Δv to a moon

[lpetrich]

NASA - NSSDCA - Spacecraft - Details

The Mars 96 spacecraft was launched into Earth orbit, but failed to achieve insertion into Mars cruise trajectory and re-entered the Earth's atmosphere at about 00:45 to 01:30 UT on 17 November 1996 and crashed within a presumed 320 km by 80 km area which includes parts of the Pacific Ocean, Chile, and Bolivia. The cause of the crash is not known.

The Russian Mars 96 mission was designed to send an orbiter, two small autonomous stations, and two surface penetrators to Mars ...

The two Mars 96 Penetrators were mounted on the bottom of the orbiter near the propulsion system. The penetrators were long thin cylinders, pointed at the bottom, or forebody, and with a widened, funnel-shaped top. Instruments were contained inside throughout the length of the cylinder.

...
After orbit insertion, adjustment to 300 km periapsis, and 7 to 28 days of orbital maneuvers, the orbiter would be properly oriented and the first penetrator would be spun about its long axis and released. When the penetrator had moved away from the orbiter, its solid rocket motor was to ignite and put it into an atmospheric entry trajectory. Entry would occur 21 to 22 hours later. The penetrator was to enter the atmosphere at about 4.9 km/sec at an angle 10-14 degrees. The probe would first be slowed aerodynamically, followed by inflation of a braking device. The penetrator was to strike the surface at approximately 80 m/s. The forebody would separate on impact and can penetrate 5 to 6 meters into the ground, attached by wires to the aftbody, the top of the aftbody remaining above the surface.

Penetration speed: 80 m/s.

 

[lpetrich]

NASA - NSSDCA - Spacecraft - Details - "The Lunar-A mission has been cancelled due to cost considerations."

The spacecraft will deploy two 13 kg penetrators over the course of a month. They will be individually released and impact the Moon at 250 to 300 m/s, burrowing 1 to 3 meters into the surface.

...
The penetrators are missile-shaped cylinders, 75 cm in length and 14 cm in diameter, and are attached to the sides of the orbiter body between the solar arrays with their long axes oriented in the same direction as the cylinder axis. The penetrators have deorbit rocket engines which are fired after separation. During free fall descent side-jets are used to orient the penetrators. The deorbit motor and attitude controls are jettisoned before impact. Each penetrometer contains a two-component seismometer, a heat flow probe, a tiltmeter, an accelerometer, a radio transmitter and an antenna. The instruments are powered by Li-SOCL2 (super lithium) batteries with an expected lifetime of one year. The penetrators are designed to withstand an impact force of 10,000 G.

Penetration speed: 250 - 300 m/s

Miniaturization technology for Lunar penetrator mission - NASA/ADS

A mother spacecraft which holds three penetrators will be launched by newly developed M-V rocket. Three penetrators will be released from the mother spacecraft orbiting around the moon. These penetrators make hard landing on the moon with shock of about 10,000 G and will penetrate about 1-3 m in depth into the soil.

 

[Bomb#20]

NASA - NSSDCA - Spacecraft - Details

The Mars 96 spacecraft was launched into Earth orbit, but failed to achieve insertion into Mars cruise trajectory and re-entered the Earth's atmosphere at about 00:45 to 01:30 UT on 17 November 1996 and crashed within a presumed 320 km by 80 km area which includes parts of the Pacific Ocean, Chile, and Bolivia. The cause of the crash is not known.

F = GMm/r^2

 

[lpetrich]

I'll now consider the big moons of Jupiter, Saturn, Uranus, and Neptune, with the delta-V needed to match velocities for them, using two parabolic orbits, one with its minimum distance at each moon, and one with its minimum distance at the planet's center.
{sqrt(2)-1, sqrt(3)} * (orbital velocity) in km/s

• Jupiter: Io {7.21, 30.14}, Europa: {5.73, 23.98}, Ganymede: {4.51, 18.84}, Callisto: {3.4, 14.21}
• Saturn: Mimas: {5.95, 24.86}, Enceladus: {5.24, 21.92}, Tethys: {4.71, 19.68}, Dione: {4.16, 17.38}, Rhea: {3.52, 14.7}, Titan: {2.31, 9.65}, Hyperion: {2.1, 8.77}, Iapetus: {1.35, 5.66}
• Uranus: Miranda: {2.77, 11.57}, Ariel: {2.28, 9.54}, Umbriel: {1.93, 8.08}, Titania: {1.51, 6.31}, Oberon: {1.31, 5.46}}
• Neptune: Triton: {1.82, 7.6}

Escape velocities: Jupiter 59.5, Saturn 35.5, Uranus 21.3, Neptune 23.5 km/s

Approach speeds 1, 2, 5, 10, 20 km/s: what injection delta-V's in km/s:

