# The Naked Scientists Forum

### Author Topic: Gravity assists for Mars mission?  (Read 5860 times)

#### Rgclark

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##### Gravity assists for Mars mission?
« on: 10/04/2012 10:59:44 »
This is a question involving the orbital mechanics of spaceflight. There are a few different components to the question. First, if our Mars rocket departed from the Moon or a Lagrange point propellant depot fully fueled towards Earth at, say, 11 km/s or more, so it's moving at speeds beyond Earth's escape velocity, then in just passing by the Earth it should pick up additional speed equal to Earth's escape velocity about 11 km/s. So at least temporarily it should have a speed of 22 km/s. But the problem is that it still will be slowed down by the Earth as it proceeds to Mars, so it will lose some of this speed. How much speed will it lose?

What I want to do is leave Earth's vicinity at such high speed so that you don't have the long travel times of the Hohmann orbit, and in fact so that the trajectory approximates a straight-line path and if you do it at closest approach of Mars then the travel time could be say 60,000,000 km/22 km/s = 2,700,000 s, about 31 days. (You would have the problem of aerocapture at Mars at such highly elevated speeds but I'll leave that to another discussion.) So another question I have is at what high speed would you need so that the path is approximately straight-line?

This is just using Earth flyby. Could we in addition also use a Venus flyby? You would need an orbital arrangement where both Venus and Mars are near the Earth at the same time. Say you are now traveling at 22 km/s towards Venus, minus the amount you're slowed by leaving the Earth. You can likewise pick up about 11 km/s additional speed by just passing by Venus on the way to Mars, perhaps arranging it so that the path is bent by Venus to aim the craft towards Mars. So you could conceivably be traveling now at 33 km/s, again though I need to know how much speed you would lose in leaving Venus. You would also have to factor in the additional time it takes to get to Venus and the longer straight-line distance to Mars from Venus. Also, in being within Venus's orbit around the Sun, the greater gravitational effects of the Sun will have a greater effect to curve the trajectory.

Finally, could we use repeatedly the gravitational boosts of Earth and Venus? Suppose we are now at 33 km/s, more or less, after leaving Venus but we arrange it so our path is bent completely around to head back towards Earth. Could we once more get an additional 11 km/s to bring our velocity to 44 km/s after the Earth boost? Could we do this repeatedly to get arbitrarily high speeds?

Bob Clark

#### Rgclark

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##### Re: Gravity assists for Mars mission?
« Reply #1 on: 10/04/2012 12:14:17 »
I'm having trouble disentangling the gravitational slingshot effect and the Oberth effect.
By the Oberth effect I can get greater velocity if I apply my rocket burn when I'm closest to the planet. Plugging in some speeds into the equation on the Wikipedia page I am able to get an additional boost about that of Earth's or Venus' escape speed if I make the rocket burn high, say, 10 km/s or above. The problem is this page seems to be suggesting to get the gravity boost, I need to apply a rocket burn but I wanted to get the gravity boost without having to apply an additional rocket burn.
On the other hand the Wikipage on the gravitational slingshot effect suggests I can get an additional boost without having to supply an additional burn. But the problem here is I want to get these additional boosts while my craft is already moving at high speed, to boost even higher, but if I'm going too fast I won't swing around the planet but instead go right by it without getting the slingshot effect.
But this slingshot effect is potentially quite large though according to the Wikipedia page. It can be as high as twice the speed of the planet around the Sun. Since for the Earth this is about 30 km/s, this means you can get a boost of about 60 km/s (!) How fast can you be going beforehand and still get swung around by the planet to still get the boost?

Bob Clark

#### yor_on

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##### Re: Gravity assists for Mars mission?
« Reply #2 on: 10/04/2012 18:45:55 »
This question sounds like one that NASA should be the recipients of?

Especially the idea to use sling shots repeatedly. I guess it is possible, as long as we assume a 'dead' ship, without anything more than the necessary fuel to make course corrections?

#### yor_on

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##### Re: Gravity assists for Mars mission?
« Reply #3 on: 10/04/2012 19:07:21 »
Gravity assist.

And for the math involved Gravitational Slingshot.

#### Rgclark

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##### Re: Gravity assists for Mars mission?
« Reply #4 on: 12/04/2012 07:01:19 »
Gravity assist.

And for the math involved Gravitational Slingshot.

Thanks for that.

Bob Clark

#### Rgclark

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##### Re: Gravity assists for Mars mission?
« Reply #5 on: 12/04/2012 07:03:08 »
...this slingshot effect is potentially quite large though according to the Wikipedia page. It can be as high as twice the speed of the planet around the Sun. Since for the Earth this is about 30 km/s, this means you can get a boost of about 60 km/s (!) How fast can you be going beforehand and still get swung around by the planet to still get the boost?

