Question

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).

Answer 1

60.85° counterclockwise

Step-by-step 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*(1-(1)/(2√(2))\sqrt{((a_1)/(a_2)+1)^3}\ )`

on substituting the respective values, we get

α =
`\pi*(1-(1)/(2√(2))\sqrt{((1.0)/(0.7)+1)^3}\ )`

or

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

or

-1.062 radians = -60.85°

Hence,

The planetary phase angle between them is 60.85° counterclockwise