What if the Sun were heavier?

Earth goes around the Sun once a year. The Sun's pull keeps it going around.

What if the Sun were heavier? Would Earth go faster or slower?

The Sun is the heavyweight of our solar system. NASA says it holds 99.8 percent of all the solar system's mass, and it would take more than 330,000 Earths to match it. All that mass pulls on Earth and keeps it circling.

So what if the Sun were heavier still, say twice as heavy? Would a year get longer, shorter or stay the same? Make a guess, then test it in the model.

The Sun's mass, 1.9884 × 10³⁰ kg on NASA's Sun Fact Sheet, is about 332,900 times Earth's. That mass sets the strength of the gravity that holds every planet in orbit.

This lab doubles the Sun's mass while keeping Earth at today's distance on a circular orbit, and asks how the orbital speed and the length of the year respond. It then shows how astronomers turn the same relationship around to measure the masses of real stars.

Earth is very far from the Sun. It zooms along about 30 kilometers every second.

One trip around the Sun takes about 365 days. That is one year.

Earth orbits about 150 million kilometers from the Sun, moving at about 30 kilometers every second. The Sun's pull is just strong enough to bend that sideways motion into a near-circle, so Earth neither falls inward nor drifts away. One lap takes about 365 days.

In the model, Earth starts at today's distance with the exact speed for a circle: 29.78 kilometers per second, and one orbit takes 365.3 days.

NASA's Earth Fact Sheet lists a semimajor axis of 149.598 million km, a sidereal period of 365.256 days and a mean orbital speed of 29.78 km/s. For a circle, gravity supplies exactly the inward pull needed: GM/r² = v²/r, so v = √(GM/r).

The model's starting state reproduces this with the Sun's real mass: r = 1 AU, v = 29.78 km/s and T = 365.3 days.

In our pretend lab, Olly makes the Sun twice as heavy.

Now the Sun pulls harder. Earth has to zoom faster to keep going around. The year gets shorter!

Set the Sun's mass to 2 in the model. A stronger pull would drag a slow Earth inward, so to stay on the same circle Earth must move faster: about 42 kilometers per second instead of about 30. The path is the same length, so the faster Earth finishes a lap sooner, in about 258 days.

Go further: with a Sun four times as heavy, the model's year is about 183 days, half of today's.

With M doubled at r = 1 AU, the circular speed becomes √2 × 29.78 = 42.12 km/s and the period 365.26/√2 = 258.3 days. At four times the mass the period halves to 182.6 days, as T ∝ M^(−1/2) predicts; at half the mass it lengthens to 516.6 days.

The model also lets you keep Earth's old speed (set the starting speed to 0.71 with a doubled Sun). Too slow for the new circle, Earth falls inward onto a squashed ellipse, swinging to about 50 million km from the Sun, with a period of 141.2 days.

More mass means a stronger pull. A stronger pull bends Earth's path harder.

To keep going around and not fall in, Earth must go faster.

Isaac Newton showed that gravity grows with mass: the more mass something has, the harder it pulls. A planet stays in orbit when its sideways speed exactly balances the inward pull. A heavier Sun pulls harder, so the balancing speed is higher, and a faster planet completes its circle sooner.

Our model keeps things simple. It only changes the Sun's pull. It does not change how bright, hot or big the Sun is, which a real heavier star would be.

Newton's law of gravitation, F = GMm/r², makes the pull proportional to the Sun's mass. Setting it equal to the centripetal force for a circle gives v = √(GM/r) and T = 2πr/v = 2π√(r³/GM): Kepler's third law with the mass written in. OpenStax notes that Kepler missed the mass term because the Sun's mass is effectively 1 in solar units.

Model limits: point masses, one plane, only the Sun and Earth, and a mass change applied instantly at the start. A real star with twice the Sun's mass would also differ in size, brightness and lifetime, none of which the model includes.

Scientists can find out how heavy a star is. They watch something go around it and time one trip.

A fast trip means a heavy star. Heavy stars also shine much more brightly.

Astronomers can't put a star on a scale, but they can time an orbit. OpenStax gives an example: a planet 1 astronomical unit from its star that takes only 0.71 of a year to go around tells you the star has twice the Sun's mass. That is the same short year our model shows. About half of all stars are pairs that circle each other, and timing their orbits reveals their masses.

Heavier stars are not just stronger pullers. They also shine far more brightly and use up their fuel faster, so a planet at Earth's distance from one would get much more light than we do.

Newton's form of Kepler's third law, D³ = (M₁ + M₂)P² in AU, years and solar masses, lets astronomers measure stellar masses from binary orbits; OpenStax applies it to Sirius and finds a combined mass of 3.2 Suns. Its worked example of a planet at 1 AU with a 0.71-year period gives a star of 2 solar masses, matching this lab.

OpenStax also gives the mass-luminosity relation, L ∝ M^3.9 (roughly the fourth power), so a star twice the Sun's mass is about 16 times as luminous. NASA notes that more massive stars burn fuel faster and live shorter lives. These effects lie outside the orbit model.