Gravity assist and increasing orbital energy

[Physgeek64]

Hi, so whilst doing some reading I came across a section that said the most efficient way to increase your orbital energy when in an elliptical orbit is to fire your 'boosters' at perigee. I understand that the satellite is moving faster, but why should this mean that more energy is imparted to the satellite than when fired at apogee, assuming the change in the velocity is the same in both cases? It makes intuitive sense, but not logical sense (or at least not to me)

Many thanks :)

 

[rcgldr]

Consider the kinetic energy increase from Δv => 1/2 m (v + Δv)² = 1/2 m (v² + 2 v Δv + Δv²). Note that the energy increase includes the term v Δv, so a higher v with the same Δv means a higher increase in energy.

 

[Physgeek64]

Consider the kinetic energy increase from Δv => 1/2 m (v + Δv)² = 1/2 m (v² + 2 v Δv + Δv²). Note that the energy increase includes the term v Δv, so a higher v with the same Δv means a higher increase in energy.

You, my friend, are a star

 

[berkeman]

Hi, so whilst doing some reading I came across a section that said the most efficient way to increase your orbital energy when in an elliptical orbit is to fire your 'boosters' at perigee. I understand that the satellite is moving faster, but why should this mean that more energy is imparted to the satellite than when fired at apogee, assuming the change in the velocity is the same in both cases? It makes intuitive sense, but not logical sense (or at least not to me)

Many thanks :)

Just curious -- you mention Gravity Assist in your thread title, but not in your post. Should I update the title? Thanks.

 

[Physgeek64]

Just curious -- you mention Gravity Assist in your thread title, but not in your post. Should I update the title? Thanks.

Well I assumed this is a form of gravity assist since you need the gravity to speed up your orbit at perigee to then be able to fire your thrusters to increase your orbital energy, more so than at perigee. But if you don't feel the title is fitting, then please feel free :)

 

[jbriggs444]

Well I assumed this is a form of gravity assist since you need the gravity to speed up your orbit at perigee to then be able to fire your thrusters to increase your orbital energy, more so than at perigee. But if you don't feel the title is fitting, then please feel free :)

What you have described is the Oberth effect. More commonly, "gravity assist" refers to a slingshot maneuver where a craft passes closely behind a planet or moon to gain speed or closely ahead to dump speed. https://en.wikipedia.org/wiki/Gravity_assist

 

[Physgeek64]

What you have described is the Oberth effect. More commonly, "gravity assist" refers to a slingshot maneuver where a craft passes closely behind a planet or moon to gain speed or closely ahead to dump speed. https://en.wikipedia.org/wiki/Gravity_assist

Thanks for the correction :)