What was the orbital period of the probe around the comet, in earth days?
In 2014, a space probe approached the rocky core of the comet Churyumov-Gerasimenko, which is only a few km in diameter. The probe then entered the orbit around the comet at a distance of 30 km. The comet was found to have a mass of 1.0×1013kg.
- billrussell42Lv 79 months ago
1.0×1013kg ?? what does this mean?
- ArgentLv 79 months ago
Use Kepler's third law: T² = kR³, where T is the orbital period; R is the orbital radius (measured from the center of the orbited body); and k is a constant that depends on the mass of the orbited body. k = 4π²/(GM), where G is the universal gravitational constant and M is the mass of the orbited body.
Here, M = 1.0 × 10¹³ kg; R = 30 km = 3.0 × 10⁴ m.
T = √(kR³). Plug in all the necessary numbers, then divide the result by 86 400 to express it in (solar) Earth days.