This set of Astronautics Multiple Choice Questions & Answers (MCQs) focuses on “Real Orbits – Gravity Anomalies – Set 2”.
1. Earth rotates from __________
a) East to West
b) West to East
c) clockwise
d) top to bottom
View Answer
Explanation: Earth rotates from West to East about its own axis. Looking down on our planet from the North Pole, this rotation is counter-clockwise.
2. How fast does Earth’s equator spin, considering that it takes 24 hours for one complete rotation? Assume Earth’s radius as 6370 km.
a) 460 km/s
b) 460 km/h
c) 460 m/s
d) 265 km/h
View Answer
Explanation: We have
Velocity = \(\frac{distance}{time}\)
Here, the distance is D = 2πr = 2 * π * (6370000) = 40023.89 * 103 meters and time T = 24 hours = 86400 seconds. Therefore,
Velocity = \(\frac{40023.89 * 10^3}{86400}\) = 463.239 meters per second = 460m/s
3. The Earth is wider at the equator than at the poles.
a) True
b) False
View Answer
Explanation: Earth’s radius is greater at the equator than that at the poles by a little more than 20 kilometers.
4. The widening of Earth along the equator is due to ________________
a) centripetal force
b) centrifugal force
c) lunar gravity
d) solar gravity
View Answer
Explanation: Centrifugal force is the outward force experienced by any spinning object by virtue of its inertia that tends to fling a rotating mass outwards in the tangential direction. In the case of our planet, this tendency is resisted by Earth’s own gravity, which still results in a slight increase in diameter at the equator due to this centrifugal force.
5. Earth’s shape is that of ____________
a) a perfect sphere
b) a perfect ellipse
c) an oblate spheroid
d) a perfect spheroid
View Answer
Explanation: Due to the centrifugal force of rotation, Earth is a bit wider at the equator than at the poles, making the planet appear a bit ‘squashed’. This shape qualifies as that of an oblate spheroid, or a ‘squashed sphere’. Earth’s true geometry, however, is actually that of an oblate ‘ellipsoid’. This means that if you were to slice the Earth along the equatorial plane and observe the cross-section of either of the resulting pieces, their shapes would resemble an ellipse with an almost unnoticeable eccentricity.
6. Earth’s real shape gives rise to _____________
a) more mass
b) a non-uniform gravitational field
c) lesser mass
d) more gravity
View Answer
Explanation: Earth’s uneven mass distribution due to its oblate geometry and rough terrain results in a slightly non-uniform gravitational potential and occasional deviations from a perfect inverse square law.
7. Earth has a greater mass at the equator than at the poles.
a) True
b) False
View Answer
Explanation: As explained in previous questions, the centrifugal force of Earth’s rotation causes the equatorial diameter to elongate a bit more. For this reason, the Earth is wider along the equator and thus accommodates additional mass compared to the polar direction. In other words, centrifugal acceleration forces some of the planet’s material to concentrate more along the equator.
8. The effects of our non-spherical Earth are the strongest for satellites in _____________
a) Low Earth Orbit
b) Geosynchronous Orbit
c) Geostationary Orbit
d) Medium Earth Orbit
View Answer
Explanation: Earth’s uneven mass distribution affects LEO satellites the most due to their close proximity to the slight variations in the planet’s gravitational field. As satellites are placed higher and higher, they orbit farther and farther away from these heterogeneities. At such high altitudes, Earth appears more and more like a uniform blob, making the gravitational perturbations at these heights lesser in magnitude.
9. Satellites in a low-altitude non-equatorial orbit accelerate more when ___________
a) crossing the North Pole
b) crossing the South Pole
c) crossing the equator
d) crossing oceanic regions
View Answer
Explanation: Because the equatorial region has a greater mass compared to near-polar latitudes, as satellites make their pass above the equator, this extra material (accumulated due to Earth’s rotation) exerts a higher-than-normal gravitational force and thus pulls more on the satellite than when it is above the poles, causing an unusually greater acceleration.
10. Equatorial satellites are not subject to a greater acceleration anywhere in their orbit.
a) True
b) False
View Answer
Explanation: Satellites in an equatorial orbit do not experience any gradient in mass distribution along the equator since the bulge occurs equally throughout the line of zero latitude. If we consider a polar orbit, the satellite repeatedly transitions from above the planet’s flattened poles to the widened equator (composed of slightly more mass compared to higher latitudes), and vice versa. If the satellite remains in the equatorial plane, no such transition exists and is thus under the influence of a constant gravitational pull.
11. Gravitational perturbations are ___________ in nature.
a) periodic
b) oscillatory
c) secular
d) short-term
View Answer
Explanation: Gravity anomalies are low in strength but persist for as long as the force of gravity exists. These perturbations constantly tug on the orbital satellite, meaning that the error in its trajectory is proportional to the duration of its stay in the orbit, making these kinds of perturbations secular in nature.
12. Perigee precession occurs for satellites in an ___________
a) elliptical equatorial orbit
b) elliptical geosynchronous orbit
c) intermediate circular orbit
d) inclined elliptical orbit
View Answer
Explanation: To make things easier to understand, consider an elliptical orbit with a 90 degree inclination (polar orbit), with its perigee right below the South Pole and apogee above the North Pole. As the satellite crosses the North Pole and moves towards the equator, it experiences a higher gravitational force as it nears the equatorial plane (due to the extra mass) and accelerates with a greater magnitude than usual, curving the trajectory a little more. This causes the perigee to shift by a small angle in the direction of the satellite’s motion. The same thing happens while moving from the South Pole to the North due to the extra gravitational influence at equatorial latitudes and results in a small angular displacement of the apogee in the direction of the satellites revolution. The net effect of this is the rotation of the orbit itself. This phenomenon is termed perigee precession, or in more general, apsidal precession. The same concept can be applied to an elliptical orbit with a finite non-zero inclination.
13. Perigee precession results in the rotation of an orbit in its own plane.
a) True
b) False
View Answer
Explanation: Perigee precession causes the major axis of an elliptical orbit (and hence the orbit itself) to rotate about an axis passing through the center of the primary body and perpendicular to the orbital plane. This is clearly an in-plane precession that occurs, as discussed earlier, due to the trajectory of the satellite curving a little more than usual near the equatorial plane, or the ‘nodes’ of the orbit.
14. Perigee precession does not occur for ___________
a) inclined orbits
b) polar orbits
c) elliptical orbits
d) equatorial orbits
View Answer
Explanation: For an equatorial orbit, the satellite is subject to a constant gravitational force from the extra mass spread around the equator only and does not encounter any gradient, keeping the orbit frozen without any sort of additional curvature to the trajectory.
15. Perigee precession results in a change in the _______________
a) inclination
b) argument of perigee
c) right ascension of ascending node
d) eccentricity
View Answer
Explanation: Perigee precession is associated with an in-plane rotation, so the inclination and right ascension remain fixed. The perigee and apogee points constantly drift in small amounts on every pass in the direction of the satellite’s motion and by equal angular displacements, keeping the eccentricity the same. The angle between the ascending node and perigee, however, always changes, making the argument of perigee the variable in this case.
So the amount of deviation for just one orbit is \(\frac{\frac{7 degrees}{day}}{\frac{15.9 orbits}{day}}\) = 0.44 degrees per orbit.
Sanfoundry Global Education & Learning Series – Astronautics.
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