Texts 1 the dwarf planet eris is currently 957 au from the...

Texts: 1. The dwarf planet Eris is currently 95.7 AU from the Sun. (a) Give this distance in km. (b) How long does it take light to travel from the Sun to Eris? Express your answer in hours. 2. Voyager 2 is currently 133.98 AU from Earth. How long does it take a signal to travel between Voyager 2 and Earth? Express your answer in hours. 3. At its average distance (i.e., 384,400 km), the Moon subtends an angle of 0.518° (approximately 'half-a-thumb'). (a) Convert this angle to arcminutes and then to arcseconds. (b) Use the small-angle formula to find the physical diameter of the Moon in km. 4. At closest approach, Jupiter is 4.2 AU from Earth. Jupiter has an actual diameter of 143,000 km. (a) Use the small-angle formula to find the angle (in arcseconds) subtended by Jupiter at closest approach. (b) Convert this angle to arcminutes and then to degrees.

Transcript

00:01 Okay, so this is a pretty cool astronomy problem talking about a new object that was found that orbits our sun.

00:11 So the object, omea, is a planet that's kind of outside of the orbit of pluto, and we're asked to find a couple of things, including its eccentricity, its perihelian, and the time it's going to take to get to its perihelian if they reached out.

00:31 Apheelian in 1994, or 1992 rather.

00:39 So first for eccentricity, we can use that the apheelian, so the apheelian, which is the furthest distance, equals the length of the semi -major axis, which i'm going to call a times one plus e.

01:14 Where a is length of semi -major axis, and e is what we're looking for, are eccentricity.

01:36 And the eccentricity just basically tells you how weird, or how far away from a circle your orbit is.

01:46 So the appelian, as given in the problem, was 51 .6 astronomical units.

01:52 The length of the semi -eye major axis was given as 43 .1 astronomical units, and that's times 1 plus e.

02:03 So 51 .6 divided by 43 .1, just moving over, just moving over the 43 .1, we get 1 .197 equals 1 plus the eccentricity, which means that our eccentricity, just subtracting one from both sides equals 0 .197.

02:31 So that's not too crazy of an orbit.

02:34 Honestly, i skipped out a little bit and already drew the picture.

02:40 But honestly, it probably wouldn't even be this crazy of an orbit.

02:43 It would be closer to a circle than what i've drawn here, but i've kind of exaggerated it so that you could see the difference between the apheelian and the semi -major axis.

02:52 So you'll notice that the drawing, the semi -major axis is just the distance from the longest axis of the ellipse.

03:04 It's taken along that longest axis, and it's just half of the distance of that longest axis, not necessarily where the sun is, which is what this is orbiting.

03:14 The sun is just one of the focal points of the foci of this orbit.

03:19 So there's another kind of fake focus that means.

03:24 Mirrors where the sun is.

03:28 But now let's find the perihelian.

03:32 So the parahelian, which is, so perihelian, closest approach.

03:50 And that is going to be incidentally right here.

03:54 So this is the parahelian.

04:04 And so that's always where it is.

04:06 It's always directly across the longest axis from the apheelian.

04:10 So this is the appelian.

04:12 Over here on the major axis.

04:19 And on the other side of the major axis is the perihelian, which is the closest approach.