WEBVTT
00:00:00.330 --> 00:00:04.400
A satellite orbits Earth at an orbital radius of 10000 kilometers.
00:00:05.080 --> 00:00:07.630
Its orbital period is 2.8 hours.
00:00:08.230 --> 00:00:09.920
How fast is the satellite moving?
00:00:10.670 --> 00:00:14.290
Give your answer in kilometers per second to two significant figures.
00:00:15.090 --> 00:00:19.520
So to answer this question, we can first start by underlining all the important bits of the question.
00:00:20.410 --> 00:00:25.290
For example, we’ve been given that the orbital radius of the satellite is 10000 kilometers.
00:00:26.090 --> 00:00:29.510
We also know that its orbital period is 2.8 hours.
00:00:30.150 --> 00:00:33.130
And we’re asked to find out how fast the satellite is moving.
00:00:34.010 --> 00:00:36.350
In other words, we have to find its speed.
00:00:37.120 --> 00:00:41.370
We’re asked to give our answer in kilometres per second to two significant figures.
00:00:42.410 --> 00:00:43.310
So guess what?
00:00:43.820 --> 00:00:45.230
It’s diagram time!
00:00:45.810 --> 00:00:46.500
And here it is!
00:00:46.780 --> 00:00:49.660
We’ve got the Earth at the center of the orbit; the Earth is in blue.
00:00:50.190 --> 00:00:51.910
And we’ve got the orange satellite orbit.
00:00:52.770 --> 00:00:55.350
It is meant to be a circle by the way, believe me!
00:00:56.420 --> 00:01:05.530
But anyway, we can label something on this diagram, we can label the orbital radius of this rather egg-shaped circle, which happens to be 10000 kilometers.
00:01:10.180 --> 00:01:17.170
Now in this case, we have been given the orbital radius, which happens to be the distance between the center of the orbit and the orbit itself.
00:01:17.830 --> 00:01:19.930
The center of the orbit is the center of the Earth.
00:01:20.170 --> 00:01:21.800
But sometimes we need to be careful.
00:01:22.330 --> 00:01:26.690
In some questions, we are given the distance between the surface of the Earth and the orbit.
00:01:28.050 --> 00:01:34.530
In that case, in order to find the radius of the orbit, we need to know the distance between the surface of the Earth and the center of the Earth as well.
00:01:35.390 --> 00:01:37.010
However, in this case we’re okay.
00:01:37.010 --> 00:01:38.660
We’ve been given the orbital radius.
00:01:39.430 --> 00:01:44.470
We can also write this down on the side of the diagram in order to be able to assign a symbol to the orbital radius.
00:01:45.130 --> 00:01:48.560
We can say that 𝑟, the radius, is equal to 10000 kilometers.
00:01:49.420 --> 00:01:56.980
This way we can also label another one of the quantities given to us in the question, the time period 𝑇, which happens to equal 2.8 hours.
00:01:57.830 --> 00:02:02.770
Now as we found out earlier, the question wants us to give our answer in kilometers per second.
00:02:03.480 --> 00:02:07.210
Now the distance that we’re working with, the radius, is already in kilometers.
00:02:07.840 --> 00:02:10.330
But the time that we have is in hours.
00:02:10.770 --> 00:02:14.210
We need to convert this to seconds so that we can give our answer in the correct form.
00:02:14.990 --> 00:02:19.310
In order to do this, we need to think about how many seconds there are in 2.8 hours.
00:02:19.900 --> 00:02:22.840
So 2.8 hours, that’s how much we’ve got.
00:02:23.140 --> 00:02:26.400
And we know that each hour has 60 minutes in it.
00:02:27.040 --> 00:02:31.410
So in 2.8 hours, there are 2.8 times 60 minutes.
00:02:32.170 --> 00:02:33.950
But that’s just how many minutes we have.
00:02:34.020 --> 00:02:35.930
We need to work out how many seconds we have.
00:02:36.510 --> 00:02:40.670
Well we know that each minute, every single minute, has 60 seconds in it.
00:02:41.520 --> 00:02:45.020
And so far we’ve got 2.8 times 60 minutes altogether.
00:02:45.650 --> 00:02:51.520
So the total number of seconds in 2.8 hours is 2.8 times 60 times 60.
00:02:52.440 --> 00:02:56.900
And we can plug that into our calculator, which gives us 10080 seconds.
00:02:57.630 --> 00:03:01.390
So we can replace our time period with 10080 seconds.
