Is momentum kept in change of motion direction by gravity?

[DimaMazin]

Spacecraft has momentum= - p . After gravitational action the spacecraft has momentum=p. Does owner of the gravitation recieve momentum= -2p ?

[Enthalpy]

Hi DimaMazin! You refer to a "planet flyby", or "gravitational assistance" or "slingshot effect", is that is?

 

It's a case where one should be very cautious about where the observer stands to measure the momentum and the energy...

 

When the observer is on the planet, the spacecraft arrives and departs wit the same (asymptotic, that is, when far) speed, momentum, energy - only the direction has changed. In this case already, the spacecraft's momentum vector (with orientation) has changed. This implies that the planet's momentum vector has changed too, by the opposite amount - but spacecraft influence a planet so little that the numbers are really negligible, and the observer wouldn't notice. An encounter with an other planet or a big moon would have observable effects.

 

When the observer is elsewhere, say immobile in the Solar system but not falling (...somehow) both the direction and the absolute value of the spacecraft's momentum change. There too, the planet's momentum has changed by the opposite amount. The kinetic energy changes as well, and so does the speed.

 

-p to +p can't happen. This would be the case of a tennis ball against a racket. Though, 180° deflection correspond to a parabolic trajectory by the spacecraft as observed from the planet, which only happens when the spacecraft has exactly the energy to evade the planet with zero remaining (asymptotic) speed. In every useful and existing case, the spacecraft has (much) asymptotic speed after and before the encounter. As a consequence, the deflection is much less than 180°, and the speed benefit is far less than twice the planet's orbital speed. Typical deflections seen by a heliocentric observer are more like 20°, and speed gains like 3km/s from a planet at 15km/s.

 

Knowing how much every km/s costs with our chemical propulsion, gravitational assistance is mandatory for many missions. Not only to gain speed, also to reach the destination with a smaller radial component of the relative speed (cut its path with a flatter angle). Necessary to observe the Sun from outside the ecliptic plane, necessary to go to Mercury orbit, extremely useful to just pass by Mercury, necessary to pass by Uranus etc within a bearable delay, very useful to have a bigger spacecraft around Jupiter or Saturn. Only better propulsion, like my sunheat engine, or Nasa's electric engines, or solar sails, makes us less dependent on gravitational assistance - but it's still very welcome.

 

This one is online and less complicated than other sources:

The slingshot effect

R.C.Johnson

University of Durham

[swansont]

Spacecraft has momentum= - p . After gravitational action the spacecraft has momentum=p. Does owner of the gravitation recieve momentum= -2p ?

 

Yes. Momentum is conserved.

 

-p to +p can't happen. This would be the case of a tennis ball against a racket.

 

Or a payload that goes up and then comes down.

[DimaMazin]

Hi DimaMazin! You refer to a "planet flyby", or "gravitational assistance" or "slingshot effect", is that is?

 

It's a case where one should be very cautious about where the observer stands to measure the momentum and the energy...

 

When the observer is on the planet, the spacecraft arrives and departs wit the same (asymptotic, that is, when far) speed, momentum, energy - only the direction has changed. In this case already, the spacecraft's momentum vector (with orientation) has changed. This implies that the planet's momentum vector has changed too, by the opposite amount - but spacecraft influence a planet so little that the numbers are really negligible, and the observer wouldn't notice. An encounter with an other planet or a big moon would have observable effects.

 

When the observer is elsewhere, say immobile in the Solar system but not falling (...somehow) both the direction and the absolute value of the spacecraft's momentum change. There too, the planet's momentum has changed by the opposite amount. The kinetic energy changes as well, and so does the speed.

 

-p to +p can't happen. This would be the case of a tennis ball against a racket. Though, 180° deflection correspond to a parabolic trajectory by the spacecraft as observed from the planet, which only happens when the spacecraft has exactly the energy to evade the planet with zero remaining (asymptotic) speed. In every useful and existing case, the spacecraft has (much) asymptotic speed after and before the encounter. As a consequence, the deflection is much less than 180°, and the speed benefit is far less than twice the planet's orbital speed. Typical deflections seen by a heliocentric observer are more like 20°, and speed gains like 3km/s from a planet at 15km/s.

 

Knowing how much every km/s costs with our chemical propulsion, gravitational assistance is mandatory for many missions. Not only to gain speed, also to reach the destination with a smaller radial component of the relative speed (cut its path with a flatter angle). Necessary to observe the Sun from outside the ecliptic plane, necessary to go to Mercury orbit, extremely useful to just pass by Mercury, necessary to pass by Uranus etc within a bearable delay, very useful to have a bigger spacecraft around Jupiter or Saturn. Only better propulsion, like my sunheat engine, or Nasa's electric engines, or solar sails, makes us less dependent on gravitational assistance - but it's still very welcome.

 

This one is online and less complicated than other sources:

The slingshot effect

R.C.Johnson

University of Durham

Can we use stars for change of motion direction? For example our space station travels from near neutron star to far neutron star and back therefore needs relatively small additional energy for change of motion direction. Of course payload should be accelerated.

I think we could use many stars for change of motion direction of fast space station.

Edited April 18, 2015 by DimaMazin

[pavelcherepan]

Can we use stars for change of motion direction? For example our space station travels from near neutron star to far neutron star and back therefore needs relatively small additional energy for change of motion direction. Of course payload should be accelerated.

 

We can use stars to change the momentum of the craft in the Galaxy rest frame, but we can't use the Sun, for example, to change our momentum within Solar system because this frame Sun is pretty much stationary and thus has next to 0 momentum.

 

On the other hand we can use stars in binary and more complicated systems to travel faster within such system, because in this case stars would be moving around the common barycenter and will have momentum to share.

 

Also it's been proposed that in an imaginary system with two black holes we can accelerate close to the speed of light by jumping back and forth from one to another. This extreme case requires black holes to be pretty big so that tidal forces are still bearable even right next to the event horizon. The other issue is that once you have accelerated to a significant portion of c using this method you will be going through gravity wells so quickly that you won't have time for the momentum to change appreciably.

Edited April 18, 2015 by pavelcherepan