Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 427 km above the earth’s surface, while that for satellite B is at a height of 873 km. Find the orbital speed for (a) satellite A and (b) satellite B.
To find the orbital speed of a satellite, we can use the formula:
v = √(GM/R)
Where:
- v is the orbital speed
- G is the gravitational constant (approximately 6.674 × 10^-11 m^3/kg/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 to the satellite)
Let's calculate the orbital speed for satellite A first:
R_A = height_A + radius of the Earth
The radius of the Earth is approximately 6,371 km or 6,371,000 meters.
R_A = 427 km + 6,371 km = 6,798 km = 6,798,000 meters
Now we can use the formula to calculate the orbital speed:
v_A = √(GM/R_A)
v_A = √(6.674 × 10^-11 m^3/kg/s^2 * 5.972 × 10^24 kg / 6,798,000 m)
Calculating this expression will give us the orbital speed for satellite A.
Similarly, we can calculate the orbital speed for satellite B:
R_B = height_B + radius of the Earth
R_B = 873 km + 6,371 km = 7,244 km = 7,244,000 meters
v_B = √(GM/R_B)
v_B = √(6.674 × 10^-11 m^3/kg/s^2 * 5.972 × 10^24 kg / 7,244,000 m)
Calculating this expression will give us the orbital speed for satellite B.