A mystery planet in another part of the galaxy has an acceleration due to gravity of 5.00 m/s^2. If the radius of this planet is 2.00 x 10^6 m, what is the mass of the mystery planet?

gottem

5=G*M/(2e6)^2 solve for Mass M

To find the mass of the mystery planet, we can use the formula for the acceleration due to gravity:

g = G * (M/r^2)

where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67 x 10^-11 N(m/kg)^2), M is the mass of the planet, and r is the radius of the planet.

Rearranging the formula, we have:

M = (g * r^2) / G

Substituting the given values:

g = 5.00 m/s^2
r = 2.00 x 10^6 m
G = 6.67 x 10^-11 N(m/kg)^2

Calculating the mass of the mystery planet:

M = (5.00 m/s^2 * (2.00 x 10^6 m)^2) / (6.67 x 10^-11 N(m/kg)^2)

M = (5.00 * 4.00 x 10^12) / (6.67 x 10^-11)

M ≈ 1.499 x 10^23 kg

Therefore, the mass of the mystery planet is approximately 1.499 x 10^23 kg.

To find the mass of the mystery planet, we can use the formula for gravitational acceleration:

g = G * (M / r^2)

Where:
g is the acceleration due to gravity,
G is the gravitational constant (approximately 6.67 x 10^-11 m^3/(kg*s^2)),
M is the mass of the planet, and
r is the radius of the planet.

In this case, we know the acceleration due to gravity on the mystery planet (5.00 m/s^2) and the radius of the planet (2.00 x 10^6 m). We need to solve for the mass (M).

Rearranging the formula, we have:

M = (g * r^2) / G

Now, let's plug in the values:

M = (5.00 m/s^2 * (2.00 x 10^6 m)^2) / (6.67 x 10^-11 m^3/(kg*s^2))

Calculating this expression will give us the mass of the mystery planet.