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^2)
since g is inversely proportional to r^2,
multiplying r by 2 means dividing g by 2^2
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.
The formula for gravitational acceleration is given by:
g = (G * M) / r^2
Where:
- g is the gravitational acceleration
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- r is the distance between the center of the Earth and the spaceship
In this case, the distance is equal to double the Earth's radius, which can be calculated by multiplying the Earth's radius by 2. The Earth's radius is approximately 6,371,000 meters.
So, r = 2 * 6,371,000 meters = 12,742,000 meters.
Substituting the values into the formula, we get:
g = (6.67430 × 10^-11 m^3/kg/s^2 * 5.972 × 10^24 kg) / (12,742,000 meters)^2
Simplifying the equation, we get:
g = 9.8 m/s^2 * (6.371 × 10^6 / 12,742,000)^2
Calculating the value, we find:
g ≈ 4.9 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 4.9 m/s^2.