Gravity assist (2013) | Hacker News Reader

Gravity assist (2013)

planetary.org

27 pointsbetolink13 comments

Honestly, the easiest way to see how this is consistent with conservation of energy is to just imagine that the craft is physically striking the planet and bouncing elastically from it. It's very obvious that if you lightly toss a whiffle ball into the path of a speeding bowling ball then the whiffle ball will exit the interaction with much more speed than it entered it (and, in fact, with as much as twice the speed of the bowling ball).

I don't think that's right. Modeling Voyager's interaction with Jupiter as an elastic collision with the planet gives an incorrect answer. The spacecraft's speed with respect to Jupiter doesn't change.

As the post discusses, Voyager's speed (scalar) in the Jupiter frame is essentially unchanged. Its velocity (vector) of course changes quite a lot because the spacecraft's direction changes as a result of the encounter, but its speed with respect to Jupiter (and therefore its kinetic energy) isn't significantly different. It approached Jupiter with enough energy that it couldn't be captured and left with pretty much the same energy with respect to Jupiter.

What matters is that Voyager's speed with respect to the sun is greatly increased during its interaction with Jupiter's gravitational field. And since the point of the mission is to escape the sun, what matters is the spacecraft's energy state with respect to the sun, not to Jupiter.

A whiffle ball's speed with respect to the bowling ball doesn't change in the bowling ball's rest frame.

But if NASA does this too much, won't Jupiter spiral into the sun?

More natural resources wasted! We must preserve the limited orbital energy that our solar system has!

Theoretically, yes.

However, that would require a lot of mass. NASA would basically need to build enough Jupiter-slingshotting spaceships for their combined mass to be a significant fraction of Jupiter's. This would probably involve dismantling entire planets or moons to build that much spaceship mass.

For an appropriate value of "too much", yes. As a rough order of magnitude, "too much" would be about 10^24 such encounters. For comparison, that is about the same as the number of microseconds since the Big Bang.

For another perspective, 10^24 voyagers is about 100 times the mass of earth. That isn't even including the propellant and rockets needed to launch them all.

> 10^24 voyagers is about 100 times the mass of earth.

Yes, or about the mass of Jupiter, which is where the number came from--the article's comparison of the two.

The mass and orbital velocity of jupiter are large enough that this is a non issue.

Article too long for you? :)

[edit: added emoticon]

Only in the Sharknado sequel.

I'm thinking "slingshot" might actually be a better term than "Gravity assist". Gravity is just the force through which energy from an object's orbit is transferred to another object. Putting it first probably makes many people wonder why it doesn't cancel out.

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