Conservation of energy

[Dart15]

Hi,

 

 

I understand that many of the plans to explore the solar system involve using a sling shot technique around other planets to increase speed to the more distant ones. In fact Nasa used this around the moon to get back to Earth.

 

What I have trouble understanding is where this energy comes from. In effect energy (speed) is transfered from "somewhere" to the object that is sling shot'd. Gravity is used in a very specific way - close enough to feel effect but not too close to be caught in orbit etc.

 

The object/craft has gained energy but nothing seems to have lost energy. Surely this breaks the "conservation of energy" rule ?

 

Confused !

 

George

[Spyman]

If you throw a ball at a speeding car the ball will gain energy from the car during the bounce and the car will loose a slight amount, since the car is much heavier than the ball a small decrease for the car will be large on the ball.

 

Likewise if a spacecraft makes a slingshot around the Moon, it will gain a small amount of energy from the Moon and the Moon will be slowed down a tiny amount, and in this case the difference in mass is much much greater.

[Cap'n Refsmmat]

Yeah, the important part is that the planet doing the slingshotting is moving. So when the spacecraft whips around it, the planet "drags" it gravitationally. The planet loses a bit of energy when doing so.

[Blahah]

Does that mean that a planet loses energy for every satellite? And if so, could the energy lost to collective satellites ever make a difference to the Earth's rotation?

Edited February 18, 2011 by Blahah

[Cap'n Refsmmat]

The Earth isn't slingshotting all the satellites currently in orbit around it, since they started on Earth moving at the same speed as Earth. It's only when you have a spacecraft at a radically different velocity swinging by that you could affect the Earth's orbit any.

 

Given how massive the Earth is, I doubt you'd have a significant impact on its orbit.

[DrRocket]

Hi,

 

 

I understand that many of the plans to explore the solar system involve using a sling shot technique around other planets to increase speed to the more distant ones. In fact Nasa used this around the moon to get back to Earth.

 

What I have trouble understanding is where this energy comes from. In effect energy (speed) is transfered from "somewhere" to the object that is sling shot'd. Gravity is used in a very specific way - close enough to feel effect but not too close to be caught in orbit etc.

 

The object/craft has gained energy but nothing seems to have lost energy. Surely this breaks the "conservation of energy" rule ?

 

Confused !

 

George

 

You are confused because it is confusing.

 

Let's stick to Newtonian gravity and consider the problem from the perspective of a distant inertial observer.

 

A gravitational field is conservative. So if you consider a planet in isolation a spacecraft appraching it speeds up and as it goes away from the planet it slows down. The speeding up and slowing exactly compensate and the spacecraft gains no net energy. There is no "slingshot" effect.

 

But a planet is in reality not isolated. It is in orbit around the sun and moving very quickly. So, a spacecraft approaching a planet "from behind" is being dragged along by the planet via a gravitational tether. The planet has a lot of mass and momentum and slows down by a miniscule amount. The spacecraft is much less massive and speeds up appreciably. That is the source of the "slingshot" effect. The energy comes, not from gravity per se, but rather from the kinetic energy of the planet. Gravity merely acts as a "rope" to couple the spacecraft to the planet.

 

Both momentum and energy are conserved.

Edited February 18, 2011 by DrRocket

[imatfaal]

You are confused because it is confusing.

 

Let's stick to Newtonian gravity and consider the problem from the perspective of a distant inertial observer.

 

A gravitational field is conservative. So if you consider a planet in isolation a spacecraft appraching it speeds up and as it goes away from the planet it slows down. The speeding up and slowing exactly compensate and the spacecraft gains no net energy. There is no "slingshot" effect.

 

But a planet is in reality not isolated. It is in orbit around the sun and moving very quickly. So, a spacecraft approaching a planet "from behind" is being dragged along by the planet via a gravitational tether. The planet has a lot of mass and momentum and slows down by a miniscule amount. The spacecraft is much less massive and speeds up appreciably. That is the source of the "slingshot" effect. The energy comes, not from gravity per se, but rather from the kinetic energy of the planet. Gravity merely acts as a "rope" to couple the spacecraft to the planet.

 

Both momentum and energy are conserved.

 

Thanks Doc - I had always disliked previous explanations I had heard, I couldn't work out why the acceleration and deceleration wouldn't cancel; your quick expo above made it clear.

[SMF]

I agree, nicely stated Doc Rocket. SM