Gravity Assist-Elliptical Trajectories

In summary, the conversation is about a mistake in an equation on page 17 of a JPL technical report. The missing term, (r2)2, is necessary because the triangular inequality expresses that r1' and r2' must add to something larger than the distance between P1 and P2, which can be found using r1, r2, and θ and the law of cosines. Ryan is seeking help to understand the relationship.
  • #1
rpthomps
182
19
Good evening,

I am working my way through a JPL technical report I found online at

link

Specifically, I am at page 17 which looks like

1tM3dJ0.png


and I am trying to understand the relation

G7cVWTH.png


I basically, don't understand where this relationship comes from and why it is necessary.

Any help would be appreciated.

Ryan
 
Physics news on Phys.org
  • #2
Well, there is a mistake in that equation. There should be another term inside the square root. The missing term is (r2)2. That triangular inequality simply expresses that r1' and r2' must add to something larger than the distance between P1 and P2 which can be found from r1, r2, and θ by use of the law of cosines.
 
Last edited:
  • Like
Likes 1 person
  • #3
Thanks Dauto
 

What is a gravity assist-elliptical trajectory?

A gravity assist-elliptical trajectory is a trajectory utilized by spacecraft to gain speed and change direction by using the gravitational pull of a celestial body, such as a planet or moon.

How does a gravity assist-elliptical trajectory work?

As a spacecraft approaches a celestial body, its velocity is altered due to the body's gravitational pull. This change in velocity is called a gravity assist. By carefully planning the trajectory and timing the approach, the spacecraft can use this gravity assist to either speed up or slow down, and change direction if needed.

Why are gravity assist-elliptical trajectories used?

Gravity assist-elliptical trajectories are used to conserve fuel and energy in space missions. By utilizing the gravitational pull of a celestial body, the spacecraft can gain speed and change direction without using its own propulsion systems, which can significantly extend the mission's lifespan and reach further destinations.

What are some examples of missions that have used gravity assist-elliptical trajectories?

Some notable missions that have used gravity assist-elliptical trajectories include NASA's Voyager missions to explore the outer planets, Cassini's mission to study Saturn and its moons, and the New Horizons mission to Pluto and beyond.

What are the potential risks or challenges of using gravity assist-elliptical trajectories?

One potential risk is that the spacecraft may be affected by the celestial body's gravity in an unpredictable way, causing it to deviate from its intended trajectory. Additionally, the timing and precision of the maneuver must be precise in order to achieve the desired results. This requires careful planning and calculations by the mission team.

Similar threads

I [Questions] Modeling a Baseball Pitch Trajectory in 3D Space
    • Mechanics
Replies
1
Views
788
A Inquiry Regarding Concept in Time and Celestial Motion
    • Beyond the Standard Models
Replies
2
Views
823
Student Course Review for my 12 y/o ESL science student in Japan
    • STEM Educators and Teaching
Replies
1
Views
1K
Possible to solve for the initial speed of a projectile?
    • Mechanics
Replies
11
Views
2K
Can someone help calculate pressure drop ?
    • Mechanics
Replies
3
Views
1K
Looking for formulations used in sea level calculations
    • Earth Sciences
Replies
2
Views
986
I Understanding Ultrasound Attenuation and Reflection in Aluminum Sheets
    • Classical Physics
Replies
15
Views
546
B Confusion while trying to build intuition of centripetal force
    • Mechanics
Replies
15
Views
2K
Projectile Trajectory - as influenced by multiple factors
    • Mechanics
Replies
1
Views
1K
I Two recent tests of loop quantum gravity theory
    • Beyond the Standard Models
Replies
9
Views
475

Hot Threads

Recent Insights

Back
Top