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) What happens to the gravitational force if you double the mass of a planet?

What happens to the gravitational force (at the surface) if the radius of the planet doubles?
The mass of Jupiter is 318 times larger than that of the Earth. The radius of Jupiter is 11.22 times larger
than the radius of the Earth. If you weigh 900 N on Earth, what is your weight on the surface of Jupiter?

1 Answer

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Final answer:

If you double a planet's mass, its gravitational force also doubles. On Jupiter, your weight is determined by proportionally scaling Earth's gravitational force by Jupiter's mass and the square of the radius difference, resulting in a weight of about 2277 N.

Step-by-step explanation:

When you double the mass of a planet, its gravitational force also doubles, according to Newton's Universal Law of Gravitation. This law states that the gravitational force (Fgravity) between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers.

To calculate your weight on Jupiter, considering you weigh 900 N on Earth, you will use the ratio of the gravitational forces which is proportional to the ratio of the mass of Jupiter to Earth (318:1) and inversely proportional to the square of the ratio of their radii (11.22:1). This gives a gravitational acceleration on Jupiter's surface greater than that on Earth's. Thus, if gJupiter is Jupiter's gravity, gEarth is Earth’s gravity (9.8 m/s²), the calculation is formulated as:

gJupiter = (318/1) / (11.22/1)² * gEarth
gJupiter ≈ 2.53 * gEarth

Your weight on Jupiter would then be approximately 900 N * 2.53 ≈ 2277 N.

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