Calculate the planetary phase angle (counterclockwise from earth, a = 1.0 au) that a probe may correctly complete a hohmann transfer orbit to venus (a = 0.7 au).

60.85° counterclockwise

Explanation:

Data provided in the question:

a₁ = 1.0 AU

a₂ = 0.7 AU

Now,

The phase angle ( α ) is calculated using the formula

α =

on substituting the respective values, we get

α =

or

α = -1.062 radians

Here, the negative sign depicts the counterclockwise direction

Now,

1 radian = degrees

therefore,

-1.062 radians = -1.062 × degrees

or

-1.062 radians = -60.85°

Hence,

The planetary phase angle between them is 60.85° counterclockwise

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.