Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above the earth's surface, while that for satellite B is at a height of 720 km. Find the orbital speed for each satellite.
Kepler's laws related period to radius. Another way, ...
g(re/(re+alt))^2=v^2/(re+ alt) and you can solve for v.
thank you
To find the orbital speed for each satellite, we can use the formula for orbital speed:
v = √(G * M / r)
Where:
v is the orbital speed,
G is the gravitational constant (6.67430 × 10^-11 m³ kg⁻¹ s⁻²),
M is the mass of the Earth (5.972 × 10^24 kg),
and r is the distance from the center of the Earth to the satellite.
For satellite A:
The distance from the center of the Earth to satellite A will be the sum of the radius of the Earth and the height above the Earth's surface.
Radius of the Earth (rE) = 6,371 km = 6,371,000 m
Height of satellite A (hA) = 360 km = 360,000 m
rA = rE + hA
Now we can calculate the orbital speed for satellite A:
vA = √(G * M / rA)
Similarly, for satellite B:
The distance from the center of the Earth to satellite B will also be the sum of the radius of the Earth and the height above the Earth's surface.
Height of satellite B (hB) = 720 km = 720,000 m
rB = rE + hB
Now we can calculate the orbital speed for satellite B:
vB = √(G * M / rB)
Let's calculate the values for vA and vB:
Step 1: Calculate rA and rB
rE = 6,371,000 m
hA = 360,000 m
hB = 720,000 m
rA = rE + hA
rB = rE + hB
rA = 6,371,000 m + 360,000 m = 6,731,000 m
rB = 6,371,000 m + 720,000 m = 7,091,000 m
Step 2: Calculate vA and vB
G = 6.67430 × 10^-11 m³ kg⁻¹ s⁻²
M = 5.972 × 10^24 kg
vA = √(G * M / rA)
vB = √(G * M / rB)
Now, we can substitute the values and calculate the orbital speeds for satellite A and satellite B.