Physics: 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).

Calculate the planetary phase angle (counterclockwise

Queenvalentin

04.01.2022

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 = $\pi\times(1-\frac{1}{2\sqrt{2}}\sqrt{(\frac{a_1}{a_2}+1)^3}\ )$

on substituting the respective values, we get

α = $\pi\times(1-\frac{1}{2\sqrt{2}}\sqrt{(\frac{1.0}{0.7}+1)^3}\ )$

α = -1.062 radians

Here, the negative sign depicts the counterclockwise direction

Now,

1 radian = $\frac{\textup{180}}{\pi}$ degrees

therefore,

-1.062 radians = -1.062 × $\frac{\textup{180}}{\pi}$ degrees

-1.062 radians = -60.85°

Hence,

The planetary phase angle between them is 60.85° counterclockwise

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