Slingshots for Increased Spacecraft Speed

[wstrohm]

I have always wondered how passing into and out of a planet's gravitational field would result in a net gain in velocity. http://pluto.jhuapl.edu/mission/whereis_nh.php" is an example: the New Horizons Jupiter/Pluto probe using Jupiter to get 9000 km/hr speed increase.

It seems to me that conservation of momentum, or conservation of something anyway, would mean that whatever speed was picked up by "falling" toward Jupiter would be lost through deceleration, by being pulled back as the probe left the field after passing the planet.

Can anyone explain the answer to this obvious question?

Thanks!

---- Bill

 

[ranger]

When the probe approaches Jupiter, the gravity causes the probe to accelerate and gain speed, on leaving the planet, the gravity pulls on the probe causing it to slow down. The net effect on the speed as seen by Jupiter is zero, but the probe has changed direction. But you must keep in mind that the planets are not standing still, they are revolving around the sun, therefore the speed of the probe is measured relative to the sun. With that said, the before and after change in speed as a result of jupiter's gravity is different from the sun's frame of reference. Depending on the trajectory, the probe can gain up to twice the orbital velocity of the planet in question.

Consider this example. The orbital velocity of a planet is U and the velocity of the approaching probe is v. If the probe heading straight to the planet (planet also moving towards the probe) and the probe makes a 180 degree turn around the planet, which puts the probe going into the direction it came from. To the planet, it would seen as if the probe [approaching at a speed U+v] some how bounced of the planet moving away at a speed U+v relative to the planet. The net effect is of course zero from the planets perspective. But if the speed is measured relative to the sun, the probe will now be moving at a speed of 2U+v.

 

[wstrohm]

Thank you, ranger. So the planet "captures" the probe to some extent. In your example, then, I would guess that if the probe is accelerated by 2U, the planet must be slowed in its orbit around the sun by some minuscule amount, depending on its mass. I think this would be noticeable if the probe were a significant fraction of the mass of the planet. Is this correct?

 

[ranger]

Thank you, ranger. So the planet "captures" the probe to some extent. In your example, then, I would guess that if the probe is accelerated by 2U, the planet must be slowed in its orbit around the sun by some minuscule amount, depending on its mass. I think this would be noticeable if the probe were a significant fraction of the mass of the planet. Is this correct?

Yup your assumption is correct. The probe is a physical entity, which means it has mass and hence gravitation. The probe will tug on Jupiter and decrease its orbital momentum by a tiny (tiny...) amount. But where does the momentum go? The probe acquires it.

 

[wstrohm]

Ranger, thanks again!

One more question... if the tangential velocity of an orbiting body is decreased in such a manner, what happens to its orbit's shape? If it was originally perfectly circular, does it become elliptic? Does the average distance to the body which it is orbiting decrease, i.e. does it "fall" due to the slow-down?

 

[ranger]

Well when an object is in orbit, it is falling towards the object being orbited. But is has enough tangential velocity to always miss. Do you know the characteristics of an object in circular motion?

 

[wstrohm]

Um, well, I know that if the tangential velocity of an object in an elliptical orbit is increased just as it reaches apogee, it tends to circularize the orbit at the distance of the apogee from the planet. So it seems to me that the inverse would be true... that if the object were slowed while in a circular orbit, it would "fall" closer to the planet, which would speed it up, which would probably (not sure) result in an elliptical orbit with the apogee at the original distance of the circular orbit, and a perigee closer to the planet - how much closer depending on how much the object's velocity was slowed... but I'm not sure.

 

[DaveC426913]

Yes, Jupiter is veeeeerrry slightly slower and in a slightly more elliptical orbit afterwards. Its perihelion will be slightly closer to the sun.

 

[wstrohm]

Thank you, Dave.

 

[DaveC426913]

This, by the way, is also why you can't "slingshot around the sun", as happens in a number of sci-fi plots.

If you were coming from outside the SS, and ended up outide the SS, you could use the sun to add speed. But within the SS your v gain and loss will balance.