# Orbital Radius of Earth Satellite: Solve for r

• Bernie Hunt
In summary, the orbital radius of an Earth satellite is the distance from the center of the Earth to the satellite's orbit, typically measured in kilometers or miles. It can be calculated using the formula r = (G*M*T^2 / 4π^2)^(1/3) and is primarily affected by the mass of the Earth and the orbital period of the satellite. Knowing and regularly monitoring the orbital radius is important for understanding and predicting the satellite's orbit and trajectory, as well as maintaining a safe distance between satellites to avoid collisions.
Bernie Hunt
Find the orbit radius of an Earth satellite in a circular orbit if the period if 1d.

I'm at a dead end. So far I have;

r^3 = (GMT^2) / (4(pi)^2)

r^3 = (6.67*10^(-11) * 6*10^(24)) / (4 * pi^2)

and I get

r = 21642

The book says 42.2Mm. I'm only off by a couple of million meters, hahaha.

Where am I going wrong?

Thanks,
Bernie

You need to use the value of T in seconds for the constants you used to be correct.

Argh! Thud, thud, thud ...

That's the sound of me banging my head against the wall!

Bernie

## What is the orbital radius of an Earth satellite?

The orbital radius of an Earth satellite is the distance from the center of the Earth to the satellite's orbit. It is typically measured in kilometers or miles.

## How is the orbital radius of an Earth satellite calculated?

The orbital radius of an Earth satellite can be calculated using the formula r = (G*M*T^2 / 4π^2)^(1/3), where G is the gravitational constant, M is the mass of the Earth, and T is the orbital period of the satellite.

## What factors affect the orbital radius of an Earth satellite?

The orbital radius of an Earth satellite is primarily affected by the mass of the Earth and the orbital period of the satellite. Other factors such as atmospheric drag and gravitational pull from other celestial bodies can also have a small impact.

## Why is calculating the orbital radius of an Earth satellite important?

Knowing the orbital radius of an Earth satellite is important for understanding and predicting the satellite's orbit and trajectory. It is also essential for maintaining a safe distance between satellites to avoid collisions.

## Can the orbital radius of an Earth satellite change?

Yes, the orbital radius of an Earth satellite can change over time due to various factors such as atmospheric drag and gravitational influences from other celestial bodies. This is why it is important to regularly monitor and adjust the orbital radius of satellites to maintain their intended orbits.

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