If the mass of a planet is 0.103 times that of the Earth and its radius is 0.592 times that of the Earth, estimate the gravitational field g at the surface of the planet. The gravitational acceleration on Earth is 9.8 m/s2.
Answer in units of m/s2
m1g = Gm1m2/r^2
so g = Gm/r^2
You can either look up the actual values for Earth's radius and mass or find the factor using .592^2/.103 times g
To estimate the gravitational field at the surface of the planet, you can use the formula:
g = G * (M / r^2)
Where:
- g is the gravitational field
- G is the gravitational constant (approximately 6.67 x 10^-11 N*m^2/kg^2)
- M is the mass of the planet
- r is the radius of the planet
Given:
Mass of the planet (M) = 0.103 times the mass of Earth
Radius of the planet (r) = 0.592 times the radius of Earth
Gravitational acceleration on Earth (g on Earth) = 9.8 m/s^2
First, we need to find the values of M and r for the planet.
Mass of Earth (M Earth) = 5.972 × 10^24 kg
Radius of Earth (r Earth) = 6,371 km = 6,371,000 m
M = 0.103 * M Earth
r = 0.592 * r Earth
Calculating M and r:
M = 0.103 * 5.972 × 10^24 kg
≈ 6.165 × 10^23 kg
r = 0.592 * 6,371,000 m
≈ 3,770,552 m
Now, we can plug in the values into the formula:
g = G * (M / r^2)
≈ 6.67 x 10^-11 N*m^2/kg^2 * (6.165 × 10^23 kg / (3,770,552 m)^2)
To calculate the value of g, let's substitute the known values into the formula and solve:
g ≈ (6.67 x 10^-11 N*m^2/kg^2) * (6.165 × 10^23 kg) / (3,770,552 m)^2
Calculating g:
g ≈ 0.107 m/s^2
Therefore, the estimated gravitational field at the surface of the planet is approximately 0.107 m/s^2.