00:01
Okay, we have a planet of mass 5 times 10 to the 24th kilograms at 4 times 10 to the 11th and negative 4 times 10 to 11th.
00:12
Let's just draw this.
00:13
So it's it.
00:14
X equals 4, y equals minus 4 times 10 to the 11th.
00:19
This is the planet.
00:21
Let's put the p.
00:22
And we have a star at minus 6 and 4.
00:30
Okay, there's our star.
00:32
Okay, so we're using newton's universal law.
00:35
Gravitation here and our first question is what is the relative position vector pointing from the planet to the star okay so what is this vector we'll call it r so to find the vector r that points from the star or sorry from the planet to the star you take the coordinates of the star and subtract the coordinates of the planet okay so that's how you would find that vector.
01:26
So if you calculate that out, so the star coordinates are the minus 6 times 10 to 11th and 4 times 10 the 11th.
01:38
Those are the star coordinates.
01:40
You're going to get, so you calculate it out, you're going to get this.
01:44
Minus 10, put it in vector form.
01:49
Minus 10 times 10 to the 11th and 8 times 10 to 11th meters.
02:04
Okay, so does that seem right? it should point in the negative x and the positive y.
02:09
Yes, that's what we got.
02:11
Okay, what's the distance between the planet and the star? so the distance, call it d, is going to just be the square root of the x component squared plus the y component squared.
02:35
So minus 10 times 10 to 11th squared plus 8 times 10 to 11th squared.
02:44
Right? because the vector gives us these x and y coordinates.
02:50
That makes a triangle.
02:51
So to find the hypotenuse, you just do the pythagorean theorem, x squared plus y squared square rooted will give you the total distance okay and this is looks like 12 .8 1 times 10 to the 11th meters okay what is the unit vector in the direction of r okay so a unit vector r hat it's just the vector r divided by the magnet of vector r or as we've drawn it we called the magnitude we just called it the maybe not the best notation but works so here's our unit vector it's just the vector r divided by its magnitude or its norm this is minus 0 .7 -81 0 .625 okay and this is unit less right okay, there's our unit vector, and if you take the magnitude of this unit vector, you should get one.
04:17
And you do.
04:18
Okay, what is the magnitude of the force exerted on the planet by the star, and the force, or the magnitude of the force exerted on the star by the planet? so we're just worried about magnitudes here.
04:35
So this is just g, mass of the star, mass of the planet, divided by the distance between them squared.
04:46
Okay, so for this, what are we going to get? let's just plug it in real quick.
04:59
Okay, 8 .13 turns 10 to 42 newtons.
05:11
Okay, so that's the magnitude of the force exerted by the planet on the star.
05:24
And that's also the answer for e, right? because the equation would be the same, except now maybe you put mass on the planet first, mass of the star over the distance between them squared.
05:37
So they are a third law pair, right? the planet's pulling the star, the star's pulling the planet, they pull with the same magnitude and opposite directions.
05:48
Okay, so now the more tricky part, we want to find the vector force exerted on the planet by the star, and the vector force exerted by the star.
05:59
Or on the star by the planet.
06:02
I may have said the same thing twice.
06:06
Okay.
06:08
So, let me just erase some of this stuff here.
06:26
So, in vector form, it's slightly confusing.
06:32
In vector form, the equation is minus, usually this is how it's written.
06:38
Mass of the star, mass of the planet, over the magnitude of r we'll just keep calling it d squared times r hat okay so this is going to be for the force on the star by the planet okay so the force on the star by the planet is equal to the negative of big g times the mass of the star the mass of the planet, divided by the distance between them squared, and then multiplied by the unit vector.
07:27
And the unit vector, in this case, let's see, so we're doing, let me just draw it out, so i don't mix myself up here.
07:38
Here's our star, here's our planet, and we're doing the force on the star by the planet...