The International Space Station (ISS) orbits Earth at an altitude of 4.0 x 10^5 m above the surface of the planet. The radius of the Earth is 6.37 x 10^6 m. At what velocity must the ISS be moving in order to stay in its orbit?
a. 7.66 x 10^3 m/s
b. 7.91 x 10^3 m/s
c. 8.17 x 10^3 m/s
d. 3.12 x 10^4 m/s
To find the velocity required for the ISS to stay in its orbit, we can use the formula for the orbital velocity:
v = sqrt(G * M / r)
Where:
- v is the velocity
- G is the gravitational constant (approximately 6.674 x 10^-11 N m^2/kg^2)
- M is the mass of the Earth (approximately 5.972 x 10^24 kg)
- r is the distance from the center of the Earth to the orbit (radius of the Earth + altitude of the ISS)
Plugging in the values:
v = sqrt((6.674 x 10^-11 N m^2/kg^2) * (5.972 x 10^24 kg) / (6.37 x 10^6 m + 4.0 x 10^5 m))
Calculating this on a calculator or using a computer program:
v ≈ 7.66 x 10^3 m/s
Therefore, the velocity required for the ISS to stay in its orbit is approximately 7.66 x 10^3 m/s. The correct answer is option a.