Calculating a Hohmann transfer orbit
1. Gather supplies. Pencil, paper, calculator.
2. Get the distance of the two planets from the sun.
3. Write down your constants. Constants are unchanging values. In our problem the constants are the planets distance from the sun and the standard gravitational parameter, this is the gravitational constant times the mass of the Sun
You should have
R1 - distance from the sun origin planet.
R2 - distance from the sun destination planet
GM - 6.674 x 10^¹¹ km³/s² is earth standard so I believe divide this by 10 for SFS?( This needs to be confirmed for SFS)
4. Convert the planets orbital period to seconds. Do this by multiplying the number of days by 86,400.
The orbital period of R1 will be denoted by P1, R2 by P2.
5. Compute the semi-major axis of the transfer orbit. Planetary orbits are ellipse's. The semi-major axis of an ellipse is the distance from it's center to it's furthest side. In this Hohmann transfer the ellipse is the path the spacecraft will take from origin planet to destination planet, this will be denoted by the variable a(transfer) such that
a(transfer) = (R1 + R2)/2
6. Find the period of the transfer orbit. This is found using Kepler's 3rd law. For the period of the transfer orbit the variable a will be a(transfer) so that
BP(transfer) = √(4π² × a³/GM)
7. Find the orbital velocity of R1. Origin planets orbit so we know how much we have to alter the spacecrafts velocity to enter into the elliptical orbit to get it to the destination planet. The velocity of origin planets orbit will be denoted by V1.
V1 = (2π × R1)/P1
8. Find The orbital velocity of R2
9. Find the velocity of the elliptical orbit at perihelion because, if you remember, due to the Oberth effect, the faster a crafts initial velocity the larger the increase in ∆v
V(perihelion) = (2π × a(transfer)/p(transfer) × √((2a(transfer) × R1) -1)
10. Find ∆v1
∆v1 is how much velocity a craft needs to switch orbits. It's the difference between v(perihelion) and v1
∆v1 = v(perihelion) -v1
This is crucial in determining how much fuel your rocket will need.
11. Find the velocity of the transfer orbit at aphelion. This is the ∆v needed to equal the difference in the elliptical at aphelion velocity and the target planets orbital velocity.
V(aphelion) = (2π ×a(transfer)/p(transfer) × √((2a(transfer) - r2) -1)
12. Find ∆v2 This is the ∆v necessary to change from the elliptical orbit to the target planets orbit.
∆v2 = v2 - v(aphelion)
13. Calculate time of flight. Time it takes to get from origin planet to target planet. The value will seem large because it's in seconds.
TOF= ½p(transfer)
14. Convert TOF to days
TOF(days) = TOF(seconds)/86,400
15. Find Ş ;window
You will do this by finding angular alignment. First find the targets angular velocity. Angular velocity will be denoted as w.8⁶
w = ∆∅ / ∆t
∅ being the number of degrees travelled and t the amount of time taken.
Angular velocity is analogous to linear velocity.
v = r • w
w = v/r
v being orbital velocity and r being radius
Here's a couple of calculators to make it even easier!
InstaCalc Online Calculator
https://www.omnicalculator.com/physics/hohmann-transfer
Credit -Instructables &
Bobblair123
1. Gather supplies. Pencil, paper, calculator.
2. Get the distance of the two planets from the sun.
3. Write down your constants. Constants are unchanging values. In our problem the constants are the planets distance from the sun and the standard gravitational parameter, this is the gravitational constant times the mass of the Sun
You should have
R1 - distance from the sun origin planet.
R2 - distance from the sun destination planet
GM - 6.674 x 10^¹¹ km³/s² is earth standard so I believe divide this by 10 for SFS?( This needs to be confirmed for SFS)
4. Convert the planets orbital period to seconds. Do this by multiplying the number of days by 86,400.
The orbital period of R1 will be denoted by P1, R2 by P2.
5. Compute the semi-major axis of the transfer orbit. Planetary orbits are ellipse's. The semi-major axis of an ellipse is the distance from it's center to it's furthest side. In this Hohmann transfer the ellipse is the path the spacecraft will take from origin planet to destination planet, this will be denoted by the variable a(transfer) such that
a(transfer) = (R1 + R2)/2
6. Find the period of the transfer orbit. This is found using Kepler's 3rd law. For the period of the transfer orbit the variable a will be a(transfer) so that
BP(transfer) = √(4π² × a³/GM)
7. Find the orbital velocity of R1. Origin planets orbit so we know how much we have to alter the spacecrafts velocity to enter into the elliptical orbit to get it to the destination planet. The velocity of origin planets orbit will be denoted by V1.
V1 = (2π × R1)/P1
8. Find The orbital velocity of R2
9. Find the velocity of the elliptical orbit at perihelion because, if you remember, due to the Oberth effect, the faster a crafts initial velocity the larger the increase in ∆v
V(perihelion) = (2π × a(transfer)/p(transfer) × √((2a(transfer) × R1) -1)
10. Find ∆v1
∆v1 is how much velocity a craft needs to switch orbits. It's the difference between v(perihelion) and v1
∆v1 = v(perihelion) -v1
This is crucial in determining how much fuel your rocket will need.
11. Find the velocity of the transfer orbit at aphelion. This is the ∆v needed to equal the difference in the elliptical at aphelion velocity and the target planets orbital velocity.
V(aphelion) = (2π ×a(transfer)/p(transfer) × √((2a(transfer) - r2) -1)
12. Find ∆v2 This is the ∆v necessary to change from the elliptical orbit to the target planets orbit.
∆v2 = v2 - v(aphelion)
13. Calculate time of flight. Time it takes to get from origin planet to target planet. The value will seem large because it's in seconds.
TOF= ½p(transfer)
14. Convert TOF to days
TOF(days) = TOF(seconds)/86,400
15. Find Ş ;window
You will do this by finding angular alignment. First find the targets angular velocity. Angular velocity will be denoted as w.8⁶
w = ∆∅ / ∆t
∅ being the number of degrees travelled and t the amount of time taken.
Angular velocity is analogous to linear velocity.
v = r • w
w = v/r
v being orbital velocity and r being radius
Here's a couple of calculators to make it even easier!
InstaCalc Online Calculator
https://www.omnicalculator.com/physics/hohmann-transfer
Credit -Instructables &
Bobblair123