00:03:02.470 --> 00:03:05.610
Now that we’ve sorted out the units of the quantities given to us in the question.
00:03:05.910 --> 00:03:08.110
We need to think about the speed of the satellite.
00:03:08.910 --> 00:03:11.640
We can call this 𝑆, and that’s what we’re being asked to find.
00:03:12.270 --> 00:03:15.920
Now we can use the definition of speed to our advantage here.
00:03:16.430 --> 00:03:20.580
Speed is defined as distance, 𝑑, divided by time, 𝑇.
00:03:21.390 --> 00:03:26.520
In other words, it’s the distance traveled by something divided by the time taken for that distance to be traveled.
00:03:27.280 --> 00:03:30.210
In this case, the satellite is travelling in a circular orbit.
00:03:30.900 --> 00:03:35.110
So when it completes one orbit, it travels a certain distance.
00:03:35.220 --> 00:03:38.530
And that distance happens to be the circumference of that circle.
00:03:38.920 --> 00:03:42.440
That’s this distance here, which we’d already drawn in orange.
00:03:42.550 --> 00:03:43.660
And now we have it in pink.
00:03:44.500 --> 00:03:44.850
Anyway!
00:03:44.880 --> 00:03:49.780
So we can also recall how to calculate the circumference of a circle knowing only its radius.
00:03:50.540 --> 00:03:54.980
The circumference of a circle, 𝐶, is equal to two 𝜋 multiplied by the radius, 𝑟.
00:03:55.660 --> 00:03:59.870
Now 𝜋 is just a number, it’s just a constant, so two 𝜋 is also just a constant.
00:04:01.070 --> 00:04:06.080
And the circumference is the distance that the satellite has traveled when it completes one orbit.
00:04:06.820 --> 00:04:11.740
So we can safely say that the circumference, 𝐶, is equal to the distance traveled, 𝑑.
00:04:12.340 --> 00:04:18.970
And so if we want to calculate the speed, we can say that 𝑆 is equal to the circumference, 𝐶, divided by the time period, 𝑇.
00:04:19.560 --> 00:04:23.440
This is because it takes the time period 𝑇 to travel exactly once around the circle.
00:04:24.400 --> 00:04:28.470
We also know that the circumference 𝐶 is equal to two 𝜋 multiplied by the radius 𝑟.
00:04:28.550 --> 00:04:29.780
So we can substitute that in.
00:04:30.640 --> 00:04:32.500
Now all that remains is to plug in our numbers.
00:04:32.990 --> 00:04:41.150
We can say that 𝑆 is equal to two 𝜋 multiplied by 10000, which is the radius 𝑟, divided by the time period 𝑇 which is 10080.
00:04:41.840 --> 00:04:46.850
Plugging that into our calculator, we get that 𝑆 is equal to 6.233 dot dot dot.
00:04:47.780 --> 00:04:49.060
But that’s not our final answer.
00:04:49.460 --> 00:04:51.090
Firstly, we need to worry about units.
00:04:51.270 --> 00:04:53.790
And secondly, we need to worry about the number of significant figures.
00:04:54.490 --> 00:05:00.600
Well we don’t actually need to worry about the units because we’d already converted all the distances to kilometers and the times to seconds.
00:05:00.950 --> 00:05:02.610
But we do need to think about putting them in.
00:05:03.560 --> 00:05:13.640
So if we look back at our calculation for 𝑆, we know that we multiplied two 𝜋 by 10000 kilometers and we divided that by 10080 seconds.
00:05:14.880 --> 00:05:17.880
So our final answer is going to be in kilometers per second.
00:05:18.210 --> 00:05:19.370
That’s exactly how we want it.
00:05:20.270 --> 00:05:21.360
And we can put that in there.
00:05:22.230 --> 00:05:25.840
Also we need to worry about the number of significant figures that we’re giving our answer to.
00:05:26.530 --> 00:05:29.420
The question asked us to give the answer to two significant figures.
00:05:29.910 --> 00:05:33.300
So here’s the first one, and here’s the second one is.
00:05:33.300 --> 00:05:39.430
It’s the one after the second one that will tell us whether the second significant figure needs to be rounded up or if it stays the same.
00:05:40.270 --> 00:05:42.240
In this case, that value is a three.
00:05:42.860 --> 00:05:44.240
This is less than five.
00:05:44.440 --> 00:05:46.860
So the second significant figure stays the same.
00:05:47.600 --> 00:05:54.510
And so our final answer is that the speed of the satellite is 6.2 kilometers per second to two significant figures.