• Jupiter: 0.008, 0.034, 0.210, 0.834, 3.271
• Saturn: 0.014, 0.056, 0.350, 1.382, 5.246
• Uranus: 0.023, 0.094, 0.579, 2.231, 7.918
• Neptune: 0.021, 0.085, 0.526, 2.039, 7.359

 

[Loren Pechtel]

British engineers report successful test of space penetrator - July 15, 2013

In the test, the penetrator was fired at a 10 tonne block of ice—it struck the block moving at approximately 340m/s, which is of course nearly the speed of sound. While the block of ice was reduced to a giant snow-cone, the electronic instruments inside the probe remained intact and in fact, continued to operate as planned, thanks to a spring mechanism engineers crafted to help soften the blow.

...
The researchers report the test penetrator experienced 24,000g as it came to a rest.

That would be suitable for most of the larger moons of the outer planets, because most of them have mostly water ice on their surfaces. Among Jupiter's four big moons, Io is an exception, with a rocky surface.

But the test penetration speed, 340 m/s, is much less than what one would need for an outer-planet moon.

And note that 340 m/s is subsonic within the materials involved. Impact dynamics get very nasty once you go supersonic.

(But there is the tactic from Robert L. Forward's Saturn Ruku--harpoon a moonlet for momentum transfer. I don't think the harpoon would hold, though.)

 

[lpetrich]

• Solids and Metals - Speed of Sound
• Liquids - Speed of Sound
• Water - Speed of Sound vs. Temperature
• Gases - Speed of Sound
• (PDF) Speed of sound in bubble-free ice

For fluids, liquids and gases, there is only one speed of sound, while for isotropic solids, those with the same properties in all directions, there are two:

• P - primary - pressure - push
• S - secondary - shear - shake

Of these, fluids have only the P one. For anisotropic solids, like single crystals, the sound speed by sound mode can vary by direction.

Gases have relatively low speed. Air is typical: 331 m/s at 0 C. To first approximation, they vary as the square root of the temperature, measured relative to absolute zero.

For liquid water, it varies with temperature: 0: 1403 - 20: 1481 - 40: 1526 - 60: 1552 - 80: 1555 - 100: 1543 -- C: m/s

For ice at 0 C, it is P 3839 S 1828 m/s, while at -20 C, it is P 3894 S 1855 m/s.

For stony materials, silica has P 5968 S 3764 m/s, granite P 5950 m/s, concrete P 3700 S 3200 m/s, brick P 4200 S 3600 m/s.

Since many surfaces are likely loose materials, I looked for measurements for sediments, and I found JMSE | Free Full-Text | Prediction Model of the Sound Speed of Seafloor Sediments on the Continental Shelf of the East China Sea Based on Empirical Equations has 1500 - 1600 m/s.


For likely penetrator metals, steel (1% C) P 5940 S 3220 m/s, titanium P 6070 S 3125 m/s.

 

[lpetrich]

Of more relevance is yield strength - what pressure will cause materials to fail.

•  Yield (engineering)
• Young's Modulus, Tensile Strength and Yield Strength Values for some Materials
• Yield Strength - Strength ( Mechanics ) of Materials

I've searched for numbers on the yield and ultimate strengths of ice, and I've found:

• Ice - Safe Loads vs. Thickness
• (PDF) Review Mechanical properties of ice and snow
• ERDC Knowledge Core: Ultimate strength of ice

So ice has an ultimate strength of around a few megapascals. Not very strong.

Steel varies between 500 and 2,700 MPa -- the champion is  Maraging steel and 2800 Maraging Steel

Titanium, its main competition, has alloys that get up to 1000 MPa.

 

[steve_bank]

You also have to worry about thermal expansion.

Sr-71 Blackbird

Flying more than three times the speed of sound generates 316° C (600° F) temperatures on external aircraft surfaces, which are enough to melt conventional aluminum airframes. That's why the SR-71's external skin is made of titanium alloy, to shield the internal aluminum airframe.

The plane leaked fuel until the skin heated up and expanded, by design. Mach 3 at high altitude and low air density.

There may also be a stability problem with aerobaking, tumbling.

The X-1 was, in principle, a "bullet with wings", its shape closely resembling a Browning . 50-caliber (12.7 mm) machine gun bullet, known to be stable in supersonic flight

 

[lpetrich]

British engineers report successful test of space penetrator
notes
British space penetrator passes icy test - BBC News - 12 July 2013
with a lot more detail.

The steel penetrator was fired at a 10-tonne cube of ice to simulate the surface of Jupiter's moon Europa.

It hit the block at a speed of 340m/s and decelerated rapidly, but its structure remained intact, as did its interior components.

...
The full-size, 20kg projectile slammed into the ice block at just under the speed of sound, producing a huge plume of snow.

