Orbits Question (Astronomy)

  • Thread starter olyviab
  • Start date
  • #1
olyviab
11
0
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?
 
Last edited:

Answers and Replies

  • #2
gneill
Mentor
20,945
2,886
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
olyviab
11
0
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 wont reach the mars orbit. How am i able to calculate the semi-major axis?
 
  • #4
gneill
Mentor
20,945
2,886
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 wont 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
olyviab
11
0
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 :)
 

Suggested for: Orbits Question (Astronomy)

Replies
1
Views
551
  • Last Post
Replies
2
Views
299
  • Last Post
Replies
4
Views
560
Replies
3
Views
243
Replies
2
Views
746
Replies
5
Views
451
Replies
1
Views
327
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
10
Views
349
Top