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Four identical satellites are in orbits around the Earth. The radii of their orbits are given in the table. For which satellite is the gravitational pull of Earth the strongest?

\begin{tabular}{|c|c|}
\hline
Satellite & Orbit radius (km) \\
\hline
A & 1200 \\
\hline
B & 900 \\
\hline
C & 1000 \\
\hline
D & 1100 \\
\hline
\end{tabular}

A. Satellite A

B. Satellite B

C. Satellite C

D. Satellite D


Sagot :

To determine which satellite experiences the strongest gravitational pull from the Earth, we need to understand the relationship between the gravitational force and the orbit radius.

Gravitational force [tex]\( F \)[/tex] between two masses is given by Newton's law of gravitation:

[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]

Where:
- [tex]\( G \)[/tex] is the gravitational constant.
- [tex]\( m_1 \)[/tex] is the mass of the Earth.
- [tex]\( m_2 \)[/tex] is the mass of the satellite.
- [tex]\( r \)[/tex] is the distance (radius) between the center of the Earth and the satellite.

Given this formula, we observe that the gravitational force is inversely proportional to the square of the orbit radius [tex]\( r \)[/tex]. This means that the smaller the radius [tex]\( r \)[/tex], the greater the gravitational force [tex]\( F \)[/tex].

We have the following orbit radii for the satellites:
- Satellite A: 1200 km
- Satellite B: 900 km
- Satellite C: 1000 km
- Satellite D: 1100 km

To find the satellite with the strongest gravitational pull, we compare the orbit radii:

1. Satellite A has an orbit radius of 1200 km.
2. Satellite B has an orbit radius of 900 km.
3. Satellite C has an orbit radius of 1000 km.
4. Satellite D has an orbit radius of 1100 km.

Since the gravitational force is stronger when the orbit radius is smaller, we look for the satellite with the smallest orbit radius. From the list above, we see that Satellite B has the smallest orbit radius of 900 km.

Therefore, the satellite for which the gravitational pull of Earth is the strongest is:

Satellite B

So, the correct answer is:
B. Satellite B
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