- Good morning.
Billy, what is the equation for the weight or the force of gravity acting on an object here on planet Earth?
Flipping Physics
- Force of gravity equals the mass of the object times the acceleration due to gravity.
- Bo, what then would be necessary for the weight or the force of gravity acting on an object to be equal to zero?
- Well, the mass of the object is not going to be zero. So the acceleration due to gravity would need to be zero.
- True.
Bobby, please derive the equation for the acceleration due to gravity.
- Didn't we already do that?
That's correct. We already did that. But, please do it again.
- Right. Okay. So, um.......
We set the two equations for force of gravity equal to one another. Billy just gave us one so that is
also equal to the Universal Gravitational Constant times the mass of object one times the mass of object two,
in this case, that is the mass of the object and the mass of the earth all
divided by the square of the distance between the centers of mass of the two objects and...
[Class]: Everybody brought the mass of the object to the party!
- And we get the acceleration due to gravity equals the Universal Gravitational Constant times the mass of the
earth all divided by the square of the distance between the center of mass of the earth
and the center of mass of the object.
Billy, what needs to happen for an object to be completely weightless?
What needs to happen so the force of gravity acting on the object equals zero?
- The distance between the center of mass of the object and all other objects would have to be infinitely large.
So, the only way for an object to have zero weight, is for the object to be the only thing in the universe?
- Actually, if you are in the center of a uniform, spherical shell,
you would be pulled equally toward all parts of the shell,
the net force on you would be zero, and you would have zero weight.
- Or you could find a point between two objects where you are pulled equally toward both objects
and your weight would be zero.
- Right, sorry, okay. Yes. There are those examples; however,
I am more concerned about the fact that astronauts in space are often referred to as weightless;
however, because none of those cases you just mentioned applied to astronauts in space,
astronauts in space are not weightless.
- That does not make any sense.
Astronauts float in the International Space Station, so clearly they are weightless.
- Yeah. Yeah.
- Okay, let's determine the acceleration due to gravity on the International Space Station.
According to NASA, the International Space Station has an orbital attitude that ranges from 304 to
528 kilometers.
So let's take an average altitude of about 420 kilometers or 4.2 times 10 to the 5th meters.
The mass of the Earth is 5.97 times 10 to the
24th kilograms and the average radius of the earth is 6.371 times 10 to the sixth meters.
Substituting all those into our equation for the acceleration due to gravity gives us
an average acceleration due to gravity on the International Space Station of roughly 8.6 meters
per second squared.
- Billy: But? -Bobby: Uh? -Bo: What?
- If you divide that by the acceleration due to gravity here on earth and multiply by 100,
you will see that astronauts in the International
Space Station experience an acceleration due to gravity which is roughly 88% of what we experience here
on Earth.
Bo: No way. Bobby: Nuh uh.
- That's not possible. I mean, have you not seen the NASA video of astronaut Scott Kelly playing ping-pong
with a ball of water in the International Space Station.
He and the ball of water are clearly floating in the space station.
How can the acceleration due to gravity acting on him be 88% of what we are experiencing right now?
- Ah, Okay, yes, so, um..
what's going on here is that astronaut Scott Kelly,
the International Space Station,
the ball of water, and the camera are all falling toward the Earth at 8.6 meters per second squared
Because everything is falling at the same rate,
objects inside the space station appear to float.
-Right, we can think about the floor of the International Space Station
relative to everything inside the space station.
The floor of the space station is always accelerating downward at the same rate as everything which is
inside of it, so the floor of the International Space Station
is basically always getting out of the way of the stuff inside of it,
basically, they are all freely falling toward the Earth at 8.6 meters per second squared.
Therefore the objects inside the space station
are never able to catch up to the floor of the Space Station and appear to float.
- If the International Space Station is falling toward the Earth at 8.6 meters per second squared,
why does it not run into the earth?
Bobby: Yeah. Billy: Yeah?
- What is the direction of the acceleration of the International Space Station?
- The in-direction. 8.6 meters per second squared is the centripetal acceleration
that keeps the International Space Station moving in a circle around the Earth.
- In other words, the International Space Station may be falling toward the Earth at 8.6 meters per second
squared, however, it also has an inertia which is trying to keep it moving tangentially in a straight line.
That is what keeps it in orbit around the Earth.
- Correct. Objects in orbit experience what I like to call “apparent weightlessness”.
Objects in orbit are not weightless, however,
they appear to be weightless because everything is falling at the same rate,
hence, “apparent weightlessness”.
Thank you very much.... Billy: Hold on Mr. P.
I think we need to compare this to the bucket of water you dropped last time.
-Yeah.
Remember, the water was flowing out of the sides of the bucket before you dropped it
and then when you dropped it, water stopped flowing out of the bucket.
- Right, we can now explain why the water stopped flowing out of
the bucket by saying the water and the bucket were falling at the same rate,
and therefore they were both experiencing apparent weightlessness.
- Wait a minute. We already discussed apparent weightlessness.
Remember when mr.p talked about dropping me off the top of a very, very tall building in an elevator?
- That’s right! I remember that.
- Oh yeah. When you fall freely in an elevator, you experience apparent weightlessness,
just like an astronaut in the International Space Station.
- If you and an elevator are falling freely, you appear to float, again,
just like an astronaut in the International Space Station. Nice!
- I could not have said it better myself.
Thank you very much for learning with me today.
I enjoyed learning with you.