Calculating Velocity Change for Hohmann Transfer Orbit

  • Thread starter godhilu
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In summary, the conversation is about finding the velocity change required to produce an elliptical orbit at specific altitudes from a circular low Earth orbit. The relevant formulas for calculating the perigee and apogee distances, as well as the velocity in circular and elliptical orbits, are provided. The person asking for help is looking for confirmation on whether their attempted solution is correct. However, the response reminds them that this is not a homework service and they will need to figure it out themselves.
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godhilu
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Homework Statement



Consider an initial circular low Earth orbit act at a 300 km altitude, find the velocity change required to produce an elliptical orbit with a 300 km altitude at perigee and 3000 km altitude at apogee. Given gravitational parameter for Earth μ=398600 kg3/s2, radius of Earth R=6378 km.

The Attempt at a Solution



The perigee and apogee distance from center of Earth is
rp= 6378+300=6678 km
ra= 6378+3000=9678 km

velocity in circular orbit =√(μ/rp)

angular momentum (H) of elliptical orbit is=√{(2μ*rp*ra/(ra+rp)}

velocity at perigee = H/rp

change in velocity (Δv)= [H/rp]- [√(μ/rp)]
 
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  • #2
And ... ?
 
  • #3
I want to know the correct solution to the problem.
 
  • #4
Well, you'll have to figure that out for yourself. As has been stated many times before, PF is not a homework service. If you provide an attempt at a solution, members will provide you with hints and feedback.
 
  • #5
Oh sorry, may I know the relevant formulas used by me in the attempt are correct or not?? As I am not getting the correct ans by substituting values to those variables.
 

1. What is a Hohmann transfer?

A Hohmann transfer is a type of orbital maneuver used to transfer a spacecraft from one circular orbit to another by using two engine burns. It is the most fuel-efficient way to transfer between two orbits that share the same orbital plane.

2. How is the Hohmann transfer calculated?

The Hohmann transfer is calculated using the vis-viva equation, which relates the orbital semi-major axis, eccentricity, and gravitational parameter of two bodies. It also takes into account the time of flight between the two orbits and the optimal timing for the engine burns.

3. What are the advantages of using a Hohmann transfer?

The main advantage of using a Hohmann transfer is its efficiency in terms of fuel usage. It requires the least amount of propellant compared to other orbital transfer methods. It also allows for a relatively simple and predictable trajectory.

4. What are the limitations of a Hohmann transfer?

One limitation of a Hohmann transfer is that it can only be used to transfer between two circular orbits in the same orbital plane. It also requires precise timing and accurate calculations, which can be difficult for longer distance transfers or when dealing with complex gravitational forces.

5. How is a Hohmann transfer used in space missions?

Hohmann transfers are commonly used in space missions, especially for transferring between planets in our solar system. For example, NASA's Mars missions have utilized Hohmann transfers to reach the red planet. It is also used for satellite deployments and other orbital maneuvers in space.

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