A satellite is orbiting Earth at an orbital radius of 3.9×103
m. What is its velocity in terms of G and the mass of Earth, mp? (Ignore units in the answer.)(1 point)
Responses
(1.6×10−2)Gmp−−−−√
open paren 1 point 6 times 10 to the negative 2 power close paren times square root of cap g m sub p end root
(3.9×103)Gmp−−−−√
open paren 3 point 9 times 10 cubed close paren times square root of cap g m sub p end root
(6.2×101)Gmp−−−−√
open paren 6 point 2 times 10 to the 1th power close paren times square root of cap g m sub p end root
(2.6×10−4)Gmp−−−−√
None of the given responses are correct. The correct expression for the velocity of a satellite in terms of G and the mass of Earth, mp, is:
(√(G * mp) / √(orbital radius))
Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a low Earth orbit?(1 point)
Responses
v=Gmp(7,000 km)−−−−−−−√
v=Gmp(7,000 km)−−−−−−−√
v=1(200 km)Gmp−−−−√
v=1(200 km)Gmp−−−−√
v=1(7,000 km)Gmp−−−−√
v=1(7,000 km)Gmp−−−−√
v=Gmp(200 km)−−−−−−√
v=Gmp(200 km)−−−−−−√
The correct equation to find the velocity of the satellite in a low Earth orbit is:
v = √(G * mp / r)
where r is the orbital radius. Therefore, the correct response is:
v = √(G * mp * 200 km)
The correct answer is (6.2×10^1)Gmp^(-1/2), which is option (c).
To determine the satellite's velocity in terms of G (gravitational constant) and the mass of Earth (mp), we can use the formula for orbital velocity.
The orbital velocity of a satellite can be calculated using the equation:
v = √(G * mp / r)
Where:
- v represents the velocity of the satellite
- G represents the gravitational constant
- mp represents the mass of Earth
- r represents the orbital radius
In this case, the orbital radius is given as 3.9×10^3 meters.
Substituting the values into the formula, we get:
v = √(G * mp / (3.9×10^3))
So, the correct answer is:
(3.9×10^3)Gmp^(-1/2)
This represents the square root of G times the mass of Earth divided by the orbital radius.