Satellite Orbiting: Understanding the Concept

[SecretSnow]

Hi guys, I'm confused when my textbook (or actually most other explanations) says that when an object is launched at a speed high enough, it orbits the Earth circularly because the Earth beneath CURVES away from it.

First thing first, I'll start by visualizing the Earth is stationary and don't rotate. This is for the sake of making things simpler first. If I throw a ball at a high speed, it will eventually reach the ground. If the speed is very high, the ball will "escape" from Earth.
Right?

To complicate things further, when the Earth rotates, it will orbit. One thing is, does the Earth rotate faster than the ball's orbiting speed? The text does not mention it :( . If it does, how does it go into orbit? Even if the Earth curves away, wouldn't it still fall down?

I'm thinking that if the speed is high enough, the ball can reach up quite high till there is sufficient space for it to orbit. Because at lower heights, it will eventually collide onto the ground although it wants to orbit circularly. At higher heights, this is then possible.

What has it got to do with curving anyway? And I find the diagrams given by textbooks are peculiar. For instance, the Earth rotates sideways but object is launched from places like North Pole to South Pole, vertical orbit when the rotation is horizontal. What difference would it even make then?

By the way, is the orientation for launching an object to escape Earth and launching an object to orbit the same? Is it upwards and tangentially respectively?

 

[TSny]

Hello, SecretSnow.

Have you seen animations like this or this?

If you want to put a ball into circular orbit by throwing it with some initial velocity and then letting gravity take over from that point, you must launch the ball from a point on the circular orbit and with a velocity that is tangent to the circular orbit.

When a spacecraft is launched from the surface of the earth, then rockets are used to propel the spacecraft for some period of time to get the spacecraft into the proper initial position and velocity for circular orbit.

 

[HallsofIvy]

Hi guys, I'm confused when my textbook (or actually most other explanations) says that when an object is launched at a speed high enough, it orbits the Earth circularly because the Earth beneath CURVES away from it.

First thing first, I'll start by visualizing the Earth is stationary and don't rotate. This is for the sake of making things simpler first. If I throw a ball at a high speed, it will eventually reach the ground. If the speed is very high, the ball will "escape" from Earth.
Right?

You are misreading your original statement. The satellite orbits because the earch CURVES away from it. That has nothing to do with the Earth rotating. If you throw a ball straight up then, ignoring the fact that gravitational acceleration drops off as r2, it will eventually fall back to the earth. If you throw it at an angle rather than straight up, where it hits the Earth will depend upon its speed. Because the Earth curves (not "rotates") you can (theoretically) throw the ball fast enough that the distance it travels before it hits the Earth is greater than the circumference of the earth.

To complicate things further, when the Earth rotates, it will orbit. One thing is, does the Earth rotate faster than the ball's orbiting speed? The text does not mention it :( . If it does, how does it go into orbit? Even if the Earth curves away, wouldn't it still fall down?

That depends upon the height at which you want the satellite to orbit. The greater the radius of the orbit, the slower the orbital speed can be.

I'm thinking that if the speed is high enough, the ball can reach up quite high till there is sufficient space for it to orbit. Because at lower heights, it will eventually collide onto the ground although it wants to orbit circularly. At higher heights, this is then possible.

Are you thinking of firing straight up or at an angle?

What has it got to do with curving anyway? And I find the diagrams given by textbooks are peculiar. For instance, the Earth rotates sideways but object is launched from places like North Pole to South Pole, vertical orbit when the rotation is horizontal. What difference would it even make then?

Again, you seem to be confusing "curving" with "rotating". If the surface of the Earth were an infinitely large plane, then no matter how high or at what angle you launched an object, it would land somewhere. Since it is not, if you launch it high enough with sufficient angle, it will "miss" the surface of the earth.

By the way, is the orientation for launching an object to escape Earth and launching an object to orbit the same? Is it upwards and tangentially respectively?

What do you mean by "escape the earth"? Theoretically, it wouldn't make any difference. It should be solely the "vertical" component that adds to "escape velocity"- which is discussed in your other thread: https://www.physicsforums.com/showthread.php?t=662201

 

[SecretSnow]

Oh I think i got it already! The animations are very useful, I can't find them elsewhere lol.

So I misunderstood the meaning of 'curve'.. I see. Actually after watching the animation, am I still right to say that there must be enough space for the satellite to orbit? I'm thinking that, when the satellite is launched tangentially with respect to the Earth (assuming it's a sphere), it should by right continue to move in a straight line if there is no gravity. Because there is gravity, there is a force acting downwards of the object towards the centre of the Earth (centripetal acceleration) and this causes the satellite to change its direction constantly and enter uniform circular motion. Gravity does not aim to make objects trying to orbit to stay on the ground as much as it wanting to let objects change their direction.

If it is at low speeds below escape speed, it will collide on to the ground eventually as it tries to orbit (correct?). At speeds above the escape speed, the satellite will travel a horizontal distance far enough away from the ground to have enough space to orbit. Can i say this??

However, why would some satellites travel in ellipses instead of a circle?? Thanks a lot people, you've been a great help!

 

[MrWarlock616]

You can get different kinds of orbits if you change the critical velocity, because it is related to the escape velocity of the object. :)

 

[SecretSnow]

You can get different kinds of orbits if you change the critical velocity, because it is related to the escape velocity of the object. :)

I see. But what is the physics behind it?

 

[MrWarlock616]

I see. But what is the physics behind it?

V_e=√(2GM/R)=V_c√2.
So, if the kinetic energy you supply to the satellite is more than what's required for a circular orbit, it will move in an elliptical orbit or even a parabolic path where it leaves the earth.