1. A space agency wants to place a low-budget satellite in orbit near the earth and near the moon. Engineers suggest the following four different points to place it as shown in the figure. In which of the points could the satellite be weightless?

 

2. The International Space Station, which orbits daily around the earth, releases a satellite. The satellite can be redirected along 3 possible paths \(X\), \(Y\), and \(Z\). How does the work done on the satellite by the gravitational field compare among the three possibilities?

 

3. A new planet \(\Omega\) is found orbiting the Sun at a distance of \(4\text{AU}\) in a circular orbit. What is the expected period of this new planet?
4. A planet orbiting a star follows the following elliptical trajectory. The perihelion \(A\) and aphelion \(B\) are highlighted. Three astronomers state the following:
  • Astronomer 1: The planet's mechanical energy at \(A\) is greater than at \(B\).
  • Astronomer 2: The planet's orbital speed at \(A\) is greater than at \(B\).
  • Astronomer 3: The planet's orbital angular momentum at \(B\) is greater than at \(A\).
 

Which astronomers are correct?
5. A physics student tracks the path of a planet in a planetary system of a galaxy far away. He finds that the trajectory around a star traces a perfect circle. The student claims that "the planet violates Kepler's first law because the path is not elliptic". This statement is:
6. To increase the gravitational force between a planet and a star, which variable should be modified?
7. Amateur astronomers are making measurements of a planet orbiting a random star. The astronomers made 2 measurements, where they identified that the planet swept the same area. With this information the astronomers could affirm that:

8. Suppose you are studying a new planet and have collected information about its orbit. You are asked to calculate the planet's mass and are given the speed at aphelion and the magnitude of angular momentum at another point on the trajectory. What other information do you need to know?
9. A planet orbits a star of mass \(M\). The distance from the star to the aphelion is \(r_1\) and the distance to the perihelion is \(r_2\). What is the period of the planet's orbit?
10. A planet is on a trajectory whose semi-major axis measures 100 units. The eccentricity of the orbit is 0.25 What is the distance between the star and the planet at perihelion?