Question

Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. What would happen if the Sun suddenly became a black hole without changing its mass? (a) The black hole would quickly suck in Earth. (b) Earth would gradually spiral into the black hole. (c) Earth would remain in the same orbit.

Short answer

(c) Earth would remain in the same orbit.

Step-by-step solution

Understanding Black Holes

When a star like the Sun becomes a black hole, it compresses to a very small point but retains its original mass. The gravitational pull it exerts on objects at its original distance does not change; hence nothing in its gravitational reach will be sucked in just because it's now a black hole.

Analyzing Gravitational Effects

If the Sun were to suddenly become a black hole without changing its mass, the gravitational force felt by Earth would remain the same as before. Gravity depends on mass and the distance between objects, and since neither the mass nor the distance changes, the force remains consistent.

Considering Earth's Orbit

Earth's orbit is determined by the gravitational pull of the Sun. As the mass remains constant and the relative positions do not alter abruptly, Earth's orbit will not change. Thus, despite the Sun becoming a black hole, Earth will continue in its current orbit unaffected.

Key concepts

Gravitational Effects

Gravitational effects are a fascinating phenomenon that keeps celestial bodies in motion and governs their interactions. Gravity is a force of attraction acting between all objects that have mass. The strength of this force depends on two factors: the mass of the objects and the distance between them. Mathematically, this relationship is expressed by the formula: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.

When discussing the gravitational effects of a black hole, it's essential to understand that a black hole retains the mass it had before collapsing. Thus, the gravitational pull experienced by objects at the same distance remains unchanged. For example, if the Sun turned into a black hole without changing its mass, the gravitational effects on Earth would be identical to those felt before. In this scenario:

• The gravitational force would stay the same because the mass and distance are unchanged.
• The Earth would not get "sucked in" by the black hole, as gravitational influence remains constant.

This demonstrates the principle that it’s the mass and distance that determine gravitational attraction, not the form or state of the mass.

Earth's Orbit

Earth's orbit around the Sun is a delicate balance of gravitational pull and inertia. Each celestial body exerts a gravitational force on others, creating a balance that keeps planets in orbit.

In an orbit, the centripetal force required to keep a planet moving in a circular path is provided by the gravitational pull of the Sun. This can be expressed with the formula: \[ F_{gravity} = \frac{G \cdot M_{sun} \cdot M_{earth}}{r^2} \]Here, the force of gravity balances the planet's inertia, the tendency of the moving planet to continue straight. This means that as long as the mass of the Sun remains the same and Earth remains at the same distance, its orbit will stay circular and unchanged.

If the Sun suddenly became a black hole but kept its mass, Earth's orbit would not change. The reason is simple: the gravitational force that keeps Earth in its path around the Sun remains the same, as both the mass and distance remain consistent. Therefore, Earth's journey around the former Sun-now black hole continues as if nothing changed.

Sun's Mass

The Sun's mass is a critical factor in maintaining the solar system's structure and dynamics. It acts as the central force that dominates and controls the orbits of all the planets, including Earth. The Sun's mass represents more than 99% of the total mass of our solar system.

If the Sun’s mass were to change, it would have a profound impact on the entire solar system. However, it's crucial to understand that even if the Sun changes form, such as becoming a black hole, as long as its mass remains constant, the gravitational force it exerts won't alter. Gravitational force is calculated based on mass and distance; thus:

• When the mass doesn't change, neither does the gravitational pull it exerts on Earth.
• The planets, including Earth, will continue their orbits unperturbed.

This scenario illustrates the idea that the mass of celestial bodies, not their form, is the key influence on the gravitational dynamics that govern their interactions.