A satellite is in a circular orbit around the Earth. If its orbital radius is tr
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the gravitational force acting on it change?
It triples
It halves
It becomes one-ninth
It remains the same
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the gravitational force acting on it change?
Step 1: Understand that gravitational force depends on the distance between two objects, in this case, the satellite and the Earth.
Step 2: Know that the formula for gravitational force (F) is F = G * (m1 * m2) / r², where G is the gravitational constant, m1 and m2 are the masses of the Earth and the satellite, and r is the distance from the center of the Earth to the satellite.
Step 3: Recognize that if the orbital radius (r) is tripled, it means r becomes 3r (where r is the original radius).
Step 4: Substitute the new radius into the formula: F = G * (m1 * m2) / (3r)².
Step 5: Simplify the equation: F = G * (m1 * m2) / (9r²).
Step 6: Compare the new force to the original force: The new force is 1/9 of the original force because the denominator increased by a factor of 9.
Gravitational Force and Orbital Radius – The gravitational force acting on an object in orbit is given by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance between the centers of the two masses.
