a polar satellite is launched at 850 km above Earth .find its orbital speed.
7431
To find the orbital speed of a satellite, we can use the formula:
v = sqrt(GM/r)
Where:
v = orbital speed (m/s)
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the Earth (5.972 × 10^24 kg)
r = distance between the center of the Earth and the satellite (850 km converted to meters -> 850,000 m)
Plugging in the values:
v = sqrt((6.67430 × 10^-11) * (5.972 × 10^24) / 850,000)
Calculating this equation:
v ≈ 7630 m/s
Therefore, the orbital speed of the polar satellite launched at 850 km above Earth is approximately 7630 m/s.
To find the orbital speed of a satellite, you can use the following formula:
Orbital speed (v) = √((G * M) / r)
Where:
- G is the universal 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 satellite's orbit above the Earth's surface, in this case, 850 km above the Earth's surface
1. Convert the altitude of the satellite from kilometers to meters:
850 km = 850,000 meters
2. Add the radius of the Earth (approximately 6,371 km or 6,371,000 meters) to the altitude to get the total distance from the center of the Earth:
Total distance = 850,000 m + 6,371,000 m = 7,221,000 meters
3. Substitute the values into the formula and calculate the orbital speed:
v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / 7,221,000 meters)
Using a calculator, perform the calculation and find the square root of the result to get the orbital speed of the satellite. The unit of the orbital speed will be in meters per second (m/s).
the gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
Earth’s mass is M = 5.97•10²⁴kg,
Earth’s radius is R = 6.378•10⁶ m.
r = 850000 m
ma=F
mv²/(R+r)= G•m•M /(R+r)²
v=sqrt{G•M /(R+r)}= …