This set of Astronautics Multiple Choice Questions & Answers (MCQs) focuses on “Basic Orbits”.

1. The shape of a closed orbit can be _________

a) parabolic

b) hyperbolic

c) elliptical

d) helical

View Answer

Explanation: The elliptical orbit is the only closed orbit amongst the options listed above.

2. The size of an elliptical orbit is defined by its ____________________

a) radius

b) semi-major axis

c) circumference

d) diameter

View Answer

Explanation: The ‘radius’ and ‘diameter’ become relevant only when talking about circular orbits, while the semi-major axis is unique to elliptical orbits and is what defines its size. The semi-major axis is nothing but half the length of the major axis, which is the line joining the opposite ends of the ellipse and passing through the two foci.

3. The inclination of an Earth-orbit is the angle between ________________

a) the orbital plane and the ecliptic

b) the orbit’s axis and the ecliptic

c) the orbit’s axis and the equatorial plane

d) the orbital plane and the equatorial plane

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Explanation: The inclination is one of several properties that defines an orbit and is the angle measured anti-clockwise from Earth’s equatorial plane to the plane of the orbit.

4. The plane of revolution of the Earth around the Sun and the Earth’s equatorial plane are offset by an angle of _____________

a) 15 degrees

b) 0 degrees

c) 23.5 degrees

d) 60.2 degrees

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Explanation: The plane in which the Earth revolves around the Sun (also called the ecliptic) and Earth’s equatorial plane are not the same, i.e., Earth’s rotational axis is not perpendicular to the ecliptic. This ‘tilt’ is what gives rise to the various seasons experienced throughout a year.

5. Apart from shape, in what way is an elliptical orbit different from a circular orbit?

a) The energy of an elliptical orbit changes with position in the orbit

b) The central body can be located at one of two points

c) Elliptical orbits are open orbits

d) Elliptical orbits are unstable

View Answer

Explanation: An ellipse is characterized by its two foci. In order to understand what the ‘focus’ of an ellipse is, it is important to know how an ellipse is constructed.

STEP 1: Take a small string.

STEP 2: Fix the ends of the string at two points on a platform in such a way that the distance between the two points is lesser than the string’s length (i.e., the string is not stretched out to its maximum length).

STEP 3: With the ends of the string firmly attached, take a pencil and trace out a complete 360 degree loop with the tip of the pencil stretching the string outward to its maximum (i.e., to the point beyond which the pencil can go no further without breaking the string or its own tip) at all times. After completing the loop, the resulting shape we get is called an ellipse.

The fixed points at which the ends of the string were held are called the foci of the ellipse. To get a circle using the same procedure, the only change that has to be made is that the two ends of the string need to be fixed at the exact same point (which in this case is called the ‘center’ of the circle).

In the case of elliptical orbits, the central body can lie at one of the foci.

6. The eccentricity of an ellipse is always __________

a) greater than 1

b) equal to 1

c) equal to 0

d) between 0 and 1

View Answer

Explanation: The eccentricity of an ellipse is defined as the ratio of the length of the line segment joining the center and one of the foci of the ellipse to the length of the semi-major axis (the line segment passing through one of the foci that joins the center of the ellipse to a point on the ellipse). This value is between 0 and 1 for ellipses, equal to 0 for circles, equal to 1 for parabolas, and greater than 1 for hyperbolas.

7. Earth’s orbit around the sun is _____________

a) an ellipse

b) a circle

c) a parabola

d) a hyperbola

View Answer

Explanation: Earth’s orbit around the Sun is slightly elliptical, with perihelion and aphelion occurring approximately in January and July, respectively.

8. In an ellipse, the points closest to and farthest from any one focus are called _______________

a) perigee and apogee

b) perihelion and aphelion

c) periapsis and apoapsis

d) perijove and apojove

View Answer

Explanation: The point closest to one of the foci of an ellipse is called periapsis and the point farthest from that focus is known as apoapsis. These are general terms that apply for an ellipse. Perigee & apogee are for orbits around Earth, perihelion & aphelion are for orbits around the sun, and perijove and apojove are for orbits around Jupiter.

9. Given that an orbit around Earth has a specified inclination, the plane of the orbit is fixed and unique.

a) True

b) False

View Answer

Explanation: While the orbit’s inclination may be fixed, the orbit itself can rotate about Earth’s center keeping its inclination constant, which gives rise to many equally-inclined orbits with various orientations in several planes.

10. Given an elliptical orbit around a planet, an object in that orbit ______________________

a) is always at a fixed distance from the planet

b) maintains a constant orbital speed

c) can move away from the planet

d) keeps changing its orbital energy.

View Answer

Explanation: Looking at the shape of an elliptical orbit with the planet situated at one of the foci, at times when the object moves from the closest point of approach towards the farthest point in the orbit, it seems to recede away from the planet (but is still under the influence of its gravity). The opposite happens when traversing from the farthest point to the closest point of approach.

11. In an elliptical orbit, which of the following properties does not change its value throughout the orbit?

a) Energy

b) Angular velocity

c) Tangential velocity

d) Orbital height

View Answer

Explanation: The energy in an orbit, which is the sum of the kinetic and potential energies of an orbiting body of unit mass, is always conserved. Close to the central body, the kinetic energy is more compared to the potential energy, while farther away, the potential energy is greater. In both cases, however, the sum of the kinetic and potential energies is constant.

12. For a circular orbit, the time period ‘T’ of revolution of an object around a central body is related to the orbital radius ‘r’ as ______________

a) T∝r^{3}

b) T∝r^{2}

c) T∝(r)^{1/2}

d) T∝(r)^{3/2}

View Answer

Explanation: We already know that \(v=\sqrt{\frac{GM}{r}\). For a circular orbit, we may also write

v=\(\frac{2πr}{T}\)

Substituting \(v=\sqrt{\frac{GM}{r}\) in the above equation, we get:

\(T=\frac{2π}{GM}(r)\frac{3}{2}\)

The same relationship applies for elliptical orbits, which can be deduced from Kepler’s third law of planetary motion (the square of the time period of revolution of a planet around the sun is proportional to the cube of the semi-major axis of the ellipse traced out by the planet).

13. What is the time period of a lunar circular orbit 50 km above the surface of the Moon (radius of the moon = 1737 km; mass of the moon = 7.35 x 10^{22} kg)?

a) 113 minutes

b) 50 minutes

c) 38 minutes

d) 197 minutes

View Answer

Explanation:

\(T^2=\frac{4π^2}{GM}r^3\)

Given,

M = 7.35 x 10

^{22}kg;

r = (1737+50) x 10

^{3}m = 1787 x 10

^{3}m.

Substituting the values, we get T = 6776.74 seconds, which is approximately 113 minutes.

**Sanfoundry Global Education & Learning Series – Astronautics.**

To practice all areas of Astronautics, __ here is complete set of Multiple Choice Questions and Answers__.