Gravity

the_monkey

I have a question on Gravity, a body in orbit around the earth - like the moon or a satellite is falling toward earth but their speed is so that the curvature of the earth "falls" in line with the orbit.

So a shuttle that needs to enter orbit needs to enter orbit at a high speed correct ?

If I could slowly rise up with just vertical speed and no horizontal and reached a height of that of a satellite and let go - I'd just fall right ?

Why are Astronauts on spacewalks weightless then ? is it that they are actually falling like a skydiver and it's more an equilibrium then a weightlessness ?


Its something I take for granted when reading/studying Physics but never really looked at the actual reasoning behind it.

dlouth15

the_monkey wrote: »

I have a question on Gravity, a body in orbit around the earth - like the moon or a satellite is falling toward earth but their speed is so that the curvature of the earth "falls" in line with the orbit.

So a shuttle that needs to enter orbit needs to enter orbit at a high speed correct ?

Yes.

If I could slowly rise up with just vertical speed and no horizontal and reached a height of that of a satellite and let go - I'd just fall right ?

Yes. At the height of the space station, for example, gravity is only about 10% lower than on earth.

Why are Astronauts on spacewalks weightless then ? is it that they are actually falling like a skydiver and it's more an equilibrium then a weightlessness ?

Because they are also moving horizontally with pretty much the same velocity as the vehicle they emerged from. They are orbiting too. There's no air to slow them down so they continue with that velocity.

the_monkey

dlouth15 wrote: »

They are orbiting too. There's no air to slow them down so they continue with that velocity.

OK, so they are in some sort of equilibrium then ?


And for example if one would do the same but at the Moon's altitude,
you would start to slowly fall toward earth ?

dlouth15

the_monkey wrote: »

OK, so they are in some sort of equilibrium then ?

Yes, objects moving in circles experience a sort of pseudo-force acting outwards from the centre of the circle. You can feel this if you are in a car going around a circle at constant speed. You are forced to the edge of the car.

You also feel a force if you press down on the accelerator. You are pushed to the back of the seat.

Acceleration is happening in both these cases. The car going round the circle is actually accelerating in the direction of the centre of the circle even though it is moving at constant speed. Because the acceleration is at right-angles to the direction of motion there is no change in the speed of the car.

In the case of orbiting and falling bodies, both are accelerating towards the centre of the earth, but the orbiting body has sufficient lateral motion so that it can maintain acceleration towards the centre while maintaining altitude.

An object in a circular orbit accelerates at right angles to its direction of motion. A normally falling object accelerates in the direction of motion.

And for example if one would do the same but at the Moon's altitude,
you would start to slowly fall toward earth ?

Yes, if you stationary above the earth at the moons altitude you would slowly fall. A small horizontal movement means that you will miss the earth and go into an elliptical orbit. A sufficiently large horizontal movement and you will go into a circular orbit about the earth.

the_monkey

Excellent post ! thanks !

FISMA

the_monkey wrote: »

a satellite is falling toward earth but their speed is so that the curvature of the earth "falls" in line with the orbit.

Even though its speed be constant, a satellite in circular motion is accelerating because the direction of its velocity is constantly changing.

The direction of the acceleration is inward. This acceleration is center seeking, the latin word for which is centripetal.

The velocity vector at any instant of the shuttle's circular motion would be tangent to the curve. So to would its differential displacement.

the_monkey wrote: »

So a shuttle that needs to enter orbit needs to enter orbit at a high speed correct ?

The higher the orbit, the faster you have to go. Orbital speed is less than escape speed. Likewise, low Earth orbits have slower speeds than high Earth orbits.

The space shuttle could not go to the moon, it simply was not fast enough. It was a low Earth orbiter. Only the Saturn V was able to go fast enough to get people to the moon and back.

the_monkey wrote: »

If I could slowly rise up with just vertical speed and no horizontal and reached a height of that of a satellite...

