a satellite of mass 1250 kg is to be placed in a circular orbit at a height 210 km above the earths surface what is the height of the satellite with what tangential speed must it be inserted into its orbit
To calculate the height of the satellite above the Earth's surface, you need to consider the radius of the Earth and the height of the satellite.
The radius of the Earth is approximately 6,371 km.
Height of the Satellite = height above Earth's surface + radius of the Earth
= 210 km + 6,371 km
= 6,581 km
So, the height of the satellite from the center of the Earth is 6,581 km.
Now, to calculate the tangential speed required for the satellite to be inserted into its orbit, you can use the formula:
Tangential speed = Square root of (G * Mass of the Earth / Distance from the center of the Earth)
Where:
G = Gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
Mass of the Earth = 5.972 × 10^24 kg
Distance from the center of the Earth = Radius of the Earth + height of the satellite
Distance from the center of the Earth = 6,581 km or 6,581,000 meters (converting km to meters)
Tangential speed = Square root of ( 6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg / 6,581,000 meters)
Calculating this equation will give you the required tangential speed for the satellite to be inserted into its orbit.