Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 418 km above the earth’s surface, while that for satellite B is at a height of 731 km. Find the orbital speed for (a) satellite A and (b) satellite B.

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To find the orbital speed for satellite A and satellite B, we can use the formula for calculating the orbital speed of an object in a circular orbit:

v = √(GM/r)

Where:
- v is the orbital speed
- G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2)
- M is the mass of the Earth (approximately 5.97 x 10^24 kg)
- r is the distance between the center of the Earth and the satellite (height above the Earth's surface + radius of the Earth)

Let's calculate the orbital speed for satellite A first.

Step 1: Calculate the distance from the center of the Earth to satellite A.
To find the distance between the center of the Earth and satellite A, we need to add the height of satellite A above the Earth's surface to the radius of the Earth.

Height of satellite A = 418 km
Radius of the Earth = 6371 km

Distance to satellite A = Height of satellite A + Radius of the Earth
= 418 km + 6371 km
= 6789 km

Step 2: Convert the distance to meters.
Since the gravitational constant is given in SI units (Nm^2/kg^2), we need to convert the distance from kilometers to meters.

Distance to satellite A in meters = 6789 km * 1000 m/km
= 6,789,000 m

Step 3: Calculate the orbital speed for satellite A.
Using the formula for orbital speed, plug in the values:

v = √(GM/r)
= √((6.67 x 10^-11 Nm^2/kg^2) * (5.97 x 10^24 kg) / (6,789,000 m))
≈ 7.66 km/s

Therefore, the orbital speed for satellite A is approximately 7.66 km/s.

Now let's calculate the orbital speed for satellite B using the same steps.

Step 1: Calculate the distance from the center of the Earth to satellite B.
Height of satellite B = 731 km

Distance to satellite B = Height of satellite B + Radius of the Earth
= 731 km + 6371 km
= 7102 km

Step 2: Convert the distance to meters.
Distance to satellite B in meters = 7102 km * 1000 m/km
= 7,102,000 m

Step 3: Calculate the orbital speed for satellite B.
Using the formula for orbital speed, plug in the values:

v = √(GM/r)
= √((6.67 x 10^-11 Nm^2/kg^2) * (5.97 x 10^24 kg) / (7,102,000 m))
≈ 6.94 km/s

Therefore, the orbital speed for satellite B is approximately 6.94 km/s.

consider cetnripetal acceleration =graviational

v1^2/(re+418) = g*(re/(re+418))^2

solve for v1, then do the same for v2