Hohmann Transfer, energy for both boosts

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In summary: So, how much energy is required to change its speed from v1 to that velocity? The same thing is required at r2 - how much energy is required to change the speed from that on the transfer ellipse to v2?In summary, for a circular orbit, the speed depends on the radius according to Equation 8.3, while for elliptical orbits, the speed varies according to the equation v2= 2GM[(1/r)-(1/2a)]. A satellite can be transferred from one circular orbit to a higher orbit using a Hohmann transfer, which involves boosting the speed at two different points. To calculate the energy required for each boost, one must first find the circular orbit velocity for the starting and
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jcook735
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Homework Statement


For a circular orbit around a massive gravitating body, the speed depends on the radius according to Equation 8.3; for elliptical orbits, the speed varies according to the equation v2= 2GM[(1/r)-(1/2a)], where r is the distance from the massive body and a is the semimajor axis of the ellipse. A satellite can be transferred from one circular orbit at radius r1 to a higher orbit at radius r2 by boosting the circular speed v1 at r1 to the appropriate speed for an elliptical orbit whose distance varies between r1 and r2, and then boosting the speed in the elliptical orbit at r2 to the circular speed v2. this is called a Hohmann transfer. (a) How much energy is required for the first boost in such a transfer to take a 250-kg satellite from a circular orbit at a 400-km altitude to the altitude of a geosynchronous orbit? (b) how much energy is required for the second boost?


Homework Equations


Conservation of energy and the v2 equation given in the problem


The Attempt at a Solution




Well, I used conservation of energy E1 + E = E2 and found the E required to move the satellite between the two orbits. However, this question is asking for the energy required for each boost, and I have no idea how to separate these. Any help would be greatly appreciated!
 
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Presumably you can find the circular orbit velocity for r1 and r2. In order to get the satellite in circular orbit at r1 onto the Hohmann transfer ellipse, what velocity must it have at r1?
 

Related to Hohmann Transfer, energy for both boosts

1. What is a Hohmann Transfer?

A Hohmann Transfer is a type of orbital maneuver used to transfer a spacecraft from one circular orbit around a central body to another circular orbit at a different altitude. It is the most efficient way to transfer between two circular orbits and is often used in space missions.

2. How does a Hohmann Transfer work?

A Hohmann Transfer involves a series of two engine burns. The first burn, known as the "boost" burn, is done at the initial orbit to increase the spacecraft's velocity and transfer it to an elliptical orbit. The second burn, known as the "capture" burn, is done at the new orbit to slow the spacecraft down and bring it into a circular orbit at the desired altitude.

3. What is the energy requirement for a Hohmann Transfer?

The energy required for a Hohmann Transfer is dependent on the difference in altitude between the two orbits. The higher the altitude difference, the more energy is required. However, a Hohmann Transfer is still the most energy-efficient method of transferring between two orbits compared to other types of orbital maneuvers.

4. Can a Hohmann Transfer be used for interplanetary travel?

Yes, a Hohmann Transfer can be used for interplanetary travel. It is commonly used by spacecraft to travel between planets in our solar system. However, the timing and accuracy of the maneuver must be precise, as the planets are constantly moving in their orbits.

5. What are the advantages of using a Hohmann Transfer?

One of the main advantages of using a Hohmann Transfer is its efficiency. It requires the least amount of energy compared to other types of orbital maneuvers. It also allows for a relatively simple and predictable trajectory, making it easier to plan and execute missions. Additionally, the spacecraft can conserve fuel by taking advantage of the gravitational pull of the central body during the transfer process.

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