Solving for Mars Encounter Orbit w/Limited Info

  • Context: Graduate 
  • Thread starter Thread starter skiboka33
  • Start date Start date
  • Tags Tags
    Mars Orbit
Click For Summary

Discussion Overview

The discussion revolves around calculating the orbit of a space probe that needs to encounter Mars, starting from an orbit at 1 AU from the Sun. Participants explore the necessary parameters such as eccentricity and changes in orbital velocity, while considering the implications of limited information provided in the problem statement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the sufficiency of the information given to solve for the required parameters, suggesting that additional data may be necessary.
  • Another participant argues that knowing the aphelion and perihelion allows for the calculation of eccentricity and energy differences between orbits, which can lead to determining the change in orbital velocity.
  • Concerns are raised about the need for phase information, as the relative positions of Mars and the probe at a specific time are crucial for a successful encounter.
  • A participant notes that if the probe's orbit were resonant with Mars, it might never encounter the planet, highlighting the complexities of real-life orbital mechanics.
  • Further elaboration indicates that Mars' eccentric orbit could lead to significant discrepancies in intercept calculations if not properly accounted for.
  • One participant suggests a simplified approach for the problem, proposing a straightforward calculation of the orbit parameters and timing the launch based on Mars' position, while acknowledging real-life complications such as orbital inclination.

Areas of Agreement / Disagreement

Participants generally agree that the problem can be approached with the information given, but there is significant discussion about the limitations of this approach and the complexities involved in real-life scenarios. Multiple competing views on the necessity of additional data and the implications of orbital mechanics remain unresolved.

Contextual Notes

Participants note that the problem simplifies real-world complexities, such as the need for precise timing based on Mars' position and the effects of orbital inclination, which are not accounted for in the question.

skiboka33
Messages
59
Reaction score
0
Ok, say there is a space probe orbitting the sun at 1 AU and it needs to be put in an orbit that will encounter Mars using the least amount of energy. The orbit hsa perihelion at Earth's orbit and apelion at mar's orbit. In the problem we are asked to solve for stuff like the eccentricity of the orbit and change in orbital velocity to achieve the orbit. No need to do the question for me, but I'm just a little confused about what information we can get from the original question. Seems like it's not enough information to solve the problems. Any ideas on what I'm missing? thanks.
 
Astronomy news on Phys.org
Well, you know the aphelion and perhelion of the tranfer orbit, you can solve for the eccentricity with that information.

You can solve for the total energy of your probe in this new orbit, and you can solve for the total energy in the original orbit. From this you can solve for the energy difference between the orbits, which at perhelion will be due to kinetic energy alone. This will allow you to get the change in orbital velocity needed.
 
skiboka33 said:
Seems like it's not enough information to solve the problems.

In real life, you would need phase information -- that is, you'd need to know the positions of Mars and the satellite at a particular time. The fact that the orbit has aphelion at Mars' orbit doesn't mean you'll encounter it in any reasonable amount of time. In fact, if your satellite's orbit was resonant with that of Mars, you'd likely never encounter it at all!

You almost certainly don't need to worry about these things, however. The problem should be solvable using the information given, along with the procedure Janus described.
 
This was a question on my assignment due today. Odds are this guy is in my class (Uvic).

Last week of school, already started studying for finals, an astronomy assignment isn't exactly on my radar. Went to school this morning, oh **** I forgot to do this assignment. And this one was actually tough! Flipped it off in an hour and a half. 60% at most. Oh well. I pwn that class anyway.

Sorry this isn't a more helpful post, although the thing was due five hours ago so I guess help now wouldn't help you too much.
 
SpaceTiger said:
In real life, you would need phase information -- that is, you'd need to know the positions of Mars and the satellite at a particular time. The fact that the orbit has aphelion at Mars' orbit doesn't mean you'll encounter it in any reasonable amount of time. In fact, if your satellite's orbit was resonant with that of Mars, you'd likely never encounter it at all!

True, and in addition, in real life you would need to know at what position Mars will be in it's orbit in relation to its perhelion when intercept is met. Mars' orbit is eccentric enough that if you based your [itex]\Delta V[/itex] on its average distance from the Sun you could find yourself missing Mars by some 21 million km.

As a result, when you launch a probe from Earth, it takes the least [itex]\Delta V[/itex] to intercept Mars when you launch in the last half of February and the most if you launch in August. (this is just for intercept and doesn't take account the [itex]\Delta V[/itex] needed to match orbit with Mars once you get there.)

This leaves a few best launch "windows" where both the energy needed is the least and Mars and Earth are in the proper relative positons of their orbits for intercept.

But again, for this question, you are allowed to simplify and assume that Mars is in a circular orbit.
 
This is pretty straightforward, in the simplest case. Just calculate the parameters of an orbit with its perihelion at Earth's orbit, and aphelion where it intersects Mars' orbit. Take half the orbital time (say 190 days), and calculate how far Mars would move in that interval. Launch on the trajectory when Mars is the requisite number of degrees ahead of the rendevous point, and boom--simple Hohmann transfer. With the set of orbit equations in hand, you can calculate a trajectory to just about any object in the Solar System. Of course, in real-life it would be complicated by orbital inclination, but anyways...
 

Similar threads

Undergrad Unexpected findings in need of an explanation (retrograde motion of Mars)
  • · Replies 83 ·
3
Replies
83
Views
5K
Undergrad New Developments In The Search For Planet X
  • · Replies 2 ·
Replies
2
Views
3K
High School How long it takes the Earth to fall halfway to the Sun--ellipse method
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Are Retrograde Satellites the Key to Stable and Optimal Orbits?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad I need some support, please, for a gravity assist analysis
  • · Replies 86 ·
3
Replies
86
Views
9K
Undergrad Is a superflare capable of changing a planets orbit?
  • · Replies 18 ·
Replies
18
Views
4K
Graduate Mars as Second Earth: Slowing Down Its Orbit
  • · Replies 29 ·
Replies
29
Views
5K
Graduate Heliocentric polar orbit crossing the Earth's orbit twice
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Travel from Mars to Earth question......
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Finding the Optimal Time to Launch a Mission to Mars
  • · Replies 1 ·
Replies
1
Views
3K