6.3k views
0 votes
A satellite in a circular orbit around the earth has a speed of

3 km/s. What is the radius of this orbit?

The mass of Neptune is × 1026

kg.

Note: Round the final answer to three decimal places

User Yunus
by
7.6k points

1 Answer

6 votes

Answer: To find the radius of the satellite's circular orbit around the Earth, we can use the following formula, which relates the speed (v) of the satellite, the radius (r) of the orbit, and the gravitational constant (G) to the mass (M) of the Earth:

v = √(G * M / r)

Given:

Speed of the satellite (v) = 3 km/s = 3000 m/s (converted to meters per second)

Mass of the Earth (M) = 5.972 × 10^24 kg (approximately)

Gravitational constant (G) = 6.67430 × 10^-11 m^3 kg^-1 s^-2

Now, let's rearrange the formula to solve for the radius (r):

r = G * M / v^2

Substitute the given values into the formula:

r = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / (3000 m/s)^2

r = (3.9876034 × 10^14 m^3 kg s^-2) / 9 × 10^6 m^2/s^2

r ≈ 44,294,485.888 meters

Now, let's round the final answer to three decimal places:

r ≈ 44,294,485.888 meters ≈ 44,294,486 meters

The radius of the satellite's orbit around the Earth is approximately 44,294,486 meters.

User Bean Taxi
by
8.0k points