The radius of Earth is about 6.38 103 km. A 7.40 103 N spacecraft travels away from Earth. What is the weight of the spacecraft at the following distances from Earth's surface?
The Earth has a radius of about 6.38 ´ 103 kilometers at the equator and rotates 360° every 24 hours. The angular displacement of a person standing at the equator for 8.0 hours is:
The Earth has a radius of about 6.38 ´ 103 kilometers at the equator and rotates 360° every 24 hours. The angular displacement of a person standing at the equator for 8.0 hours is:
To calculate the weight of the spacecraft at different distances from Earth's surface, we can use the gravitational force equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 * 10^-11 N(m/kg)^2),
m1 is the mass of the spacecraft (in kg),
m2 is the mass of Earth (approximately 5.97 * 10^24 kg),
r is the distance between the center of Earth and the spacecraft (in meters).
Let's calculate the weight of the spacecraft at different distances from Earth's surface.
To calculate the weight of the spacecraft at various distances from Earth's surface, we need to use the formula:
Weight = mass × acceleration due to gravity.
The mass of the spacecraft is not provided, but since weight is directly proportional to mass, we can assume that the mass remains constant.
The acceleration due to gravity, or "g", is the gravitational force exerted by Earth on an object near its surface. It is approximately 9.8 m/s² or 9.8 N/kg.
Since the given radius of Earth is in kilometers, we need to convert it to meters by multiplying it by 1000.
Radius of Earth = 6.38 × 10³ km × 1000 = 6.38 × 10⁶ m
Now, let's calculate the weight of the spacecraft at different distances from Earth's surface:
1. At the surface of Earth (radius = 6.38 × 10⁶ m):
Weight = mass × g = mass × 9.8 N/kg.
2. Away from Earth's surface at a distance x:
Weight = mass × g' = mass × (g / ((radius + x) / radius)²).
For example, given a distance of 7.40 × 10³ km away from Earth's surface, we need to convert it to meters by multiplying by 1000:
Distance x = 7.40 × 10³ km × 1000 = 7.40 × 10⁶ m.
Now, we can calculate the weight at this distance using the formula above.
Repeat this process for other distances, plugging in the appropriate values for the distance x.
Please note that the mass of the spacecraft is not provided, so we can't give the actual weight values without knowing the mass. However, if you provide the mass, we can help you calculate the weight at each distance.