A hypothetical planet has a radius 3.3 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface? (downward)
g is inversely prop to rad^2
g= 9.8/3.3^2
To calculate the acceleration due to gravity near the surface of a planet, we can use the following formula:
acceleration due to gravity (g) = (G * M) / (r^2)
Where:
G = Universal gravitational constant = 6.67430 × 10^-11 m^3 kg^-1 s^-2
M = mass of the planet
r = radius of the planet
Given that the mass of the hypothetical planet is the same as Earth, and the radius is 3.3 times that of Earth, we can say:
M = mass of Earth
r = 3.3 * radius of Earth
The radius of Earth is approximately 6,371 km. Therefore, we can substitute these values into the formula to calculate the acceleration due to gravity near the surface of the hypothetical planet. Here are the steps:
Step 1: Calculate the radius of the hypothetical planet
radius of the hypothetical planet = 3.3 * 6,371 km
Step 2: Calculate the acceleration due to gravity
acceleration due to gravity = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * mass of Earth) / (radius of the hypothetical planet)^2
Solving this equation will give you the value of the acceleration due to gravity on the hypothetical planet's surface.
To determine the acceleration due to gravity near the surface of a hypothetical planet, we can use the formula for gravitational acceleration:
a = (G * M) / r^2
where:
- a is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the planet
- r is the distance from the center of the planet to the point of interest (in this case, the surface)
Given that the mass of the hypothetical planet is the same as Earth's mass, we can use the Earth's mass value, which is approximately 5.972 × 10^24 kg.
Since the hypothetical planet has a radius 3.3 times that of Earth's radius, we need to determine the radius of this planet.
If we assume Earth's radius as approximately 6,371 km (or 6,371,000 meters), we can calculate the radius of the hypothetical planet:
Radius of the hypothetical planet = 3.3 * Earth's radius
= 3.3 * 6,371,000 meters
Now, we can substitute the values into the formula to find the acceleration due to gravity near the surface of the hypothetical planet:
a = (G * M) / r^2
= (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / (3.3 * 6,371,000 meters)^2
Evaluating this expression will give us the acceleration due to gravity near the surface of the hypothetical planet.