I have two (maybe equal) question
1- Is this possible to send a spacecraft to the moon without any acceleration(Constant speed)?
2-Is this possible to throw a ball on the top of tree without any acceleration(Constant speed)?
Constant speed and no acceleration is obviously not possible, unless you only consider a certain time frame which does not include the start or the end of the trajectory. Plus you'd have to limit yourself to purely classical, macroscopic scales, because on molecular/atomic level, everything is constantly accelerating. Having said that:
1) Is it possible to send a spacecraft to the moon without any acceleration?
While this is theoretically possible, it is certainly not technologically possible. Moving at constant speed to the moon would mean you're not in an orbit, and you're thus constantly preventing falling back to the Earth (or to the Moon). You'd have to force the spacecraft from the Earth all the way up to the moon for it to maintain constant speed, which is possible but probably the least efficient way to get to the Moon. If the spacecraft is 1kg, taking this path would require more rocket propellant than there is mass in Mount Everest (rough numbers here...)
But, you might actually be surprised:
If you mean no active acceleration, e.g., thrust (I suppose physicists would call that induced acceleration), then yes you can, provided you start out in a specific spot in space (not even necessarily Lagrange points). This is called a low energy transfer. In scientific circles it is called the weak stability boundary, a very active field of research. You can view it as taking advantage of chaos in the context of the three body problem (or $N$-body problem, usually).
A popularized version of this is the interplanetary superhighway, which enables spacecraft to travel to distant planets using very little or no energy at all. The only drawback of all this is that it usually requires an awfully long time. A simple trip to the moon might take weeks or months (depending on how little energy you want to expend), whereas a few days would suffice if you had rockets.
2) Is it possible to throw a ball on the top of tree without any acceleration?
I'm not sure I get what you mean with this...You want to throw a ball to a treetop without accelerating it? I'm very curious to see you do that...
But let's assume you mean the same as before, then the answer is the same as well. If you have a rope or so from the ground to the treetop, wrapped around some pulleys, you'd have a basic elevator. This elevator can carry your apple up at constant speed, no problem.
You should only close your eyes when you start the elevator, and close them again when the apple reaches the top, but otherwise, there'll be no acceleration at all :)
No. How would you get the object to your constant speed? If it starts at rest, and there is no acceleration, it will remain at rest.
If you allow for a brief acceleration, it might be possible with the spaceship but it would be extremely difficult to burn the fuel in exactly the correct way to counteract the Earth's gravity to allow for constant acceleration.
In the case of the ball, no. Unless your ball has some form of propulsion to counteract the force of gravity, it will accelerate downward on the path to the top of the tree.
If you can throw them with 0.999999 c , then it will be nearly perfectly constant speed(~c)
There is a way to get to the moon without using any rocket power to accelerate the spacecraft. It's called a Space Elevator. This is a cable that stretches from the earth to geostationary orbit (GEO, 35,786 km). It also needs to stretch beyond GEO, in order to counterbalance the weight of the cable below GEO. How far it stretches depends on whether a counterweight is used at the top of the cable, and how much mass is in the counterweight.
As you climb up the cable, your orbital speed changes and when you reach GEO you have exactly the speed required to stay in that orbit. At that point, you could let go of the cable and float alongside it. Below GEO you would fall back, and above it you would actually move away from the earth. Depending how far out you travel along the cable, you could get enough speed to fling you even to the outer planets.
Of course, you're still using acceleration; you're just not aware of it as all you're doing is to travel along a cable at constant speed. As you travel up, you'd experience less and less gravity, reaching zero at GEO. Beyond that, you would start feeling an outward g force, throwing you out from earth.