Question

A new planet with mass 3.75 × 10 25 k g and radius 6.93 × 10 7 m has been discovered. How many times more or less is the gravity of this new planet? Calculate this by taking the ratio of g p l a n e t g e a r t h .

Answer 1

To find how many times the gravity of the new planet is more or less than Earth's gravity, we compute the ratio of their gravities using the universal gravitational constant and their respective masses and radii. The calculated ratio allows direct comparison without needing the gravitation constant value or Earth's exact gravitational force.

Step-by-step explanation:

The student's question involves calculating the gravitational force on a newly discovered planet and comparing it with Earth's gravitational force. To do so, we need to use the formula for the acceleration due to gravity, which is g = G * (mass of the planet) / (radius of the planet)^2, where G is the universal gravitational constant.

Using the given values for the new planet, the gravitational pull of the new planet is gplanet = G * (3.75 × 1025 kg) / (6.93 × 107 m)^2. To compare it to Earth's gravity, we calculate the ratio gplanet / gearth. Since the known values of Earth's mass and radius are used to calculate Earth's gravity (approximately 9.81 m/s2), this ratio will allow us to determine how many times more or less gravity the new planet has compared to Earth. Without needing to use the exact values of G, Earth's mass, and radius, the ratio simplifies the computation.

Answer 2

To find how gravity on the new planet compares to Earth's, we use Newton's Law of Universal Gravitation to calculate the gravitational acceleration and then take the ratio of the gravity on the new planet to that of Earth. By plugging in the respective masses and radii, we can determine the strength of gravity on the new planet as a multiple of Earth's gravity.

Step-by-step explanation:

To calculate how the gravity on the new planet compares to Earth's gravity, we can use Newton's Law of Universal Gravitation:

g = G * (M / R^2), where G is the gravitational constant (6.67 × 10^-11 Nm^2/kg^2), M is the mass of the planet, and R is the radius of the planet.

For Earth, we have: g_earth = G * (M_earth / R_earth^2) with M_earth = 5.98 × 10^24 kg and R_earth = 6.38 × 10^6 m.

For the new planet, we have: g_planet = G * (M_planet / R_planet^2) with M_planet = 3.75 × 10^25 kg and R_planet = 6.93 × 10^7 m.

Now, we can find the ratio g_planet / g_earth to see how many times more or less the gravity of this new planet is:

g_planet / g_earth = (G * M_planet / R_planet^2) / (G * M_earth / R_earth^2) = (M_planet / R_planet^2) / (M_earth / R_earth^2)

Plugging in the values we have, we get: g_planet / g_earth = (3.75 × 10^25 kg / (6.93 × 10^7 m)^2) / (5.98 × 10^24 kg / (6.38 × 10^6 m)^2)

This calculation will give us the ratio and tell us how many times more or less the planet's gravity is compared to Earth's gravity.