Do you mean if you had a ladder tall enough to get into outer space, you could just climb up, not going escape velocity? Nice try! You don't get something for nothing. Do the math and see what happens. First, consider how to keep the ladder from falling over.

the_monkey wrote: »

If I could slowly rise up with just vertical speed and no horizontal and reached a height of that of a satellite and let go - I'd just fall right ?

If you mean fall back down the way you came up? No.

If we constructed this space ladder and you climbed to the space station and "slipped" getting on, you would now be in orbit with the space station. If you could fall "straight" down, then why not the station?

the_monkey wrote: »

Why are Astronauts on spacewalks weightless then ?

They are not. Weight is defined as mg, when you are on the surface of the Earth and mag - when you are in orbit, where ag standards for the acceleration due to gravity at that position.

In general, in low Earth orbit, most astronauts are about 92% of their weight on the surface. However, they feel weightless because if they step on a scale while in the shuttle or on a space walk the scale reads zero. This is more correctly called apparent weightlessness.

What is happening is that both the scale and the astronaut are in an accelerated frame of reference. Our senses do not like these non-inertial frames of reference.

Imagine you were standing in an elevator, on a scale, in a tall building. If the elevator cable breaks and the elevator free falls, your scale will read zero.

the_monkey wrote: »

it's more an equilibrium then a weightlessness ?

the_monkey wrote: »

OK, so they are in some sort of equilibrium then ?

No. They area accelerating. Newton's first Law tells us that things do not like to accelerate. If they are accelerating, then there is a Force on them that is not balanced. An unbalanced force, by definition, tells us that we are not in equilibrium.

The space shuttle is in free fall. It is freely falling back to the Earth. However, since it is going so fast, it is going to take a while before it comes back down.

the_monkey wrote: »

And for example if one would do the same but at the Moon's altitude,
you would start to slowly fall toward earth ?

Not sure what you mean by this. At this altitude where is the Earth and moon?

If you were that close to the Moon, it's gravity would dominate the Earth's and you would fall back to the moon.

the_monkey

ehh .. confused again.

Just on the point on why the ISS doesn't fall straight down ... the ISS is orbiting at a high velocity ... , I mean if I could be teleported to this position but with 0 velocity - then for sure I would just fall to earth - correct ?

FISMA

the_monkey wrote: »

ehh .. confused again.

Just on the point on why the ISS doesn't fall straight down ... the ISS is orbiting at a high velocity ... , I mean if I could be teleported to this position but with 0 velocity - then for sure I would just fall to earth - correct ?

The ISS is going too fast to fall straight down. It is falling back to the Earth, but its high speed, prevents it from falling radially towards the Earth.

If you were "beamed up" to the ISS, you may have 0m/s speed with respect to the station, but with respect to the Earth, you are going over 17,000mph.

Have a look at Newton's cannon. Vary firing speed. First, see what happens when you fire at 1.0km/s. Then try 3.0km/s and 7.70km/s.

All of the above speeds are less than orbital speed so you should crash back to Earth.

Going with a speed like 8.2km/s will put you in to a stable low Earth orbit.

Once you have a stable orbit - that's what the Space station is doing. It is falling back to Earth over a long period of time. Neither it or yourself will fall "straight"/radially back towards the center of the Earth.

dlouth15

the_monkey wrote: »

ehh .. confused again.

Just on the point on why the ISS doesn't fall straight down ... the ISS is orbiting at a high velocity ... , I mean if I could be teleported to this position but with 0 velocity - then for sure I would just fall to earth - correct ?

Correct. You need a horizontal speed the similar to the ISS to remain in an orbit similar to that of the ISS.

the_monkey

FISMA wrote: »

The ISS is going to fast to fall straight down. It is faling back to the Earth, but its high speed, prevents it from falling radially towards the Earth.

If you were "beamed up" to the ISS, you may have 0m/s speed with respect to the station, but with respect to the Earth, you are going over 17,000mph.

Have a look at Newton's cannon. Vary firing speed. First, see what happens when you fire at 1.0km/s. Then try 3.0km/s and 7.70km/s.

All of the above speeds are less than orbital speed so you should crash back to Earth.

