It is connected to the ground in the sense that the air it is flying through is connected to the ground. i.e. the air is moving at generally the same velocity as the ground, give or take 20 or 30 knots or so. In a Westerly wind of 40 knots, the plane will be 40 knots faster if going East. In an Easterly wind of 40 knots, the plane will be 40 knots slower if going East. As far as the plane is concerned, the Earth is not rotating, nor is the shell of atmo.

The plane flies by propelling itself through the air. If the air is moving with respect to the ground,(such as when there is a wind), then the plane's speed and path relative to the ground will be a vector addition of the plane's path relative to the air and the air's path relative to the ground. If you are flying "into" the wind, your ground speed will be less than your airspeed, if you are flying "with" the wind. it will be greater. If you are flying "crosswind", both your ground speed and direction will be effected. (likewise, if you are in an updraft, your plane will gain altitude and if in a down draft it will lose altitude. Both while maintaining "level flight" with respect to the air.) If you are trying to fly due North and you have an Easterly wind, you actually aim the nose the plane slightly to the East to maintain a South to North path with respect to the ground. Since wind speeds and directions can change with altitude(winds aloft), you need to know what they are for your flight altitude in order to know what heading you need to fly. To help with this, you can use a flight computer such as the one here after getting the winds aloft from the National weather service: Please Register or Log in to view the hidden image! On the right is the side which you can use to construct the "wind triangle" for determining your course heading. ( of course now you can get an electronic version). But all of this just relies on the local winds and not on the rotation of the Earth.

We know that all planets are revolving around the Sun with different speeds. For a rocket to reach Mars, does it mean it must travel with a speed faster than the tangential velocity of Mars?

First we have to deal with what is meant by "the Speed of light". In this case, it cannot mean 'c' the speed of light in a vacuum, since a material object like a plane cannot travel at c, and even light, traveling through medium like air does not travel at c. Thus we will take it to mean the speed that light travels in the air. So, yes, a wind triangle will have to be applied. However, due to the high speed involved, you would have to use relativistic velocity addition in order to arrive at the correct answer. But since wind speed is going to be really small compared to the speed of light, for all practical purposes dealing with travel across the surface of the Earth, it will have a negligible effect on our heading.

This scenario deals with orbital mechanics, which means that the gravitational effect of the Sun must be taken into account along with the relative velocities. It also involves objects traveling in circular paths at different radii. To illustrate the effect this second point makes, let's ignore the Sun's gravity for now, and just assume that you want to travel from a point at rest with respect to the Sun and at the Earth's distance from the Sun, to Mars. Mars has an orbital velocity of ~24 km/sec. Would you have to travel faster than this to reach Mars? No. All you would have to do is travel in some straight line that intersects Mars orbit, and time your arrival so that you intersect it when Mars reaches that point in its orbit. It doesn't matter how fast you are traveling or how long it took you to get there, just as long as you time it correctly. There are an infinite number of such straight lines to follow from your starting point that intersect with Mars orbit at different points. Of course, you can't ignore the Sun's gravity, and it is this and not Mar's orbital velocity that determines how fast you need to start off to reach Mars. To illustrate, consider the following scenario: You are standing on an open field holding a small ball. Somebody off to the side of you throws another ball in an arc that passes directly over you. You want to hit this ball with your ball, and you do so by throwing your ball straight up at the right time to hit the other ball. So you are going to have to time your throw according to speed you throw it in order to hit the other ball as it passes over you. But there is one other thing you have to consider. You can't throw the ball up at just any speed. The top height your ball will reach will depend on how fast you threw it. If it leaves your hand at too low a speed, it will not reach the height of the ball passing over your head, and you simply cannot hit it. This means there is a minimum speed that you can throw your ball and still have any chance of hitting your target. The same is true for launching a rocket from Earth orbit to Mars, it has to start with enough speed so that the Sun's gravity does stop its climb outward before it even reaches Mars orbit distance. Luckily we have a little help here, the Earth is already traveling at some 30 km/sec relative to the Sun, and our path to Mars does not have to be straight out from the Sun. We can just add speed in the same direction we are already moving and gain enough speed to get us to Mars' orbit (In fact, adding speed this way requires the least amount of added speed). All we have to do is wait until Earth and Mars are in the proper positions relative to each other so that when we launch, Mars and our rocket reach the same point at the same time. To get to Mars from Earth requires an additional 2.9 km/sec (notice that this is less than the 6 km/sec difference between Earth's and Mars' orbital speeds.) This means that the rocket starts off with a velocity relative to the Sun of some 32.9 km/sec, which is greater than Mars' orbital speed of 24 km/sec. But as the rocket climbs from the Sun, it loses speed, so, by the time it reaches Mar's orbit. it will be moving slower than Mars. For a part of its path, it will "ahead" of Mars, and Mars will catch up to it. [/i] Going the opposite direction (from Mars to Earth) requires another change in velocity. This time in the opposite direction of Mars' motion. We subtract speed from the object and let it fall in towards the Earth. It starts out moving slower than the Earth relative to the Sun, but by the time its reaches Earth orbit, it will be moving faster (by 2.9 km/sec) So when we ask how fast a rocket must be traveling to get from one planet to another, we have to consider what we mean. Do we mean relative to the Sun, or relative to the launch planet, and do we mean at the time of launch or the time of arrival.

I find diagrams often work to explain that which can take up much text Hope this diagram helps Please Register or Log in to view the hidden image! Earth launch May 2018 seems very ambitious but I'm hoping for the January 2019 landing You can see in the diagram at both Earth and Mars departures the two planets are at their closest But unfortunately it is not possible to stop the orbits and in effect hop across in a straight line After launch in both cases the spacecraft has to play catch up with the target planet Please Register or Log in to view the hidden image!

Of course neither of these trajectories are minimum energy or Hohmann transfers. For those your arrival point at the other planet's orbit is 180 degrees from your point of launch and take ~24 more days.