at this farthest point when the orbital speed is reduced in kilometers. So let's go ahead and just draw a quick little sketch of what's going on here. So we've got the, the sun that's gonna be over here, and the orbit of Pluto is gonna be this very elliptical orbit dotted in blue. Now, what are we told? We're told that at the closest distance, remember, that is the periapsis. It has a velocity here, and we're told that this velocity is equal to, 6 point 12, and that's in kilometers per second. And now we're supposed to find out, given this other velocity here, v equals 3 point 71 kilometers per second, what is the periapsis sorry. What is this apoapsis distance over here? In other words, r a is what we're actually looking for. So let's go ahead and set up because we're actually comparing 2 different speeds and 2 different points in the orbit. So we know we can set up, if we're looking for r a, we can set up our equation v 1 r one is equal to v 2 r 2. Remember, we can always use this formula when we're comparing 2 points in an orbit and we're given 3 out of the 4 variables. Now, really, we're comparing actually the velocity at periapsis and apoapsis. So we can say v a r a is equal to vprp. Now, the the variable we're looking for is r a, so all we have to do is just move this to the other side and we have what this apoapsis velocity is. We have what the other velocity is and we're, we have the periapsis distance right here. The only thing we have to make sure of is that these two units over here, vp and rp, are in the same units. Right? So we have kilometers per second and we have, kilometers per second. So we can go ahead and just directly compare those relationships and those variables. Alright? So let's go ahead and do that. Let's see. So that means that r a is just going to be vprp divided by v a. A. Now I just plug everything in. Now the velocity of periapsis was 6.12. Now the distance is gonna be 4.43 times 10 to the, 9th in kilometers. So now what happens is whatever unit this is in kilometers is gonna be the unit that this is going to be in as well, which is important because we actually need this in kilometers. So we're good to go. So we've got this. Let's see. And then we have divided by 3.71. And then when you plug that all into your calculator, a, apoapsis distance of 7.31 times 10 to the 9th. And then remember, again, we're in kilometers. Alright? So if it had said any other units, we would have had to do an extra step by converting. But because we're here we have the right units, we can just stop right there. Alright? Let me know if you guys have any questions.

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Pluto travels in a fairly elliptical orbit around the Sun. At its closest distance of 4.43×1094.43\(\times\)10^9 km, its orbital speed is 6.12 km/s. At its farthest, its orbital speed reduces to just 3.71 km/s. How far is it from the Sun at this point (in km)?

다음 시청

Pluto travels in a fairly elliptical orbit around the Sun. At its closest distance of $4.43 \times 10^{9}$ km, its orbital speed is 6.12 km/s. At its farthest, its orbital speed reduces to just 3.71 km/s. How far is it from the Sun at this point (in km)?