How Do Satellite Tangential Speeds Compare to Earth's Orbital Momentum?

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Tangential speed refers to the linear speed of an object moving along a circular path, which for satellites is calibrated so gravity only alters their travel direction. Both satellites and Earth possess momentum that keeps them from spiraling into the Sun or each other. While satellites in circular orbits maintain a steady speed, those in elliptical orbits do not. Launching satellites toward the East from the Earth's surface, especially near the equator, utilizes the Earth's rotational speed to reduce fuel requirements. This principle aligns with Newton's Second Law, where the force exerted by Earth aids in accelerating the satellite in the direction of its motion.
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Tangential speed is the linear speed of something moving along a circular path. So for a satellite the tangential speed of the satellite is just right so that gravity only has the effect of changing the direction of travel.

So now can we compare this satellite to the Earth? Since the Earth has some initial momentum - it is moving in a direction,which is perpendicular to the direction of the Sun from the Earth.

So that means both the satellite and the Earth have (Initial) momentum that prevents them from getting close to the Sun or Earth (In case of satellite).
 
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You don't need the "initial" part. Any orbiting body possesses momentum.

avito009 said:
Tangential speed is the linear speed of something moving along a circular path. So for a satellite the tangential speed of the satellite is just right so that gravity only has the effect of changing the direction of travel.

In a perfectly circular orbit, yes. Objects in elliptical, parabolic, or hyperbolic orbits will not have a steady speed.
 
You are correct. Every object on Earth already has the velocity needed to orbit the Sun, whether it is on Earth or not. To put a satellite in orbit around the Earth, it is easier to launch it toward the East so that its velocity on the surface of the rotating Earth can help it reach the orbital velocity. The advantage is larger on the equator than in the U.S., and there is no advantage at the North Pole.
 
Ok so you mean that according to Newton's Second Law of Motion, the Force Law, the effect of a force on an object is to accelerate it in the direction of the force, according to the formula

F=m a

So the direction of the force of the Earth is towards the East as it rotates towards the East. Now if we were near the Equator we would move at 1000 mph speed. So a spacecraft launched from near the equator would need lesser fuel and would acquire the speed of 1000 mph. So since the direction of force is to the East and velocity is 1000 mph then the satellite also travels in the direction of this force.
 
For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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