# Calculating Kinetic Energy for Rotating Planets

• Bjarne
In summary, the kinetic energy of a rotating planet can be calculated by using the equation KE=RKE+TKE=\frac{1}{2}(I\omega ^{2}+mv^{2}) and making certain assumptions about the planet, such as it being a uniform solid sphere. However, these assumptions may not be completely accurate for real planets, and it is important to consider the planet's moment of inertia, which can be found through research.
Bjarne
How can the kinetic energy of a rotaing planet be calculate?
I know the KE equation, - but how can I calculated the mass momentum (average speed) of the mass of a rotating body.

mgb_phys said:
You probably have to make some assumptions that the planet is a uniform solid sphere (a bit of an overestimate for a real planet)
Alternatively, do a google search for the Earth's moment of inertia. The simplistic assumption of a uniform sphere yields a value that is off by more than 20%. In other words, while it is in the right ball park, it is not very good.

According to The Earth's Variable Rotation- Kurt Lambeck, the moment of inertia of the Earth around its polar axis is about

I=8.034(10^36) kg m^2

Remember
Kinetic Energy=Rotational Kinetic Energy+Translational Kinetic Energy

The TKE will vary because the translational speed of the Earth varies along its orbit. However, the average velocity is about 29,800 m/s (lenghth of orbit/365 days) so that $$KE=RKE+TKE=\frac{1}{2}(I\omega ^{2}+mv^{2})$$
plug the numbers in yourself.

D H said:
Alternatively, do a google search for the Earth's moment of inertia..
Nobody said anything about Earth !

mgb_phys said:
Nobody said anything about Earth !
Fine. Look up the moment of inertia for any planet. The uniform density assumption overstates the moment of inertia for the Sun by almost an order of magnitude, the gas giants by 60% to 100%, and the terrestrial planets by 10% (Mars) to 20% (Earth).

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## How is kinetic energy calculated for a planet?

Kinetic energy for a planet can be calculated using the equation KE = 1/2 * m * v^2, where m is the mass of the planet and v is its velocity.

## Does a planet's kinetic energy change?

Yes, a planet's kinetic energy can change as its mass or velocity changes. For example, as a planet moves closer to or further away from its star, its velocity and therefore its kinetic energy will change.

## What factors affect a planet's kinetic energy?

The main factors that affect a planet's kinetic energy are its mass, velocity, and distance from its star. Other factors such as gravitational pull from other celestial bodies and atmospheric drag can also have an impact.

## How does kinetic energy impact a planet?

Kinetic energy plays a crucial role in a planet's motion and orbit. It determines the speed at which a planet moves and how far it can travel. It also influences the planet's gravitational pull and can affect its interactions with other planets and celestial bodies.

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