Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 511 km above the earth's surface, while that for satellite B is at a height of 895 km. Find the orbital speed for satellite A and satellite B.
I've already done this problem as for satellite A has a velocity of 7610.238 m/s and satellite B has a velocity of 7406.412 m/s.
Am I correct in this case?
v^2/(re+h)=9.8*(re/(re+h))^2
v^2=9.8*re^2/(re+h)
v^2=9.8 (6.37e6)^2/(6.37e6+.895e6)
v= (6.37e6)/(6.37e6+.895e6)sqrt9.8=7398m/s
and that needs to be reduced in significant digits to 7.40e3 m/s
To find the orbital speed for a satellite, you can use the formula:
v = √(µ / r)
where v is the orbital speed, µ is the gravitational parameter of Earth (approximately 3.986 × 10^14 m^3/s^2), and r is the distance from the center of the earth to the satellite.
For satellite A, with a height of 511 km above the Earth's surface, the distance from the center of the Earth is:
rA = (511 km + 6371 km) = 6882 km = 6882000 m
Now, we can plug in the values into the formula:
vA = √(3.986 × 10^14 m^3/s^2 / 6882000 m)
vA ≈ 7610.238 m/s
So, your calculation for the orbital speed of satellite A is correct.
For satellite B, with a height of 895 km above the Earth's surface, the distance from the center of the Earth is:
rB = (895 km + 6371 km) = 7266 km = 7266000 m
Again, plugging in the values into the formula:
vB = √(3.986 × 10^14 m^3/s^2 / 7266000 m)
vB ≈ 7406.412 m/s
Your calculation for the orbital speed of satellite B is also correct.
To find the orbital speed of a satellite in a circular orbit, you can use the formula:
v = sqrt(G * M / r)
Where:
- v is the orbital speed
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- r is the radius of the orbit (distance from the center of the Earth)
For satellite A:
r = height above the Earth's surface + radius of the Earth
r = 511 km + 6371 km (mean radius of the Earth)
r = 6882 km = 6,882,000 m
Plugging these values into the formula:
v_A = sqrt(G * M / r_A)
v_A = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6,882,000 m))
v_A ≈ 7610.238 m/s
For satellite B:
r = height above the Earth's surface + radius of the Earth
r = 895 km + 6371 km (mean radius of the Earth)
r = 7266 km = 7,266,000 m
Plugging these values into the formula:
v_B = sqrt(G * M / r_B)
v_B = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (7,266,000 m))
v_B ≈ 7406.412 m/s
So, your calculated values of 7610.238 m/s for satellite A and 7406.412 m/s for satellite B are correct.