A satellite of mass 620 kg is placed into an Earth orbit of radius 23 000 km - Scottish Highers Physics - Question 6 - 2023

The gravitational force can be calculated using Newton's law of universal gravitation, which is given by the formula:

$F = G \frac{m_1 m_2}{r^2}$

where:

• $F$ is the gravitational force,
• $G$ is the gravitational constant, approximately $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$,
• $m_1$ is the mass of the Earth, $6.0 \times 10^{24} \text{ kg}$,
• $m_2$ is the mass of the satellite, $620 \text{ kg}$,
• $r$ is the distance from the center of the Earth to the satellite, which is the radius of the Earth plus the height of the orbit. Given that the Earth's radius is approximately 6.4 x 10^6 m, the total radius for the orbit is $23,000,000 m$. Therefore:

1. Calculate the gravitational force:

   • First, compute the total mass $m_1 m_2$: $6.0 \times 10^{24 \text{ kg}} \times 620 \text{ kg} = 3.72 \times 10^{27} \text{ kg}^2$.

2. Then plug the values into the gravity formula:

   • $F = 6.674 \times 10^{-11} \frac{(3.72 \times 10^{27})}{(2.3 \times 10^7)^2}$
   • Calculate $(2.3 \times 10^7)^2 = 5.29 \times 10^{14}$ m².

3. Substituting, you will find: $F = 6.674 \times 10^{-11} \frac{3.72 \times 10^{27}}{5.29 \times 10^{14}} = 4.7 \times 10^{17} \text{ N}.$ Therefore, the answer is:

A. 4.7 x 10^17 N.