Question

a new planet is found with a density one third as much at earth and a radius twice that of earth. what is the acceleration due to gravity on this new planet?

Answer 1

The acceleration due to gravity on the new planet would be one third that of Earth's, or about 9.8 m/s^2.

What is planet?
This question might seem to have an easy solution, but it doesn't. The planets Earth, Mars, and Jupiter are well known. But before recent discoveries sparked a passionate debate about how to best characterise them, both Pluto and Ceres have been thought of as planets. This debate is still going strong today. The International Astronomical Union adopted the most recent definition of the a planet in 2006.

It specifies three requirements for a planet:

-It must move about a star (in our cosmic neighborhood, the Sun).
-It must be large enough for gravity to pull it in a spherical direction.
-It must have been large enough that any nearby objects of the a similar size were removed by its gravitational pull.

Given that the mass of the new planet is one third that of Earth's and its radius is twice that of Earth's, we can say that its volume is eight times that of Earth's.  This means that its average density is one third that of Earth. Therefore, the acceleration due to gravity on the new planet would be one third that of Earth's, or about 9.8 m/s^2.

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