1:45 PM - 3:15 PM
[O07-P11] A Consideration of a Landing Exploration on Europa
Keywords:Europa, Landing Exploration, Lives, Probe, Space Exploration, Reverse Thrust
Europa, a Jovian moon, is said to have a huge ocean under its ice-surface, drawing attention as a major target of astrobiological research. Although NASA plans to send a probe and to do many flybys of Europa in 2020s, no landing project exists. So, I concentrated my research on a landing exploration.
Because a landing exploration on Europa can give us crucial information about the essence of lives, I regard this research extraordinarily significant.
Europa’s atmosphere is rarefied. Therefore, I thought that parachutes would not be effectual. Hence, the purpose of this research is to consider the way to land softly with reverse thrust for an astrobiological exploration. The hypotheses I made are as follows:
[the Hypotheses]
The lander will be loaded onto a mother machine and undock at a height of 20km above Europa. The landing engine: hydrazine thruster (specific impulse: approx. 220 to 235s) The undocked lander whose initial velocity is 0m/s starts free fall, starts reverse thrust at an altitude, and comes to halt on the surface. The lander moves only vertically. The thrust, the effective exhaust velocity, and the propellant mass flow rate are constant.
In launching, they accelerate an object from 0 to a velocity, while, in reverse thrust, they decelerate an object from 0 to a velocity. In other words, you can think of soft landing as playing launching backwards. Grounded on this similarity, I thought if I could apply the derivation of the Tsiolkovsky rocket equation related to launching of rockets.
ΔV=c ln(1/μ)
Provided that, ΔV: velocity change due to jetting, c: effective exhaust velocity, μ: mass ratio. In addition, based on relational expressions I created, I input a concrete condition,
Let
g as the gravitational acceleration of the target of landing
m_Max as the maximum mass of the lander
μ as the mass ratio of the lander
c as the effective exhaust velocity of the thruster
F as the thrust of the thruster
Then,
the Total Fall Altitude: x_total=c^2/F*m_Max(μ ln(1/μ)-(1-μ))+c^2/2g*(ln(1/μ))^2
the Altitude to Start Reverse Thrust: x_jet=c^2/F*m_Max (ln(1/μ)-(1-μ)-m_Max/2F*g(1-μ)^2 )
the Altitude of Free Fall: x_free=1/2g*(c ln(1/μ)-(c m_Max (1-μ))/F* g)^2
the Total Fall Time: t_total=c/g*ln(1/μ)
the Time of Reverse Thrust: t_jet=(c m_Max (1-μ))/F
the Time of Free Fall: t_free=c/g ln(1/μ)-(c m_Max (1-μ))/F
the Velocity to Start Reverse Thrust: v_Max=c ln(1/μ)-(c m_Max (1-μ))/F*g
Here, I made a Python program which outputs an approximate value of the thrust by using the bisection method with any accuracy, calculates each altitudes and times of reverse thrust, free fall and total, and draws graphs. If I run the program by taking 9.8m/s2 for the gravitational acceleration of the Earth, 1.3m/s2 for the gravitational acceleration of Europa, 500kg for the maximum mass, 220s for the specific impulse, 0.8 for the mass ratio, and 20km for the altitude to start falling, it outputs these approximate values:
F = 723.46875 ± 0.03125 [N] x_total = 19.9992723959987 ± 0.002981374671238882 [km] x_jet = 16.623466418409254 ± 0.0017754098712466657 [km] x_free = 3.3758059775894473 ± 0.0012059647999922163 [km] t_total = 370.0749974103356 [s] t_jet = 298.0087258810587 ± 0.012872391079497447 [s] t_free = 72.06627152927692 ± 0.012872391079469025 [s] v_Max = 93.68615298805997 ± 0.016734108403312575 [m/s]
and following graphs.
As a result, I could set when and where to start falling, start reverse thrust and reach the surface by deciding the performance of the lander.
Because a landing exploration on Europa can give us crucial information about the essence of lives, I regard this research extraordinarily significant.
Europa’s atmosphere is rarefied. Therefore, I thought that parachutes would not be effectual. Hence, the purpose of this research is to consider the way to land softly with reverse thrust for an astrobiological exploration. The hypotheses I made are as follows:
[the Hypotheses]
The lander will be loaded onto a mother machine and undock at a height of 20km above Europa. The landing engine: hydrazine thruster (specific impulse: approx. 220 to 235s) The undocked lander whose initial velocity is 0m/s starts free fall, starts reverse thrust at an altitude, and comes to halt on the surface. The lander moves only vertically. The thrust, the effective exhaust velocity, and the propellant mass flow rate are constant.
In launching, they accelerate an object from 0 to a velocity, while, in reverse thrust, they decelerate an object from 0 to a velocity. In other words, you can think of soft landing as playing launching backwards. Grounded on this similarity, I thought if I could apply the derivation of the Tsiolkovsky rocket equation related to launching of rockets.
ΔV=c ln(1/μ)
Provided that, ΔV: velocity change due to jetting, c: effective exhaust velocity, μ: mass ratio. In addition, based on relational expressions I created, I input a concrete condition,
Let
g as the gravitational acceleration of the target of landing
m_Max as the maximum mass of the lander
μ as the mass ratio of the lander
c as the effective exhaust velocity of the thruster
F as the thrust of the thruster
Then,
the Total Fall Altitude: x_total=c^2/F*m_Max(μ ln(1/μ)-(1-μ))+c^2/2g*(ln(1/μ))^2
the Altitude to Start Reverse Thrust: x_jet=c^2/F*m_Max (ln(1/μ)-(1-μ)-m_Max/2F*g(1-μ)^2 )
the Altitude of Free Fall: x_free=1/2g*(c ln(1/μ)-(c m_Max (1-μ))/F* g)^2
the Total Fall Time: t_total=c/g*ln(1/μ)
the Time of Reverse Thrust: t_jet=(c m_Max (1-μ))/F
the Time of Free Fall: t_free=c/g ln(1/μ)-(c m_Max (1-μ))/F
the Velocity to Start Reverse Thrust: v_Max=c ln(1/μ)-(c m_Max (1-μ))/F*g
Here, I made a Python program which outputs an approximate value of the thrust by using the bisection method with any accuracy, calculates each altitudes and times of reverse thrust, free fall and total, and draws graphs. If I run the program by taking 9.8m/s2 for the gravitational acceleration of the Earth, 1.3m/s2 for the gravitational acceleration of Europa, 500kg for the maximum mass, 220s for the specific impulse, 0.8 for the mass ratio, and 20km for the altitude to start falling, it outputs these approximate values:
F = 723.46875 ± 0.03125 [N] x_total = 19.9992723959987 ± 0.002981374671238882 [km] x_jet = 16.623466418409254 ± 0.0017754098712466657 [km] x_free = 3.3758059775894473 ± 0.0012059647999922163 [km] t_total = 370.0749974103356 [s] t_jet = 298.0087258810587 ± 0.012872391079497447 [s] t_free = 72.06627152927692 ± 0.012872391079469025 [s] v_Max = 93.68615298805997 ± 0.016734108403312575 [m/s]
and following graphs.
As a result, I could set when and where to start falling, start reverse thrust and reach the surface by deciding the performance of the lander.