Find the gravitational acceleration if a spaceship at a distance equal to double of earth's radius from the centre of the earth (g on earth is 9.8 m/s)
since F = GMm/r^2,
twice the radius means 1/4 the force.
To find the gravitational acceleration at a distance equal to double the Earth's radius from the center of the Earth, we can use the formula for gravitational acceleration:
g = G * M / R^2
where:
g is the gravitational acceleration,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the Earth (approximately 5.972 × 10^24 kg),
R is the distance from the center of the Earth.
In this case, R is double the Earth's radius, so we can substitute the value of R with 2 times the Earth's radius:
R = 2 * Earth's radius
Now let's calculate:
R = 2 * Earth's radius = 2 * (6,371,000 meters) = 12,742,000 meters
Substituting the values into the formula:
g = (6.67430 × 10^-11 * 5.972 × 10^24) / (12,742,000)^2
Calculating the expression:
g ≈ 9.8 / 4 = 2.45 m/s^2
Therefore, the gravitational acceleration at a distance equal to double the Earth's radius from the center of the Earth is approximately 2.45 m/s^2.