Going with a speed like 8.2km/s will put you in to a stable low Earth orbit.

Once you have a stable orbit - that's what the Space station is doing. It is falling back to Earth over a long period of time. Neither it or yourself will fall "straight"/radially back towards the center of the Earth.

You are right but I'm not saying that i'd be beamed up to ISS at it's speed, im saying id be beamed up to it's "position" (height say) with 0 m/s
see the post ^^

FISMA

the_monkey wrote: »

im saying id be beamed up to it's "position" (height say) with 0 m/s

0.0m/s? With respect to what?

Morbert

the_monkey wrote: »

ehh .. confused again.

Just on the point on why the ISS doesn't fall straight down ... the ISS is orbiting at a high velocity ... , I mean if I could be teleported to this position but with 0 velocity - then for sure I would just fall to earth - correct ?

If I could slowly rise up with just vertical speed and no horizontal and reached a height of that of a satellite...

What is your frame of reference? If you are standing on the equator, your horizontal speed is approximately 1,600 km/h according to a distant observer in an inertial frame stationary with respect to the centre of the earth. In this frame, if you set your velocity to 0, you would always fall back to earth no matter how far away you started your decent, but as you approach Earth, the ground would be whirling past you at 1,600 km/h

If you mean stationary with respect to the earth's surface (E.g. Building an elevator to the stars), then there will be pseudo force called the centrifugal force, as we are dealing with a non-inertial frame. At a height of 36,000 km, the centrifugal force will roughly equal the gravitational force. (See below for a nice picture of the centrifugal force in action). This type of orbit is called a geostationary orbit.

If you mean you hopped on a rocket and blasted straight skyward, then that would be a mix of the two scenarios above, and you would need to reach an orbit of almost 2 million km before the centrifugal force cancelled out the gravitational force. (This is a back of the envelope calculation, and assumes the rocket gets you to the 2 million km mark instantly)

the_monkey

FISMA wrote: »

0.0m/s? With respect to what?

with respect to a position directly below on the earth, so if the ISS did pass if would whack me at high velocity ..

dlouth15

the_monkey wrote: »

with respect to a position directly below on the earth, so if the ISS did pass if would whack me at high velocity ..

If we keep it simple and imagine that point to be the South or North pole, then we don't need to worry about the rotation of the Earth. In this case you would fall directly downward.

It might be overcomplicating matters a bit but if it is a point on the equator then there will be a relatively small horizontal component (~0.44 km/s) that would have to be taken into account. The ISS itself travels at about 7.7 km/s. So you are traveling at only about 6% of the speed needed for the roughly circular orbit of the earth. You will go into a tight elliptical orbit which will intercept with the atmosphere and surface of the earth. But to all intents and purposes it will look as if you are falling directly downward.

FISMA

the_monkey wrote: »

with respect to a position directly below on the earth, so if the ISS did pass if would whack me at high velocity ..

The_Monkey,
On the first day of Physics class, the first thing we learn is that all motion is relative.

Easy to state. Hard to fully understand.

Have you seen the below video entitled "Frames of Referece?" It is required viewing for all Physicists. If you have not already done so, have a look as it should help clear up a lot of your questions.

https://www.youtube.com/watch?v=pyBNImQkRuk

Carawaystick

dlouth15 wrote: »

So you are traveling at only about 6% of the speed needed for the roughly circular orbit of the earth. You will go into a tight elliptical orbit which will intercept with the atmosphere and surface of the earth. But to all intents and purposes it will look as if you are falling directly downward.

Isn't this going to be a parabola? like a ballistic missile trajectory? If you ignore air resistance slowing you down.

dlouth15

Carawaystick wrote: »

Isn't this going to be a parabola? like a ballistic missile trajectory? If you ignore air resistance slowing you down.

It would be a parabola in a uniform gravitational field, and indeed for experiments on the surface of earth such as throwing a ball in the air, the field is uniform to all intents and purposes. But strictly speaking the ball (again ignoring air resistance) follows an ellipse with one of the focuses being the centre of the Earth.