Why Nasa vessel went farther than necessary
Posted Saturday, September 22 2012 at 19:00
- It is not true that the planet Mars is 230 million km away from Earth
- The distance is constantly changing all the time but it varies from about 52m km to just over 400m km. The oft quoted 230m km is just the average of these two numbers
- The reason is that the spacecraft did not travel along a straight line from Earth to Mars. It followed a spiral path
J.G. Kameru is wondering about the flight of NASA’s spacecraft, the Curiosity Rover, which landed on Mars recently. She writes: “How come the Rover travelled 560 million km to Mars and we know the actual distance is 230m km? Why the difference of 330m km?”
Well, first of all, it is not true that the planet Mars is 230 million km away from Earth. The distance is constantly changing all the time but it varies from about 52m km to just over 400m km. The oft quoted 230m km is just the average of these two numbers.
To understand this, bear in mind that the Earth is the third planet from the Sun and Mars is the fourth. While we are about 150 million km from the sun, Mars is 229 million km. Now it is very tempting to subtract these two distances and conclude that Mars is 79 million km. But that would be wrong – very wrong indeed.
The problem is that such a calculation assumes that the two planets revolve around the sun synchronously and at the same rate. But the reality is that the Earth takes 365 days and Mars 780 days. Therefore, there are times when the two planets are on opposite sides of the sun and others when they are on the same side. Furthermore, the orbits of planets are not circular; they are elliptical.
Because of the elliptical orbit, the distance of the Earth from the sun varies from about 147m to 152m km. That of Mars is 206m to 249m km. So, the closest separation between the two planets occurs when they are on the same side of the sun with the Earth at its farthest distance (152m km) and Mars at its nearest (206m km). In that arrangement, the two are 52m km apart (206m minus 152m).
The maximum separation occurs when the two are on opposite sides and at their farthest from the sun. In that case the distance between them is about 401m km (152m plus 249m).
Still, that does not explain why the Curiosity Rover covered 560m km. The reason is that the spacecraft did not travel along a straight line from Earth to Mars. It followed a spiral path. Whereas a straight line might appear as the best path to follow, it would require too much fuel. The more efficient method is to accelerate the spacecraft to a higher orbital velocity than that of the Earth (107,000km/h).
That way, the craft drifts naturally away from the Sun and, if the timing is right, it will cross paths with Mars and get trapped by the planet’s gravity. In this manoeuvre, the engines of the spacecraft are switched off as soon as it reaches the desired velocity. This saves immense amounts of energy. The resultant path is thus a spiral, which is longer than a straight line.