A planet has a radius of about 0.85 times Earth's radius and a mass of only 0.74 times Earth's mass. Estimate the acceleration due to gravity on the planet.
Use M_{Earth} = 5.972 x 10^{24} kilograms
and
r_{Earth} = 6370 kilometers
a_{planet} = ________________{m}/{s^2}
(no rounding up)
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To estimate the acceleration due to gravity on the planet, we can use the formula for acceleration due to gravity:
a = (G * M) / r^2
where:
a = acceleration due to gravity
G = gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
M = mass of the planet
r = radius of the planet
Given that the radius of the planet is about 0.85 times Earth's radius (r_{Earth}) and the mass of the planet is only 0.74 times Earth's mass (M_{Earth}), we can plug in these values into the formula:
a = (G * M_{planet}) / r_{planet}^2
First, let's convert the Earth's radius and the mass to the appropriate units:
r_{Earth} = 6,370 kilometers = 6,370,000 meters (since there are 1,000 meters in a kilometer)
M_{Earth} = 5.972 x 10^24 kilograms
Now, we can substitute the known values into the formula:
a = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 0.74 * 5.972 x 10^24 kg) / (0.85 * 6,370,000)^2
Simplifying the expression, we get:
a = (4.95294 x 10^14 m^3 kg^-1 s^-2) / (7.75 x 10^12 m^2)
Dividing these numbers, we find:
a ≈ 63.928 m/s^2
Therefore, the estimated acceleration due to gravity on the planet is approximately 63.928 m/s^2.