Understanding Orbital Motion: The Role of Gravity and Speed

good morning today our goal is to explore orbital motion and the question we'll be answering is

this how is it possible for an object to stay in orbit

around the earth so to begin with we have to discuss gravity when the object is sitting on the earth

when its altitude is exactly zero kilometers the acceleration due to gravity is 9.8

meters per second per second what this means is that for an object that is falling

every 1 second its speed will increase by 9.8 this gravitational attraction gets

weaker as you go further away from the earth so for example

at the surface of the earth it's 9.8 but 100 kilometers above the earth it's only 9.5

at 400 kilometers above the earth where the international space station orbits it's 8.7 notice

the acceleration due to gravity is still significant it's still 8.7 so the first

myth i'd like to dispel is that there is no gravity in space no there is a significant amount of

gravity in space even at a thousand kilometers above the

earth it's still 7.3 and at one thousand five hundred

kilometers above the earth it's six point four and even at

five thousand kilometers above the earth it's still 3.1 so what would happen

if i removed my hand if i let this shuttle go would it just float in space at 5000

kilometers above the earth let's see no as you can see even when an object is

5 000 kilometers above the earth it's still

false it's just like dropping a pencil on the earth except you're 5000 kilometers away and

you're dropping that pencil so objects don't simply float in space so now the question is how do they stay

in orbit let's start off with our object at a thousand kilometers above the earth

to maintain an orbit you need some speed so we're initially going to give it a push

my hand over here is going to give it a push at a thousand meters per second which is

3 600 kilometers an hour let's see what happens

i don't know nothing happens it smashes into the earth that speed is not fast enough

let's try 3000 meters per second no it still smashes into the earth we've got to go faster let's try

6000 meters per second no faster faster i say faster let's try 7000 meters per second

we're close as you can see we're really close if we go just a little faster and in fact

the number has been written right over here 7351.7 meters per second

it's been there all long and sure enough the object at that specific speed

orbits the earth so now the question is what would happen if we gave it a speed that was slightly

greater let's try 8 000 meters per second notice now the orbit is no longer

circular the orbit is an oval or an ellipse most objects orbit

with an ellipse let's go back to the circular orbit for a moment now in a moment we are going to create a

cosmic catastrophe with this button here when the cosmic catastrophe is created the earth will disappear

let's see if the object still stays in orbit when the earth disappears

all right i'm going to create the cosmic catastrophe right now

as you can see the object no longer stays in orbit it travels in a straight line

newton's first law says that an object moving in a straight line will continue moving

in a straight line unless there's a force so you see there are two factors

required for an orbit one the object needs speed if it doesn't

have any speed if it doesn't have any speed it smashes right into the earth

when we give it a speed of zero no good it can't stay in orbit but two not only does the object need

speed but the object also needs gravity it needs some sort of attraction when we

remove that attraction it travels in a straight line so keep that in mind there are

two things required for an orbit one the object needs speed but two

the object needs gravity now what's really interesting with the simulation is that i could change the

mass of the earth let's change the mass of the earth and see what happens to the gravitational

attraction so right now at a thousand kilometers above the earth

it's 7.3 meters per second squared we're going to increase the mass of the earth notice

as i increase the mass of the earth we're getting new continents appearing so we've effectively doubled the mass of

the earth there's some new continents here and notice what's happened to the

acceleration due to gravity it's increased i'll show you that again with the regular mass of the earth at

7.3 when you double the mass of the earth well the acceleration due to gravity has

also doubled to 14.6 now let's see what happens if we don't change the speed

ah with more gravity we need a higher speed that speed just doesn't cut it

when we doubled the acceleration due to gravity and so let's see the speed we have to

dial in well according to the program it's 10 396.8

let's try that and notice now with more gravity with greater

gravitational attraction we need a higher speed to orbit the planet so the take home message today

you need speed to orbit and you also need gravity without gravity the object will travel

in a straight line finally let's go back to our base case we're going to launch it and now the

question is is this speed unique to that altitude well as you just saw that speed depended

on the mass of the earth but what else does it depend upon well i'm going to

reduce the altitude to 400 kilometers let's see if we leave that same speed in notice once again that speed is not fast

enough we need a higher speed why because when we reduce the altitude when the object gets closer to the earth

it experiences greater gravitational attraction so let's see the speed we need according

to the simulation it's seven thousand six hundred and seventy point one

notice also the new acceleration due to gravity at a thousand kilometers it was 7.3

now because we reduced the altitude we've gone closer to the earth it's 8.7 and sure enough at the higher speed the

object is now able to orbit the earth so that initial launch speed required is

dependent on the altitude of the earth and also the mass of the earth because altitude and mass

influence the gravitational attraction now obviously there aren't people's hands in earth giving objects pushes

the objects that give those pushes are rockets so the rocket provides that speed for

the object to maintain its orbit i hope you enjoyed today's discussion have a great day bye-bye