A ball was thrown on a planet with a density of 4.6 g/cm^3 and a radius of 4600 km at the speed of 400 m/s and an angle of 70 degrees. Calculate the maximum altitude of the ball from the surface and the distance between the initial point to the impact point of the ball with the surface of the planet.
To solve this problem, we can use the equations of motion and some basic principles of physics.

First, we need to calculate the initial vertical and horizontal components of the velocity of the ball:
```
Vy = V * sin(θ) = 400 * sin(70°) = 375.4 m/s
Vx = V * cos(θ) = 400 * cos(70°) = 123.2 m/s
```
Next, we can use the equation of motion to calculate the time of flight of the ball:
```
Vy = Voy - gt
0 = 375.4 - gt
t = 375.4/g ≈ 38.3 s
```
Using this time, we can calculate the maximum height reached by the ball:
```
y = Voyt - 1/2g*t^2
y = 375.4 * 38.3 - 1/2 * 9.81 * (38.3)^2
y ≈ 716941 m
```
So the maximum altitude of the ball from the surface of the planet is approximately 716941 meters.

Finally, we can use the horizontal component of the velocity and the time of flight to calculate the distance traveled by the ball:
```
x = Vx*t
x = 123.2 * 38.3
x ≈ 4714.96 km
```
Since the radius of the planet is 4600 km, we can subtract the radius from the distance traveled to get the impact point:
```
impact point = x - planet radius
impact point ≈ 114.96 km
```
So the distance between the initial point to the impact point of the ball with the surface of the planet is approximately 114.96 km.
Does your calculation consider the decrease in gravity when the ball is farther away from the surface of the planet?
No, the calculation I provided assumes a constant acceleration due to gravity throughout the entire flight of the ball. In reality, the acceleration due to gravity does decrease as the ball gets farther away from the surface of the planet. However, the radius of the planet in this problem is much larger than the maximum altitude of the ball, so the effect of this decrease in gravity is likely to be small and can be ignored for the purposes of this calculation.