One of the Echo satellites consisted of an inflated spherical aluminum balloon 30 m in diameter and of mass 20 kg. Suppose a meteor having a mass of 9.2 kg passes within 4.4 m of the surface of the satellite. What is the gravitational force on the meteor from the satellite at the closest approach?

Use Newton's universal law of gravity,

F = G M1 M2 /R^2

M1 and M2 are the two masses

R must be measured center to center, so in this case R = 19.4 m

Solve for F

You may have to look up the universal constant G

To find the gravitational force on the meteor from the satellite at the closest approach, we can use Newton's law of universal gravitation. Newton's law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula for the gravitational force between two objects is:

F = (G * m1 * m2) / r^2

Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between their centers

In this case, the mass of the meteor is given as 9.2 kg, and the distance between the meteor and the satellite's surface is given as 4.4 m.

First, let's calculate the mass of the satellite. The question states that the satellite consists of an inflated spherical aluminum balloon with a diameter of 30 m and a mass of 20 kg. Since we know the diameter, we can calculate the radius as half of the diameter:

Radius (r) = Diameter / 2 = 30 m / 2 = 15 m

Now, to find the volume of the sphere, we can use the formula for the volume of a sphere:

Volume (V) = (4/3) * π * r^3

Plugging in the values, we get:

V = (4/3) * π * (15 m)^3
= (4/3) * π * (3375 m^3)
≈ 14137 m^3

Since the satellite is made of aluminum, which has a density of approximately 2700 kg/m^3, we can calculate the mass using the formula:

Mass = Density * Volume

Mass = 2700 kg/m^3 * 14137 m^3
≈ 3.82 x 10^7 kg

Now, we can substitute the masses and the distance into the formula for the gravitational force:

F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 N m^2/kg^2 * 9.2 kg * 3.82 x 10^7 kg) / (4.4 m)^2

Performing the calculations, we get:

F ≈ 2.95 x 10^-3 N

Therefore, the gravitational force on the meteor from the satellite at the closest approach is approximately 2.95 x 10^-3 Newtons.