Calculate the force of the Earths gravity on a spacecraft 12,800 km (2 earth radii) above the Earths surface if its mass is 1350 kg?
F = GMm/r^2 = 6.673*10^-11 * 5.973*10^24 * 1350 / (6378*3000)^2 = 1464N
makes sense - roughly 3 times as far, so 1/9 the force at the surface
To calculate the force of gravity on the spacecraft, you can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where:
F is the force of gravity
G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2)
m1 is the mass of one object (in this case, the mass of the spacecraft)
m2 is the mass of the other object (in this case, the mass of the Earth)
r is the distance between the centers of the two objects (in this case, the distance from the Earth's surface to the spacecraft)
Given information:
Mass of the spacecraft (m1) = 1350 kg
Distance from the Earth's surface to the spacecraft (r) = 2 Earth radii = 2 * radius of the Earth
First, we need to calculate the radius of the Earth:
Radius of the Earth (R) ≈ 6,371 km
Now, we can calculate the force of gravity:
F = (G * m1 * m2) / r^2
F = (6.67 × 10^-11 N(m/kg)^2 * 1350 kg * m2) / (2 * R)^2
F = (6.67 × 10^-11 N(m/kg)^2 * 1350 kg * m2) / (2 * 6,371 km)^2
To simplify the calculation, we can convert the units of 6,371 km to meters (1 km = 1000 m):
F = (6.67 × 10^-11 N(m/kg)^2 * 1350 kg * m2) / (2 * 6,371,000 m)^2
Now, we can calculate the force:
F = (6.67 × 10^-11 N(m/kg)^2 * 1350 kg * m2) / (2 * 6,371,000 m)^2
F ≈ 2.981 N
Therefore, the force of gravity on the spacecraft 12,800 km (2 earth radii) above the Earth's surface is approximately 2.981 Newtons.
To calculate the force of Earth's gravity on a spacecraft located above its surface, you can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 is the mass of the spacecraft,
m2 is the mass of the Earth, and
r is the distance between the spacecraft and the center of the Earth.
In this case, the mass of the spacecraft (m1) is given as 1350 kg, and the distance from the Earth's surface to the spacecraft (r) is given as 12,800 km or 2 Earth radii.
First, convert the distance from kilometers to meters:
r = 12,800 km * 1000 m/km = 12,800,000 m
Next, you need to determine the mass of the Earth (m2). The mass of the Earth is approximately 5.972 × 10^24 kg.
Now, you can substitute the known values into the formula:
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1350 kg * (5.972 × 10^24 kg)) / (12,800,000 m)^2
Simplifying the equation:
F = (6.67430 × 10^-11) * (1350 * 5.972 × 10^24) / (12,800,000)^2
F = approximately 6.68 * 10^3 Newtons
Therefore, the force of Earth's gravity on the spacecraft 12,800 km above Earth's surface is approximately 6.68 * 10^3 Newtons.