- Practical Exercise 1 RADIANS OR DEGREES?
- Practical Exercise 2 MARS IN OPPOSITION AND QUADRATURE
- Practical Exercise 3 MEASURING MERCURY AND VENUS
- Practical Exercise 4 “MERCUAN”
- Practical Exercise 5 THE EARTH FROM MARS
- Practical Exercise 6 HOW BIG IS THE MOON?
- Practical Exercise 7 THE MOON AGAIN
- Practical Exercise 8 PARAMETERS OF PLANET TRAJECTORIES
- Practical Exercise 9 LIKE FROM ANOTHER PLANET...
- Practical Exercise 10 FEET FIRMLY ON THE EARTH...
- Practical Exercise 11 GREEK, HOW BIG IS THE EARTH?
- Practical Exercise 12 THE MOON IN ACTION FOR THE THIRD TIME
Practical Exercise 3: MEASURING MERCURY AND VENUS
Determine the radii of circular orbits of Mercury and Venus when you know that:
a) the greatest elongation of Mercury is 23° and of Venus 47°,
b) synodic orbital period of Mercury is 116 days, Venus 584 days.
Answer:
a) From Figure 1 and the greatest elongation we will determine the main half-axes of the planets: Mercury a☿ = a⊕ sin 23° ≐ 0,39 au, Venus: a☿ = a⊕ sin 23° ≐ 0,39 au, Venus: a☿ = a⊕ sin 47° ≐ 0,73 au.
b) For mutual angular motion of the inferior planet and the Earth it applies: 
. We will start from the definition of angular velocity .We start from the definition of angular velocity 
, after substitution we get: We start from the definition of angular velocity , after substitution we get:
i.e. . We start from the definition of angular velocity after substitution we get: i.e. 
.
For Mercury we get: . We start from the definition of angular velocity after substitution we get: i.e. .
For Mercury we get: T☿ ≐ 88 days ≐ 0,241 years, for Venus: .
We start from the definition of angular velocity , substitution we get:
i.e. . . For Mercury we get: T☿ ≐ 88 days ≐ 0,241 years , for Venus: T☿ ≐ 245 days ≐ 0,615 years.
From the 3rd Kepler’s law a' = 
we get: a☿ ≐ 0,391 au, 
. We start from the definition of angular velocity ,substitution we get:
i.e. . .For Mercury we get: T☿ ≐ 88 dní ≐ 0,241 years , for Venus: T☿ ≐ 245 days ≐ 0,615 years From the 3rd Kepler’s law a' = we get: a☿ ≐ 0,391 au, a☿ ≐ 0,723 au.