a day on a distant planet observed orbiting a nearby star is 521 hr521 hr also a year on the pla

1. We need to convert the planet's day from hours to seconds.

A day on a distant planet observed orbiting a nearby star is...

A day on a distant planet observed orbiting a nearby star is 52.1 hr. Also, a year on the planet lasts 59.1 Earth days. In other words, for the purposes of unit conversion, there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, as it would for astronomers on Earth observing the planet. A) Calculate the average angular speed of the planet about its own axis of rotation in radians per second, with the second as measured on Earth. _________ rad/s B) Calculate the average angular speed of the planet as it travels around its neighboring star, with the second as measured on Earth. _________ rad/s

Transcript

00:01 A planet is rotating about its axis, and when the planet makes one full rotation, we call that one day.

00:12 Okay? so here we have that one day on the planet is equal to 52 .1 hours, and the amount of time it takes for the planet to make one full rotation is also.

00:32 Called the period of rotation t -sum -r okay so the the rotational period is the same as one day on that planet and the average angular speed omega is equal to the angle that it is rotated by the total angle it's rotated by divided by the time that has passed so here we have i'm going to look at an aerial view of the planet.

01:09 Here's its axis of rotation.

01:11 So if it is traveling, it's making one full rotation, it's traveling an angle, or it's rotating by this full angle.

01:19 Okay.

01:21 So that is an angle of 2 pi.

01:24 So we have that theta equals 2 pi.

01:29 And the time that it takes to make that full rotation, we already know is t sub r, which is 52.

01:37 Point one hours.

01:41 And i'm sorry, this is two pi radians.

01:46 Okay, so we have omega equals two pi radians divided by 52 .1 hours.

01:56 And there are 60 minutes in one hour, and there are 60 seconds in one minute.

02:07 So i made those, included those factors so that we can adjust the units.

02:12 So hour cancels with our minutes, cancels with minutes, and we're left with radians per second.

02:19 So when i calculate this, and i'm going to call this omega -r, the omega of rotation, okay, that we get and we get 3 .35 5 times 10 to the negative 5th power radiance per second.

02:42 So this is the average angular speed of rotation about its axis.

02:49 And next we have that one year on a planet is equal to the time that it takes to orbit, to complete one orbit around its star.

03:02 Okay.

03:02 So in other words, the amount of time it takes to complete one orbit is the orbital period.

03:12 Okay, so this is orbital period, t .o...

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