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Europa orbits Jupiter at an average speed of 13.7 km/s. At the same time Jupiter orbits the Sun at a speed of 13.1 km/s. This means that Europa has an orbital speed relative to the Sun of 26.8 km/s when it is in the shadow behind Jupiter once every 85 hours.

Earth's orbital speed is 29.8 km/s which is only 3.0 km/s different from Europa's max solar orbital speed. Compared with Mars which has an orbital speed of 24.0 km/s which is 5.8 km/s different form Earth's.

  • Does this mean that it is easier to land a spacecraft on Europa, than it is to land on Mars?
  • Io with 17.3 km/s around Jupiter gives it a max of 13.1 + 17.3 = 30.4 km/s around the Sun when in shadow once every 43 hours. Just a 0.6 km/s difference, our own Luna orbits us at 1.0 km/s. Does any sizable object have a more similar speed to Earth than Io does?

And considering that Europa has no atmosphere and just about 1/3 of Mars' surface gravity, it looks like an easy target to go to! According to a table on this page (which refers to a calculator by Erik Max Francis) a Hohmann transfer from Earth to Jupiter takes 2 years and 9 months. That's pretty quick compared to many of the current missions which travel even 10 years.

Shouldn't also radiation problems be smaller for a lander than for an orbiter (either of Europa itself or an orbiter around Jupiter which makes repeated close Europa fly bys) because the moon covers half of the radiating source. And even more in a deep crack. And sensitive electronics might perhaps be drilled/melted down a few meters into the ice to get complete shielding.

Is there a monster factor in the Jupiter system which makes it much harder to land on Europa (or Io) than I've made it look here? Harder than to land on Mars.

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Francis' Python BOTEC looks at Hohmann orbits. To simplify he assumes circular coplanar orbits.

Here is a pic comparing an earth-to-Mars Hohmann vs an earth-to-Jupiter Hohmann:

enter image description here

At perihelion the Mars transfer orbit is moving 33 km/s vs earth's 30 km/s. Departure Vinf is 3 km/s. At aphelion the transfer is 21.5 km/s vs Mars 24 km/s. Arrival Vinf is 2.5 km/s

At perihelion the Jupiter transfer orbit is 39 km/s. Departure Vinf is 9 km/s. At aphelion the transfer is 7.5 km/s vs Jupiter's 13 km/s. Arrival Vinf is 5.5 km/s. You wouldn't want to rendezvous with the moon when it's on the far side of the moon when it's moving fastest wrt sun. Rather on the near side of Jupiter when the moon's moving slowest wrt to the sun.

To depart for Trans Mars insertion you would need to inject into a hyperbolic orbit wrt earth. Speed of a hyperbolic orbit is sqrt(vinf^2 + Vesc^2). To remember speed of a hyperbolic orbit I use this device:

enter image description here

At LEO, Vesc is about 11 km/s. Vinf is for Mars insertion is 3 km/s. Sqrt(11^2 + 3^2) = 11.4 km/s. LEO velocity is about 7.8 km/s. So from LEO you'd need 3.6 km/s for Trans Mars Insertion (TMI).

From LEO Trans Jupiter Insertion (TJI) is about 6.3 km/s. The departure delta V is much higher for a Jupiter trip than a Mars trip.

Francis' table shows delta Vs from a low circular orbit about 1 planet to a low circular orbit about another planet. It takes a lot less delta V to park in a capture orbit. I talk about this at Inflated Delta Vs.

We can make Mars' atmosphere work for us. It suffices to park in a Mars capture orbit with periapsis passing through Mars upper atmosphere. At each periapsis atmospheric friction will slow the orbit, thus saving reaction mass. .7 km/s is needed to park in a Mars capture orbit.

Exiting an earth-to-Jupiter orbit and parking in a 599408 km altitude orbit (Europa) takes 6.5 km/s. Parking in Io altitude orbit takes about 7.8 km/s. That doesn't take into account descending the moons' gravity wells.

In summary, takes a lot less delta V to get to Mars than Jupiter's moons

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  • $\begingroup$ "From LEO Trans Jupiter Insertion (TJI) is about 6.3 km/s." Isn't that much mitigated once per orbit by Europa's orbital speed of 13.7 km/h? A lander wouldn't need to get into Jupiter orbit, but just tangent Europa when their velocity difference is the smallest. Shouldn't the faster Io be easier to reach? And the high eccentricity of Europa should give even better landing opportunities when its speed is even higher than the average. Isn't the problem with reaching planets far away that their relative orbital speed is much different from Earth's? The speed of their moons should help alot. $\endgroup$ – LocalFluff May 29 '14 at 18:18
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    $\begingroup$ They do help a lot. Jupiter arrival Vinf is ~5.5 km/s. At Europa's altitude Jupiter escape velocity is about 19.5 km/s. Sqrt(5.5^2 + 19.5^2) is about 20 km/s. BUt Europa's velocity is about 14 km/s, so you get to subtract that 14 from 20 for a 6 km/s delta V. $\endgroup$ – HopDavid May 29 '14 at 18:37
  • $\begingroup$ You go deeper in Jupiter's gravity well and orbits are faster. But escape velocity is also higher and that makes the hyperbolic speed higher. It takes more delta V to park in lower orbits than the higher ones. $\endgroup$ – HopDavid May 29 '14 at 18:39
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    $\begingroup$ Don't compare velocities of departure and destination orbits. I'll give an example: LEO is 7.7, GEO is 3.1. Difference between them is 4.6. But Hohmann delta V to move between the orbits is 3.8 km/s. An orbit at 800,000 km altitude moves .7 km/s. Difference between that orbit and LEO is 7 km/s. But Hohmann delta V from LEO to a 800,000 km altitude orbit is less, about 3.7 km/s. $\endgroup$ – HopDavid May 29 '14 at 19:00
  • $\begingroup$ @LocalFluff You need that 6.3 km/sec to get to Jupiter in the first place no matter what you intend to do there. Assuming aerobraking that 6.3 km/sec is sufficient to get you to the surface of Mars. $\endgroup$ – Loren Pechtel May 30 '14 at 17:51

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