... The probe experienced a peak deceleration of 24,000g

...
"Penetrators offer a number of advantages over 'soft landers', which have to slow down to reach the surface safely," explained Esa project manager Sanjay Vijendran.

"They would enable you to get deep into the sub-surface essentially for free, up to three metres without having to drill. And being light means you can deploy a few at once from a single spacecraft orbiter."

Another article about this penetrator test:
Research with impact | UCL Mathematical & Physical Sciences - UCL – University College London

Nothing about the size of this penetrator. I'm guessing a cross section of 10 to 100 cm^2.

The force on it was 20 kg * 25,000 * 10 m/s^2 = 20 kg * 250,000 m/s^2 = 5*10^6 newtons. The cross section is 0.001 - 0.01 m^2. The pressure is thus 5*10^8 to 5*10^9 pascal - 0.5 - 5 gigapascal.

However, the probe survived its impact almost intact.

 

[bilby]

And being light means you can deploy a few at once from a single spacecraft orbiter.

So they envisage these being deployed after deceleration to orbital velocity on arrival at Europa; They are shedding re-entry velocity from orbit, rather than the much higher (relative to Europa) interplanetary transfer velocity.

 

[Swammerdami]

The Mars 96 spacecraft was launched into Earth orbit, but failed to achieve insertion ... and crashed within a presumed 320 km by 80 km area which includes parts of the Pacific Ocean, Chile, and Bolivia. The cause of the crash is not known.

F = GMm/r^2

Isn't the Pauli Exclusion Principle the real culprit here? Without it wouldn't the spacecraft have cuddled into the earth gently rather than "crashing"?

 

[bilby]

The Mars 96 spacecraft was launched into Earth orbit, but failed to achieve insertion ... and crashed within a presumed 320 km by 80 km area which includes parts of the Pacific Ocean, Chile, and Bolivia. The cause of the crash is not known.

F = GMm/r^2

Isn't the Pauli Exclusion Principle the real culprit here? Without it wouldn't the spacecraft have cuddled into the earth gently rather than "crashing"?

Or just passed through unnoticed, like a cloud of neutrinos.

 

[lpetrich]

And being light means you can deploy a few at once from a single spacecraft orbiter.

So they envisage these being deployed after deceleration to orbital velocity on arrival at Europa; They are shedding re-entry velocity from orbit, rather than the much higher (relative to Europa) interplanetary transfer velocity.

I was thinking of deploying penetrators from a low-periapsis orbit around Jupiter, because that would mean a low delta-V for getting into orbit around that planet. But these space probes would crash onto Europa's surface at around 15 - 20 km/s.

One can get a low Europa-relative velocity by getting into a very close orbit, but that would require a lot of delta-V. For interplanetary velocity 0, 5, 10, 20 km/s, that gives delta-V 5.7, 6.3, 8.1, 14.1 km/s. Getting into a low Europa orbit from an interplanetary one will require a delta-V of 4.6, 5.2, 6.9, 12.9 km/s, though it would likely be safer to go into a nearby orbit then go into orbit around the moon.

By comparison, going into a low orbit from a Hohmann transfer orbit requires for Venus 3.38 km/s, for Mars 2.09 km/s and for the Moon 0.84 km/s.

 

[lpetrich]

Ignoring the rotation of the target body, the minimum impact speed of a penetrator is the orbital velocity of a "surface satellite". In km/s:

Mercury 3.01, Venus* 7.33, Earth* 7.91, Moon 1.68, Mars* 3.56, (Jupiter) Io 1.81, Europa 1.43, Ganymede 1.94, Callisto 1.73, (Saturn) Mimas 0.05, Enceladus 0.17, Tethys 0.28, Dione 0.36, Rhea 0.45, Titan* 1.87, Hyperion 0.05, Iapetus 0.41, (Uranus) Miranda 0.14, Ariel 0.38, Umbriel 0.38, Titania 0.54, Oberon 0.52, (Neptune) Triton 1.03

* = atmosphere thick enough for aerobraking

Equatorial rotation speeds in m/s
Mercury 3, Venus 2, Earth 465, Moon 5, Mars 240, (Jupiter) Io 75, Europa 32, Ganymede 27, Callisto 11, (Saturn) Mimas 15, Enceladus 20, Tethys 15, Dione 15, Rhea 12, Titan 12, Hyperion 1, Iapetus 1, (Uranus) Miranda 12, Ariel 17, Umbriel 10, Titania 7, Oberon 4, (Neptune) Triton 17

Note: Venus's rotation is retrograde, and all of the moons listed here rotate synchronously, except for Hyperion, with its chaotic tumbling with a period of around 13 days, compared to its orbital period of 21.276 days.

(Rotation speed) << (surface-satellite speed) in every case.