Celestial Mechanics: Earth Orbit Time & Why 80 Minutes is Impossible

• a.a
In summary, the greater the altitude of an Earth satellite, the longer it takes to complete one orbit. It is impossible for any vehicle to orbit Earth in less than 80 minutes due to the excessive energy expenditure and the risk of entering the atmosphere. The centrifugal force would be greater than the gravitational force, unless compensated for in some other way, resulting in a minimal orbital period of about 84 minutes. Additionally, orbiting at sea level is not possible due to the presence of air resistance.
a.a
The greater the altitude of an Earth satellite, the longer it takes to complete one orbit. Why is it impossible for any vehivle to go aroung Earth in less than 80 minutes?

Is this a homework question?
You have to at least try and answer it, describe what you know and any ideas you have about the solution

It's not impossible, but the energy expenditure would be ridiculous. If you're referring to ballistic orbits, I suspect that it's because an orbital period of less than 80 minutes would put the object inside the atmosphere. (Although, I haven't actually heard of that limit before.)

edit: Sorry, Mgb; didn't mean to step on your toes here. I started this response before seeing yours. It didn't occur to me that it might be a homework problem.

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Because the centrifugal force would be greater than gravitational, unless you compensate it some other way. Computing this you get the minimal period something about 84 minutes.

Its not a homework question. It was a question that arose in class and I didnt really understand the explanation and as a result didnt take notes.

Im sorry michalll but i didnt quite get why the centrifugal force would be greater than the gravatational force.

michalll said:
Because the centrifugal force would be greater than gravitational, unless you compensate it some other way. Computing this you get the minimal period something about 84 minutes.

Surely the definition of an orbit is that centrifugal force equals the gravitational.

If you calculate the height necessary for an 84min orbit and compare it to the height of the atmosphere / density of the atmosphere at that height you will see why a satelite orbiting at that height isn't going to last long.

you could orbit the Earth at sea level if you had an air free pipe to avoid air resistance.

1. What is celestial mechanics?

Celestial mechanics is the branch of astronomy that deals with the motion of celestial bodies, such as planets, moons, and stars, under the influence of gravity and other forces.

2. How long does it take for the Earth to complete one orbit around the Sun?

The Earth takes approximately 365.24 days, or one year, to complete one orbit around the Sun.

3. Why is it impossible for Earth's orbit time to be exactly 80 minutes?

This is because the Earth's orbit is determined by its distance from the Sun and the force of gravity between them. If the orbit time were to suddenly change to 80 minutes, it would mean that either the Earth's distance from the Sun or the force of gravity has drastically changed, which is not possible.

4. What factors affect Earth's orbit time?

Earth's orbit time is primarily affected by its distance from the Sun and the force of gravity between them. Other factors that can have a minor impact include the gravitational pull of other planets and the Earth's axial tilt.

5. How is Earth's orbit time calculated?

Earth's orbit time is calculated using Kepler's third law of planetary motion, which states that the square of a planet's orbital period is proportional to the cube of its average distance from the Sun. By knowing the Earth's average distance from the Sun (149.6 million kilometers), we can calculate its orbit time of 365.24 days.

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