Tuesday, May 28, 2013

Mileage in extraterrestrial vehicles - Moon and Mars distances

I recently run into a cool infographic showing distances driven by vehicles on the surface of the Moon and Mars, and a great time-lapse of the martian rover Curiosity - its 9 month squeezed into a minute.
That’s all dandy, but one has to get to the Moon and Mars before being able to enjoy some offroading. How far are they? The answer is not one number.
In this post: distances to ponder.

Earth, Mars and Moon to scale   --   source: ESA



Out-of-this-world driving records

Below, you can see the record-holding lunar and martian rovers. Among these there are ones that have been on the surface of the alien world for decades and stopped working a long time ago, and there are ones that are still active today. Most are robotic missions, but here are the only human-driven extraterrestrial rovers - the Apollo Lunar Roving Vehicles.
All these rovers have done their work in very harsh environments (which, perhaps, is worthy of another post), so the following distances are pretty impressive.

   ---   source: NASA/JPL

Leading is the Lunokhod 2 (moonwalker in Russian), which traveled 37 km on the surface of the Moon, followed by Opportunity, which is roaming the martian surface even today along with Curiosity. (Shown are the distances driven as of May 15, 2013.)

Let's take a closer look at the Soviet Lunokhod 2 and the American Curiosity.
The Lunokhod 2, among other things, was sent to the lunar surface to collect images, and to study the soil mechanics of the lunar surface. It operated for about 4 months, roaming hills and rilles.
Curiosity, the six-wheeled rover, is on Mars to investigate the climate and geology, and it is looking to see if Mars ever could have supported life. The rover has "only" made a 700 m journey yet, but it's been pretty busy since its arrival to Mars. In the video below you can see Curiosity's 9-month of work compressed into a minute.





Watch out though, because within the next two years there will be some more rovers making it out there, and among these will be the ones competing for the Google Lunar X Prize. According to the rules, the robots have to travel at least 500 meters on the lunar surface. So they definitely will mean competition for the top ranking rovers presented in the infographic.

So how far is the Moon?
When it comes to distances in space, it becomes quite impractical to think in meters and kilometers. We can use another unit of distance instead: light-years.
A light-year is the distance that light travels in vacuum in one year. Light has a constant speed, in vacuum it is 299,792,458 m/s (300,000 km/s).
So you can calculate that one light-year is 9,460,730,472,580,800 meters, about 10 trillion km.
Of course, we can talk about light-minutes (the distance that light travels in one minute) and light-seconds (the distance that light travels in one second) as well. 
Then, 1 light-second is 299,792,458 m.

Because the Moon orbits Earth not in a circle, but in an ellipse, the distance between them varies over the course of the orbit. There is a point where the Moon is closest to Earth on this ellipse (called perigee), and there is one where it's farthest (called apogee).

   --   source: Astro Bob
The average distance between the Earth and Moon is 384,400 km. It is approximately 30 times Earth's diameter, or with another unit: they are 1.26 light-seconds apart. Which means that it takes a beam of light 1.26 seconds to travel between them. Below is an animation of this with the Earth, Moon and the distance between them to scale.

It takes 1.26 seconds for a light beam to travel from the Earth to the Moon   --   source: Wikipedia


How far is Mars?

It is a little trickier. The average distance between Earth and Mars is 225 million km. But as for he Moon and Earth, the distance between them changes constantly.

Both Earth and Mars orbit the Sun in an ellipse. As for the Moon orbiting the Earth, there is a point where the planet (let it be Earth or Mars) is closest to the Sun on its ellipse (called perihelion) and there is one where it is farthest from the Sun (called and aphelion).

But there is something else here: Earth, being closer to the Sun, orbits more quickly around it than Mars. Earth makes two trips around the Sun in about the same time that Mars takes to make one trip. So sometimes the two planets are on opposite sides of the Sun, very far apart, and other times, they are on the same side of the Sun: Earth catches up with Mars and passes closer to it. You can see this on the animation below.

Blue is the orbit of Earth around the Sun, red is the orbit of Mars
  --   source: Wikipedia

For the Earth and Mars to be closest to each other, they need to be on the same side of the Sun, and Earth needs to be at its most distant point from the Sun on the ellipse, while Mars is at its closest point to the Sun. Then - theoretically - Mars and Earth will be only 54.6 million kilometers from each other.
When they are farthest apart, they are separated by 401 million km. This happens when they are on opposite sides of the Sun, and Earth is closest to the Sun on the ellipse, while Mars is farthest from it.
Now averaging the minimum and maximum distance we get 225 million km. Tada!

Earth and Mars get close to each other in approximately every two years. During this time it would take a beam of light from Earth about 3 minutes to make the journey, and then another 3 minutes for it to get back to Earth. In other words, Mars is 3 light-minutes away this time. But when they’re most distant from each other, it takes about 21 minutes to send a beam to Mars, and then another 21 minutes to receive a return message, the distance is 21 light-minutes.

To sum up, here is a great visualization showing you how far the Moon and Mars are from Earth. How would it all look, to scale, if we assumed Earth had a 100-pixel diameter? Click on the image to find out.

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