The gravitational slingshot won't work from Earth since the spacecraft even if you launch from the Moon is still moving in the same direction as Earth with respect to the Sun.
It might work from Venus. I remember reading some of the plans to reduce the return time from a Mars mission is to do a swingby of Venus. As I recall though, the reduction in time was not that dramatic as to reduce the trip time to days instead of months, so likely the same would be true for using a Venus swingby for the outbound trip.
I think we could use the Oberth effect though.

Bob Clark

#### syhprum

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##### Re: Gravity assists for Mars mission?
« Reply #6 on: 12/04/2012 07:22:21 »
There have been many satellites sent to Mars I am sure that if anything could have been gained by using slingshot effects it would have been done long ago.

#### CliffordK

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##### Re: Gravity assists for Mars mission?
« Reply #7 on: 12/04/2012 08:46:35 »
Essentially with the slingshot, if you are travelling in opposite directions of the planet, you can add the orbital speed of the planet to the speed of the spacecraft with a reversal of direction.
If you are travelling in the same direction of the planet, you would subtract the orbital speed of the planet with a reversal of direction.

Anyway, if you start on Earth, then you might be able to slingshot around Venus or Mercury.

As far as the moon...  that may actually be important.
Say you assemble and fuel your rocket at the Earth-Moon-L1, you would add the orbital speed of the moon to your launch speed.  However, Earth-Moon-L2 would have almost twice the orbital velocity, so it would be best to make a half circle around the moon as part of the launch.

Would it be possible to catch an Earth/Mars crossing asteroid?  I suppose that would mean that one would have to match its orbit which would take the same energy as doing trip without the asteroid, unless one could recover fuel and resources from the asteroid.

#### Soul Surfer

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##### Re: Gravity assists for Mars mission?
« Reply #8 on: 14/04/2012 08:47:37 »
In general, gravity assist routes are low energy routes rather than quick ones.  The original questioner was looking for routes to Mars that involved high speeds and therefore took less time to complete the journey.

The main problem with high speed orbits is that you also need to expend energy slowing down when you get there.  The best way of using high speed orbits involves low thrust, long duration rockets like ion thrusters when you can accelerate continuously for half the journey and then slow down continuously for the other half.

#### Rgclark

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##### Re: Gravity assists for Mars mission?
« Reply #9 on: 31/05/2012 21:13:46 »
The Moon's velocity around the Earth is 1 km/s. Then since you could add twice the body's speed to the spacecraft you could conceivably get 2 km/s extra delta-v this way:

Gravity assist.

http://en.wikipedia.org/wiki/Gravitational_slingshot#Explanation

So is there some reason why this wouldn't work?

Bob Clark

#### CliffordK

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##### Re: Gravity assists for Mars mission?
« Reply #10 on: 31/05/2012 23:49:18 »
Bob,

Yes...  it would work a bit.

Presumably your rocket is either built in Earth's orbit, or goes through a stage that is in Earth's orbit.

Typical rocket launches are from West to East to utilize the rotation of the Earth as part of the launch (and thus Cape Canaveral is in Florida, and not in California).  So, you gain the equatorial rotational velocity of Earth, 465 m/s.

However, for a true Earth-Moon slingshot as described above, you would need to launch in the opposite direction of the moon's orbit.  To launch in the opposite direction, you would have to launch at an excess speed of (465 m/s) x 2, or about 930 m/s just to get back to the speed you would be moving just due to Earth's surface rotation.

Thus, if you did an East to west launch for the purpose of doing a lunar slingshot, the gain would be minimal.

I still think the highest energy launch point would be to flip the rocket around the the far side of the moon, and go through the Earth/Moon L2.

#### graham.d

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##### Re: Gravity assists for Mars mission?
« Reply #11 on: 01/06/2012 08:09:52 »
Could you really, practically, slingshot around Mercury, Clifford? It may get a bit hot and I'm not sure our technology is up to that.

#### CliffordK

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##### Re: Gravity assists for Mars mission?
« Reply #12 on: 01/06/2012 09:11:45 »
Could you really, practically, slingshot around Mercury, Clifford? It may get a bit hot and I'm not sure our technology is up to that.

I think you could deal with the temperature.  The surface temperature of mercury is 100K to 700K, or a max of about 800°F.  It is certainly within the heat tolerances of many metals.

A multi-layer heat shield like on the JWST should be able to passively deal with those temperatures quite easily.  The solar panels should get pretty intense power generation.  However, feathering them at an angle would prevent them from overheating.

The speed of Mercury is 48 km/s, which could potentially give a significant boost to the spacecraft velocity.  Earth's orbital velocity is about 30km/s.  However, one would likely have to waste a lot of energy trying to reach Mercury so the benefit might be minimal.  Mercury is further away than Mars, so it wouldn't be good for a slingshot to get to Mars, but perhaps for going to Jupiter and beyond.

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##### Re: Gravity assists for Mars mission?
« Reply #12 on: 01/06/2012 09:11:45 »