A new, previously unknown, planet Vulcan was discovered in our solar system. We measure an orbital period of 103 Earth days for the new planet. We send some astronauts to travel to the planet and they measure the planet's gravitational acceleration to be 8.2 m/s2 on its surface. They also determine that the planet's radius is half the radius of Earth.
1. How far away from the sun is the new planet?
a. 8.3 x 100 m
b. 6.4 x 100 m
c. 1.7 x 100 m
d. 9.5 x 1010 m
e. 2.3 x 1010 m
2. What is the mass of planet Vulcan?
a. 1.3 x 1024 kg
b. 5.4 x 1024 kg
c. 9.8 x 1024 kg
d. 0.2 x 102 kg
e. 4.8 x 1024 kg
3. The astronauts also discover a moon that orbits planet Vulcan with a period of 63 days. How far away is the moon from the planet Vulcan?
a. 1 x 108 m
b. 20 x 108 m
c. 460 x 108 m
d. 9 x108 m
e. 4 x 10 m
4. The astronauts visit the newly discovered moon to study it. They measure the gravitational acceleration on the surface of the moon to be 2.7 m/s. When their mission is finished, they try to escape from the moon. They measure that the minimum velocity to escape the moon is 3,000 m/s. What is the mass of the moon?
a. 1.1 x 1023 kg
b. 5.0 x 1023 kg
c. 7.8 x 1023 kg
d. 29 x 104 kg
e. 370 x 1023 kg