Optimizing Orbital Trajectories for Efficient Mars Encounter

In summary, the space probe initially intended to put in a 1 AU circular orbit around the sun, but the change in velocity was mistakenly made in a radial direction. This would not have been enough to reach Mars, and the space probe would have to use a different method to get there.
  • #1
olyviab
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A space probe initially moving in a 1 AU circular orbit around the sun (i.e. moving with the earth). The aim is to put this space probe in an orbit that will encounter Mars, using the least possible expenditure of rocket fuel (energy). This orbit, it turns out, is one in which perihelion (closest approach to the sun) is at the Earth's orbit (r=1AU), and aphelion (furthest approach from the sun) is at Mars' orbit.Suppose that the rockets had fired so that the change in velocity was in the radial direction (outwards). Calculate a (semi major axis) Will this orbit ever reach Mars?
 
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  • #2
olyviab said:
A space probe initially moving in a 1 AU circular orbit around the sun (i.e. moving with the earth). The aim is to put this space probe in an orbit that will encounter Mars, using the least possible expenditure of rocket fuel (energy). This orbit, it turns out, is one in which perihelion (closest approach to the sun) is at the Earth's orbit (r=1AU), and aphelion (furthest approach from the sun) is at Mars' orbit.


Suppose that the rockets had fired so that the change in velocity was in the radial direction (outwards). Calculate a (semi major axis) Will this orbit ever reach Mars?

Do you mean that the original velocity change intended for the Hohmann orbit injection was mistakenly made in a radial direction? If so, then no, the orbit would not reach Mars. The Hohmann transfer is the least energy direct transfer orbit. If it's not the Hohmann orbit, then it can't reach Mars with the same energy expenditure.
 
  • #3
gneill said:
Do you mean that the original velocity change intended for the Hohmann orbit injection was mistakenly made in a radial direction? If so, then no, the orbit would not reach Mars. The Hohmann transfer is the least energy direct transfer orbit. If it's not the Hohmann orbit, then it can't reach Mars with the same energy expenditure.

Yeah i assume it was the least energy in the Hohmann orbit directed outwards. I understand if its the 3 km/s (i calculated that number as being the least v) being directed outward that it won't reach the Mars orbit. How am i able to calculate the semi-major axis?
 
  • #4
olyviab said:
Yeah i assume it was the least energy in the Hohmann orbit directed outwards. I understand if its the 3 km/s (i calculated that number as being the least v) being directed outward that it won't reach the Mars orbit. How am i able to calculate the semi-major axis?

If you have the new velocity (after the ∆V) and the radius, then you can calculate the total mechanical energy, ξ. Then 2a = -µ/ξ.
 
  • #5
gneill said:
If you have the new velocity (after the ∆V) and the radius, then you can calculate the total mechanical energy, ξ. Then 2a = -µ/ξ.

Great! Thanks for all the help :)
 

Related to Optimizing Orbital Trajectories for Efficient Mars Encounter

1. What is an orbit?

An orbit is the path that an object takes around another object due to the force of gravity. In astronomy, this typically refers to a smaller object, like a planet or satellite, orbiting around a larger object, like a star.

2. What factors determine the shape of an orbit?

The shape of an orbit is primarily determined by the speed and direction of the object's motion and the gravitational pull of the larger object it is orbiting. The shape can also be affected by other factors, such as the presence of other objects in the system.

3. What is the difference between a circular and an elliptical orbit?

A circular orbit is a perfectly round shape, while an elliptical orbit is more oval-shaped. In a circular orbit, the distance between the two objects remains constant, whereas in an elliptical orbit, the distance varies at different points in the orbit.

4. How do orbits affect the motion of objects in space?

Orbits play a crucial role in the stability and movement of objects in space. Without orbits, objects would either crash into each other or fly off into space. Orbits also allow for the predictability of objects' movements, which is essential for space travel and satellite communication.

5. Can an object have more than one orbit?

Yes, it is possible for an object to have multiple orbits, depending on its speed and direction of motion. For example, the Earth has multiple orbits, including its orbit around the Sun and its orbit around the center of the Milky Way galaxy. Objects can also have multiple orbits around a single object, such as a moon orbiting a planet while the planet is also orbiting a star.

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