Question

An extraterrestrial civilisation lives on a planet with a very elliptical orbit. Additionally, thousands of large asteroids orbit their solar system. The civilisation uses the light from their home star to count the number of asteroids in the direct line between the star and their planet. For a first measurement, they count the asteroids for 60 days and detect 1000 objects. Several months later, they start a second measurement: This time, they count for 80 days. How many asteroids will they detect during the second measurement? Explain why. (Note: Assume that the asteroids are homogeneously distributed in their solar system.)
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Answer 1

According to Keplar's second law of planetary motion, "The areas swept by the radial vector connecting the star (sun) and the planet orbiting it are equal for equal intervals of time

Answer 2

For Kepler's third law this can be solved as normal ratios

• 1000/60=x/80
• 100/6=x/80
• 6x=8000
• x=8000/6
• x=1333.34asteroids